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cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Statistical data subsection</span> </button> <ul id="toc-Statistical_data-sublist" class="vector-toc-list"> <li id="toc-Data_collection" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Data_collection"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Data collection</span> </div> </a> <ul id="toc-Data_collection-sublist" class="vector-toc-list"> <li id="toc-Sampling" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Sampling"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1.1</span> <span>Sampling</span> </div> </a> <ul id="toc-Sampling-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Experimental_and_observational_studies" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Experimental_and_observational_studies"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1.2</span> <span>Experimental and observational studies</span> </div> </a> <ul id="toc-Experimental_and_observational_studies-sublist" class="vector-toc-list"> <li id="toc-Experiments" class="vector-toc-list-item vector-toc-level-4"> <a class="vector-toc-link" href="#Experiments"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1.2.1</span> <span>Experiments</span> </div> </a> <ul id="toc-Experiments-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Observational_study" class="vector-toc-list-item vector-toc-level-4"> <a class="vector-toc-link" href="#Observational_study"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1.2.2</span> <span>Observational study</span> </div> </a> <ul id="toc-Observational_study-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </li> <li id="toc-Types_of_data" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Types_of_data"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Types of data</span> </div> </a> <ul id="toc-Types_of_data-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Methods" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Methods"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Methods</span> </div> </a> <button aria-controls="toc-Methods-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Methods subsection</span> </button> <ul id="toc-Methods-sublist" class="vector-toc-list"> <li id="toc-Descriptive_statistics" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Descriptive_statistics"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Descriptive statistics</span> </div> </a> <ul id="toc-Descriptive_statistics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Inferential_statistics" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Inferential_statistics"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Inferential statistics</span> </div> </a> <ul id="toc-Inferential_statistics-sublist" class="vector-toc-list"> <li id="toc-Terminology_and_theory_of_inferential_statistics" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Terminology_and_theory_of_inferential_statistics"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2.1</span> <span>Terminology and theory of inferential statistics</span> </div> </a> <ul id="toc-Terminology_and_theory_of_inferential_statistics-sublist" class="vector-toc-list"> <li id="toc-Statistics,_estimators_and_pivotal_quantities" class="vector-toc-list-item vector-toc-level-4"> <a class="vector-toc-link" href="#Statistics,_estimators_and_pivotal_quantities"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2.1.1</span> <span>Statistics, estimators and pivotal quantities</span> </div> </a> <ul id="toc-Statistics,_estimators_and_pivotal_quantities-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Null_hypothesis_and_alternative_hypothesis" class="vector-toc-list-item vector-toc-level-4"> <a class="vector-toc-link" href="#Null_hypothesis_and_alternative_hypothesis"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2.1.2</span> <span>Null hypothesis and alternative hypothesis</span> </div> </a> <ul id="toc-Null_hypothesis_and_alternative_hypothesis-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Error" class="vector-toc-list-item vector-toc-level-4"> <a class="vector-toc-link" href="#Error"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2.1.3</span> <span>Error</span> </div> </a> <ul id="toc-Error-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Interval_estimation" class="vector-toc-list-item vector-toc-level-4"> <a class="vector-toc-link" href="#Interval_estimation"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2.1.4</span> <span>Interval estimation</span> </div> </a> <ul id="toc-Interval_estimation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Significance" class="vector-toc-list-item vector-toc-level-4"> <a class="vector-toc-link" href="#Significance"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2.1.5</span> <span>Significance</span> </div> </a> <ul id="toc-Significance-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Examples" class="vector-toc-list-item vector-toc-level-4"> <a class="vector-toc-link" href="#Examples"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2.1.6</span> <span>Examples</span> </div> </a> <ul id="toc-Examples-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </li> <li id="toc-Exploratory_data_analysis" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Exploratory_data_analysis"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3</span> <span>Exploratory data analysis</span> </div> </a> <ul id="toc-Exploratory_data_analysis-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Misuse" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Misuse"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Misuse</span> </div> </a> <button aria-controls="toc-Misuse-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Misuse subsection</span> </button> <ul id="toc-Misuse-sublist" class="vector-toc-list"> <li id="toc-Misinterpretation:_correlation" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Misinterpretation:_correlation"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1</span> <span>Misinterpretation: correlation</span> </div> </a> <ul id="toc-Misinterpretation:_correlation-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Applications" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Applications"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Applications</span> </div> </a> <button aria-controls="toc-Applications-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Applications subsection</span> </button> <ul id="toc-Applications-sublist" class="vector-toc-list"> <li id="toc-Applied_statistics,_theoretical_statistics_and_mathematical_statistics" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Applied_statistics,_theoretical_statistics_and_mathematical_statistics"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.1</span> <span>Applied statistics, theoretical statistics and mathematical statistics</span> </div> </a> <ul id="toc-Applied_statistics,_theoretical_statistics_and_mathematical_statistics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Machine_learning_and_data_mining" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Machine_learning_and_data_mining"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.2</span> <span>Machine learning and data mining</span> </div> </a> <ul id="toc-Machine_learning_and_data_mining-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Statistics_in_academia" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Statistics_in_academia"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.3</span> <span>Statistics in academia</span> </div> </a> <ul id="toc-Statistics_in_academia-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Statistical_computing" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Statistical_computing"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.4</span> <span>Statistical computing</span> </div> </a> <ul id="toc-Statistical_computing-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Business_statistics" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Business_statistics"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.5</span> <span>Business statistics</span> </div> </a> <ul id="toc-Business_statistics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Statistics_applied_to_mathematics_or_the_arts" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Statistics_applied_to_mathematics_or_the_arts"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.6</span> <span>Statistics applied to mathematics or the arts</span> </div> </a> <ul id="toc-Statistics_applied_to_mathematics_or_the_arts-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Specialized_disciplines" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Specialized_disciplines"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Specialized disciplines</span> </div> </a> <ul id="toc-Specialized_disciplines-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Further_reading" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>Further reading</span> </div> </a> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">11</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Statistics</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 154 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-154" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">154 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Statistiek" title="Statistiek – Afrikaans" lang="af" hreflang="af" data-title="Statistiek" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Statistik" title="Statistik – Alemannic" lang="gsw" hreflang="gsw" data-title="Statistik" data-language-autonym="Alemannisch" data-language-local-name="Alemannic" class="interlanguage-link-target"><span>Alemannisch</span></a></li><li class="interlanguage-link interwiki-am mw-list-item"><a href="https://am.wikipedia.org/wiki/%E1%8B%A8%E1%8B%9D%E1%88%AD%E1%8B%9D%E1%88%AD_%E1%88%82%E1%88%B3%E1%89%A5_(%E1%8A%A5%E1%88%B5%E1%89%B3%E1%89%B2%E1%88%B5%E1%89%B2%E1%8A%AD%E1%88%B5)" title="የዝርዝር ሂሳብ (እስታቲስቲክስ) – Amharic" lang="am" hreflang="am" data-title="የዝርዝር ሂሳብ (እስታቲስቲክስ)" data-language-autonym="አማርኛ" data-language-local-name="Amharic" class="interlanguage-link-target"><span>አማርኛ</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%A5%D8%AD%D8%B5%D8%A7%D8%A1" title="إحصاء – Arabic" lang="ar" hreflang="ar" data-title="إحصاء" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Estatistica" title="Estatistica – Aragonese" lang="an" hreflang="an" data-title="Estatistica" data-language-autonym="Aragonés" data-language-local-name="Aragonese" class="interlanguage-link-target"><span>Aragonés</span></a></li><li class="interlanguage-link interwiki-as mw-list-item"><a href="https://as.wikipedia.org/wiki/%E0%A6%AA%E0%A7%B0%E0%A6%BF%E0%A6%B8%E0%A6%82%E0%A6%96%E0%A7%8D%E0%A6%AF%E0%A6%BE" title="পৰিসংখ্যা – Assamese" lang="as" hreflang="as" data-title="পৰিসংখ্যা" data-language-autonym="অসমীয়া" data-language-local-name="Assamese" class="interlanguage-link-target"><span>অসমীয়া</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Estad%C3%ADstica" title="Estadística – Asturian" lang="ast" hreflang="ast" data-title="Estadística" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-gn mw-list-item"><a href="https://gn.wikipedia.org/wiki/Papyrekokuaa" title="Papyrekokuaa – Guarani" lang="gn" hreflang="gn" data-title="Papyrekokuaa" data-language-autonym="Avañe'ẽ" data-language-local-name="Guarani" class="interlanguage-link-target"><span>Avañe'ẽ</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Statistika" title="Statistika – Azerbaijani" lang="az" hreflang="az" data-title="Statistika" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%D8%A2%D9%85%D8%A7%D8%B1" title="آمار – South Azerbaijani" lang="azb" hreflang="azb" data-title="آمار" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AA%E0%A6%B0%E0%A6%BF%E0%A6%B8%E0%A6%82%E0%A6%96%E0%A7%8D%E0%A6%AF%E0%A6%BE%E0%A6%A8" title="পরিসংখ্যান – Bangla" lang="bn" hreflang="bn" data-title="পরিসংখ্যান" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/Th%C3%B3ng-k%C3%A8-ha%CC%8Dk" title="Thóng-kè-ha̍k – Minnan" lang="nan" hreflang="nan" data-title="Thóng-kè-ha̍k" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="Minnan" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%A1%D1%82%D0%B0%D1%82%D0%B8%D1%81%D1%82%D0%B8%D0%BA%D0%B0" title="Статистика – Bashkir" lang="ba" hreflang="ba" data-title="Статистика" data-language-autonym="Башҡортса" data-language-local-name="Bashkir" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%A1%D1%82%D0%B0%D1%82%D1%8B%D1%81%D1%82%D1%8B%D0%BA%D0%B0" title="Статыстыка – Belarusian" lang="be" hreflang="be" data-title="Статыстыка" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%A1%D1%82%D0%B0%D1%82%D1%8B%D1%81%D1%82%D1%8B%D0%BA%D0%B0" title="Статыстыка – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Статыстыка" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bcl mw-list-item"><a href="https://bcl.wikipedia.org/wiki/Estadistika" title="Estadistika – Central Bikol" lang="bcl" hreflang="bcl" data-title="Estadistika" data-language-autonym="Bikol Central" data-language-local-name="Central Bikol" class="interlanguage-link-target"><span>Bikol Central</span></a></li><li class="interlanguage-link interwiki-bi mw-list-item"><a href="https://bi.wikipedia.org/wiki/Statistikis" title="Statistikis – Bislama" lang="bi" hreflang="bi" data-title="Statistikis" data-language-autonym="Bislama" data-language-local-name="Bislama" class="interlanguage-link-target"><span>Bislama</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A1%D1%82%D0%B0%D1%82%D0%B8%D1%81%D1%82%D0%B8%D0%BA%D0%B0" title="Статистика – Bulgarian" lang="bg" hreflang="bg" data-title="Статистика" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Statistika" title="Statistika – Bosnian" lang="bs" hreflang="bs" data-title="Statistika" data-language-autonym="Bosanski" data-language-local-name="Bosnian" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-br mw-list-item"><a href="https://br.wikipedia.org/wiki/Stadegouriezh" title="Stadegouriezh – Breton" lang="br" hreflang="br" data-title="Stadegouriezh" data-language-autonym="Brezhoneg" data-language-local-name="Breton" class="interlanguage-link-target"><span>Brezhoneg</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Estad%C3%ADstica" title="Estadística – Catalan" lang="ca" hreflang="ca" data-title="Estadística" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%A1%D1%82%D0%B0%D1%82%D0%B8%D1%81%D1%82%D0%B8%D0%BA%D0%B0" title="Статистика – Chuvash" lang="cv" hreflang="cv" data-title="Статистика" data-language-autonym="Чӑвашла" data-language-local-name="Chuvash" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Statistika" title="Statistika – Czech" lang="cs" hreflang="cs" data-title="Statistika" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cbk-zam mw-list-item"><a href="https://cbk-zam.wikipedia.org/wiki/Estadistica" title="Estadistica – Chavacano" lang="cbk" hreflang="cbk" data-title="Estadistica" data-language-autonym="Chavacano de Zamboanga" data-language-local-name="Chavacano" class="interlanguage-link-target"><span>Chavacano de Zamboanga</span></a></li><li class="interlanguage-link interwiki-co mw-list-item"><a href="https://co.wikipedia.org/wiki/Statistica" title="Statistica – Corsican" lang="co" hreflang="co" data-title="Statistica" data-language-autonym="Corsu" data-language-local-name="Corsican" class="interlanguage-link-target"><span>Corsu</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Ystadegaeth" title="Ystadegaeth – Welsh" lang="cy" hreflang="cy" data-title="Ystadegaeth" data-language-autonym="Cymraeg" data-language-local-name="Welsh" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Statistik" title="Statistik – Danish" lang="da" hreflang="da" data-title="Statistik" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Statistik" title="Statistik – German" lang="de" hreflang="de" data-title="Statistik" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-dv mw-list-item"><a href="https://dv.wikipedia.org/wiki/%DE%8C%DE%A6%DE%8A%DE%A7%DE%90%DE%B0_%DE%80%DE%A8%DE%90%DE%A7%DE%84%DE%AA" title="ތަފާސް ހިސާބު – Divehi" lang="dv" hreflang="dv" data-title="ތަފާސް ހިސާބު" data-language-autonym="ދިވެހިބަސް" data-language-local-name="Divehi" class="interlanguage-link-target"><span>ދިވެހިބަސް</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Statistika" title="Statistika – Estonian" lang="et" hreflang="et" data-title="Statistika" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%A3%CF%84%CE%B1%CF%84%CE%B9%CF%83%CF%84%CE%B9%CE%BA%CE%AE" title="Στατιστική – Greek" lang="el" hreflang="el" data-title="Στατιστική" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Estad%C3%ADstica" title="Estadística – Spanish" lang="es" hreflang="es" data-title="Estadística" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Statistiko" title="Statistiko – Esperanto" lang="eo" hreflang="eo" data-title="Statistiko" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-ext mw-list-item"><a href="https://ext.wikipedia.org/wiki/Esta%C3%ADstica" title="Estaística – Extremaduran" lang="ext" hreflang="ext" data-title="Estaística" data-language-autonym="Estremeñu" data-language-local-name="Extremaduran" class="interlanguage-link-target"><span>Estremeñu</span></a></li><li class="interlanguage-link interwiki-eu badge-Q17437796 badge-featuredarticle mw-list-item" title="featured article badge"><a href="https://eu.wikipedia.org/wiki/Estatistika" title="Estatistika – Basque" lang="eu" hreflang="eu" data-title="Estatistika" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%A2%D9%85%D8%A7%D8%B1" title="آمار – Persian" lang="fa" hreflang="fa" data-title="آمار" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-hif mw-list-item"><a href="https://hif.wikipedia.org/wiki/Aankrraa" title="Aankrraa – Fiji Hindi" lang="hif" hreflang="hif" data-title="Aankrraa" data-language-autonym="Fiji Hindi" data-language-local-name="Fiji Hindi" class="interlanguage-link-target"><span>Fiji Hindi</span></a></li><li class="interlanguage-link interwiki-fo mw-list-item"><a href="https://fo.wikipedia.org/wiki/Hagfr%C3%B8%C3%B0i" title="Hagfrøði – Faroese" lang="fo" hreflang="fo" data-title="Hagfrøði" data-language-autonym="Føroyskt" data-language-local-name="Faroese" class="interlanguage-link-target"><span>Føroyskt</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Statistique" title="Statistique – French" lang="fr" hreflang="fr" data-title="Statistique" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-fy mw-list-item"><a href="https://fy.wikipedia.org/wiki/Statistyk" title="Statistyk – Western Frisian" lang="fy" hreflang="fy" data-title="Statistyk" data-language-autonym="Frysk" data-language-local-name="Western Frisian" class="interlanguage-link-target"><span>Frysk</span></a></li><li class="interlanguage-link interwiki-fur mw-list-item"><a href="https://fur.wikipedia.org/wiki/Statistiche" title="Statistiche – Friulian" lang="fur" hreflang="fur" data-title="Statistiche" data-language-autonym="Furlan" data-language-local-name="Friulian" class="interlanguage-link-target"><span>Furlan</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Staitistic" title="Staitistic – Irish" lang="ga" hreflang="ga" data-title="Staitistic" data-language-autonym="Gaeilge" data-language-local-name="Irish" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gv mw-list-item"><a href="https://gv.wikipedia.org/wiki/Staydraa" title="Staydraa – Manx" lang="gv" hreflang="gv" data-title="Staydraa" data-language-autonym="Gaelg" data-language-local-name="Manx" class="interlanguage-link-target"><span>Gaelg</span></a></li><li class="interlanguage-link interwiki-gd mw-list-item"><a href="https://gd.wikipedia.org/wiki/Staitistearachd" title="Staitistearachd – Scottish Gaelic" lang="gd" hreflang="gd" data-title="Staitistearachd" data-language-autonym="Gàidhlig" data-language-local-name="Scottish Gaelic" class="interlanguage-link-target"><span>Gàidhlig</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Estat%C3%ADstica" title="Estatística – Galician" lang="gl" hreflang="gl" data-title="Estatística" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-gan mw-list-item"><a href="https://gan.wikipedia.org/wiki/%E7%B5%B1%E8%A8%88%E5%AD%B8" title="統計學 – Gan" lang="gan" hreflang="gan" data-title="統計學" data-language-autonym="贛語" data-language-local-name="Gan" class="interlanguage-link-target"><span>贛語</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%ED%86%B5%EA%B3%84%ED%95%99" title="통계학 – Korean" lang="ko" hreflang="ko" data-title="통계학" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-haw mw-list-item"><a href="https://haw.wikipedia.org/wiki/Kumuhana" title="Kumuhana – Hawaiian" lang="haw" hreflang="haw" data-title="Kumuhana" data-language-autonym="Hawaiʻi" data-language-local-name="Hawaiian" class="interlanguage-link-target"><span>Hawaiʻi</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%8E%D5%AB%D5%B3%D5%A1%D5%AF%D5%A1%D5%A3%D6%80%D5%B8%D6%82%D5%A9%D5%B5%D5%B8%D6%82%D5%B6" title="Վիճակագրություն – Armenian" lang="hy" hreflang="hy" data-title="Վիճակագրություն" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%B8%E0%A4%BE%E0%A4%82%E0%A4%96%E0%A5%8D%E0%A4%AF%E0%A4%BF%E0%A4%95%E0%A5%80" title="सांख्यिकी – Hindi" lang="hi" hreflang="hi" data-title="सांख्यिकी" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Statistika" title="Statistika – Croatian" lang="hr" hreflang="hr" data-title="Statistika" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Statistiko" title="Statistiko – Ido" lang="io" hreflang="io" data-title="Statistiko" data-language-autonym="Ido" data-language-local-name="Ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Statistika" title="Statistika – Indonesian" lang="id" hreflang="id" data-title="Statistika" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Statistica" title="Statistica – Interlingua" lang="ia" hreflang="ia" data-title="Statistica" data-language-autonym="Interlingua" data-language-local-name="Interlingua" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-iu mw-list-item"><a href="https://iu.wikipedia.org/wiki/%E1%91%AD%E1%93%AF%E1%91%A6%E1%93%AF%E1%93%AF%E1%96%95%E1%96%91%E1%95%90%E1%93%97%E1%92%8B%E1%91%A6_%E1%90%B9%E1%93%AF%E1%94%85%E1%93%B1%E1%91%8E%E1%94%85%E1%93%B4%E1%91%A6" title="ᑭᓯᑦᓯᓯᖕᖑᕐᓗᒋᑦ ᐹᓯᔅᓱᑎᔅᓴᑦ – Inuktitut" lang="iu" hreflang="iu" data-title="ᑭᓯᑦᓯᓯᖕᖑᕐᓗᒋᑦ ᐹᓯᔅᓱᑎᔅᓴᑦ" data-language-autonym="ᐃᓄᒃᑎᑐᑦ / inuktitut" data-language-local-name="Inuktitut" class="interlanguage-link-target"><span>ᐃᓄᒃᑎᑐᑦ / inuktitut</span></a></li><li class="interlanguage-link interwiki-zu mw-list-item"><a href="https://zu.wikipedia.org/wiki/Izibalomininingo" title="Izibalomininingo – Zulu" lang="zu" hreflang="zu" data-title="Izibalomininingo" data-language-autonym="IsiZulu" data-language-local-name="Zulu" class="interlanguage-link-target"><span>IsiZulu</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/T%C3%B6lfr%C3%A6%C3%B0i" title="Tölfræði – Icelandic" lang="is" hreflang="is" data-title="Tölfræði" data-language-autonym="Íslenska" data-language-local-name="Icelandic" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Statistica" title="Statistica – Italian" lang="it" hreflang="it" data-title="Statistica" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A1%D7%98%D7%98%D7%99%D7%A1%D7%98%D7%99%D7%A7%D7%94" title="סטטיסטיקה – Hebrew" lang="he" hreflang="he" data-title="סטטיסטיקה" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-jv mw-list-item"><a href="https://jv.wikipedia.org/wiki/Statistika" title="Statistika – Javanese" lang="jv" hreflang="jv" data-title="Statistika" data-language-autonym="Jawa" data-language-local-name="Javanese" class="interlanguage-link-target"><span>Jawa</span></a></li><li class="interlanguage-link interwiki-kbp mw-list-item"><a href="https://kbp.wikipedia.org/wiki/Sama%C9%A3_%C3%B1%CA%8A%CA%8A_t%C9%A9l%CA%8A%CA%8A" title="Samaɣ ñʊʊ tɩlʊʊ – Kabiye" lang="kbp" hreflang="kbp" data-title="Samaɣ ñʊʊ tɩlʊʊ" data-language-autonym="Kabɩyɛ" data-language-local-name="Kabiye" class="interlanguage-link-target"><span>Kabɩyɛ</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%B8%E0%B2%82%E0%B2%96%E0%B3%8D%E0%B2%AF%E0%B2%BE%E0%B2%B6%E0%B2%BE%E0%B2%B8%E0%B3%8D%E0%B2%A4%E0%B3%8D%E0%B2%B0" title="ಸಂಖ್ಯಾಶಾಸ್ತ್ರ – Kannada" lang="kn" hreflang="kn" data-title="ಸಂಖ್ಯಾಶಾಸ್ತ್ರ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="Kannada" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%A1%E1%83%A2%E1%83%90%E1%83%A2%E1%83%98%E1%83%A1%E1%83%A2%E1%83%98%E1%83%99%E1%83%90" title="სტატისტიკა – Georgian" lang="ka" hreflang="ka" data-title="სტატისტიკა" data-language-autonym="ქართული" data-language-local-name="Georgian" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%A1%D1%82%D0%B0%D1%82%D0%B8%D1%81%D1%82%D0%B8%D0%BA%D0%B0" title="Статистика – Kazakh" lang="kk" hreflang="kk" data-title="Статистика" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-kw mw-list-item"><a href="https://kw.wikipedia.org/wiki/Statystek" title="Statystek – Cornish" lang="kw" hreflang="kw" data-title="Statystek" data-language-autonym="Kernowek" data-language-local-name="Cornish" class="interlanguage-link-target"><span>Kernowek</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Takwimu" title="Takwimu – Swahili" lang="sw" hreflang="sw" data-title="Takwimu" data-language-autonym="Kiswahili" data-language-local-name="Swahili" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Estatistik" title="Estatistik – Haitian Creole" lang="ht" hreflang="ht" data-title="Estatistik" data-language-autonym="Kreyòl ayisyen" data-language-local-name="Haitian Creole" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-gcr mw-list-item"><a href="https://gcr.wikipedia.org/wiki/Statistik" title="Statistik – Guianan Creole" lang="gcr" hreflang="gcr" data-title="Statistik" data-language-autonym="Kriyòl gwiyannen" data-language-local-name="Guianan Creole" class="interlanguage-link-target"><span>Kriyòl gwiyannen</span></a></li><li class="interlanguage-link interwiki-ku mw-list-item"><a href="https://ku.wikipedia.org/wiki/Amar" title="Amar – Kurdish" lang="ku" hreflang="ku" data-title="Amar" data-language-autonym="Kurdî" data-language-local-name="Kurdish" class="interlanguage-link-target"><span>Kurdî</span></a></li><li class="interlanguage-link interwiki-lad mw-list-item"><a href="https://lad.wikipedia.org/wiki/Estadistika" title="Estadistika – Ladino" lang="lad" hreflang="lad" data-title="Estadistika" data-language-autonym="Ladino" data-language-local-name="Ladino" class="interlanguage-link-target"><span>Ladino</span></a></li><li class="interlanguage-link interwiki-lo mw-list-item"><a href="https://lo.wikipedia.org/wiki/%E0%BA%AA%E0%BA%B0%E0%BA%96%E0%BA%B4%E0%BA%95%E0%BA%B4%E0%BA%AA%E0%BA%B2%E0%BA%94" title="ສະຖິຕິສາດ – Lao" lang="lo" hreflang="lo" data-title="ສະຖິຕິສາດ" data-language-autonym="ລາວ" data-language-local-name="Lao" class="interlanguage-link-target"><span>ລາວ</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Statistica" title="Statistica – Latin" lang="la" hreflang="la" data-title="Statistica" data-language-autonym="Latina" data-language-local-name="Latin" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Statistika" title="Statistika – Latvian" lang="lv" hreflang="lv" data-title="Statistika" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-lb mw-list-item"><a href="https://lb.wikipedia.org/wiki/Statistik" title="Statistik – Luxembourgish" lang="lb" hreflang="lb" data-title="Statistik" data-language-autonym="Lëtzebuergesch" data-language-local-name="Luxembourgish" class="interlanguage-link-target"><span>Lëtzebuergesch</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Statistika_(mokslas)" title="Statistika (mokslas) – Lithuanian" lang="lt" hreflang="lt" data-title="Statistika (mokslas)" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lij mw-list-item"><a href="https://lij.wikipedia.org/wiki/Statistega" title="Statistega – Ligurian" lang="lij" hreflang="lij" data-title="Statistega" data-language-autonym="Ligure" data-language-local-name="Ligurian" class="interlanguage-link-target"><span>Ligure</span></a></li><li class="interlanguage-link interwiki-li mw-list-item"><a href="https://li.wikipedia.org/wiki/Sjtatistiek" title="Sjtatistiek – Limburgish" lang="li" hreflang="li" data-title="Sjtatistiek" data-language-autonym="Limburgs" data-language-local-name="Limburgish" class="interlanguage-link-target"><span>Limburgs</span></a></li><li class="interlanguage-link interwiki-lfn mw-list-item"><a href="https://lfn.wikipedia.org/wiki/Statistica" title="Statistica – Lingua Franca Nova" lang="lfn" hreflang="lfn" data-title="Statistica" data-language-autonym="Lingua Franca Nova" data-language-local-name="Lingua Franca Nova" class="interlanguage-link-target"><span>Lingua Franca Nova</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Statistega" title="Statistega – Lombard" lang="lmo" hreflang="lmo" data-title="Statistega" data-language-autonym="Lombard" data-language-local-name="Lombard" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Statisztika" title="Statisztika – Hungarian" lang="hu" hreflang="hu" data-title="Statisztika" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mad mw-list-item"><a href="https://mad.wikipedia.org/wiki/Statistika" title="Statistika – Madurese" lang="mad" hreflang="mad" data-title="Statistika" data-language-autonym="Madhurâ" data-language-local-name="Madurese" class="interlanguage-link-target"><span>Madhurâ</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%A1%D1%82%D0%B0%D1%82%D0%B8%D1%81%D1%82%D0%B8%D0%BA%D0%B0" title="Статистика – Macedonian" lang="mk" hreflang="mk" data-title="Статистика" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Statistika" title="Statistika – Malagasy" lang="mg" hreflang="mg" data-title="Statistika" data-language-autonym="Malagasy" data-language-local-name="Malagasy" class="interlanguage-link-target"><span>Malagasy</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%B8%E0%B5%8D%E0%B4%A5%E0%B4%BF%E0%B4%A4%E0%B4%BF%E0%B4%97%E0%B4%A3%E0%B4%BF%E0%B4%A4%E0%B4%82" title="സ്ഥിതിഗണിതം – Malayalam" lang="ml" hreflang="ml" data-title="സ്ഥിതിഗണിതം" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%B8%E0%A4%82%E0%A4%96%E0%A5%8D%E0%A4%AF%E0%A4%BE%E0%A4%B6%E0%A4%BE%E0%A4%B8%E0%A5%8D%E0%A4%A4%E0%A5%8D%E0%A4%B0" title="संख्याशास्त्र – Marathi" lang="mr" hreflang="mr" data-title="संख्याशास्त्र" data-language-autonym="मराठी" data-language-local-name="Marathi" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-xmf mw-list-item"><a href="https://xmf.wikipedia.org/wiki/%E1%83%A1%E1%83%A2%E1%83%90%E1%83%A2%E1%83%98%E1%83%A1%E1%83%A2%E1%83%98%E1%83%99%E1%83%90" title="სტატისტიკა – Mingrelian" lang="xmf" hreflang="xmf" data-title="სტატისტიკა" data-language-autonym="მარგალური" data-language-local-name="Mingrelian" class="interlanguage-link-target"><span>მარგალური</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Perangkaan" title="Perangkaan – Malay" lang="ms" hreflang="ms" data-title="Perangkaan" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-mwl mw-list-item"><a href="https://mwl.wikipedia.org/wiki/Stat%C3%ADstica" title="Statística – Mirandese" lang="mwl" hreflang="mwl" data-title="Statística" data-language-autonym="Mirandés" data-language-local-name="Mirandese" class="interlanguage-link-target"><span>Mirandés</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%85%E1%80%AC%E1%80%9B%E1%80%84%E1%80%BA%E1%80%B8%E1%80%A1%E1%80%84%E1%80%BA%E1%80%B8_%E1%80%95%E1%80%8A%E1%80%AC" title="စာရင်းအင်း ပညာ – Burmese" lang="my" hreflang="my" data-title="စာရင်းအင်း ပညာ" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="Burmese" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Statistiek" title="Statistiek – Dutch" lang="nl" hreflang="nl" data-title="Statistiek" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ne mw-list-item"><a href="https://ne.wikipedia.org/wiki/%E0%A4%A4%E0%A4%A5%E0%A5%8D%E0%A4%AF%E0%A4%BE%E0%A4%99%E0%A5%8D%E0%A4%95" title="तथ्याङ्क – Nepali" lang="ne" hreflang="ne" data-title="तथ्याङ्क" data-language-autonym="नेपाली" data-language-local-name="Nepali" class="interlanguage-link-target"><span>नेपाली</span></a></li><li class="interlanguage-link interwiki-new mw-list-item"><a href="https://new.wikipedia.org/wiki/%E0%A4%A4%E0%A4%A5%E0%A5%8D%E0%A4%AF%E0%A4%BE%E0%A4%99%E0%A5%8D%E0%A4%95" title="तथ्याङ्क – Newari" lang="new" hreflang="new" data-title="तथ्याङ्क" data-language-autonym="नेपाल भाषा" data-language-local-name="Newari" class="interlanguage-link-target"><span>नेपाल भाषा</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E7%B5%B1%E8%A8%88%E5%AD%A6" title="統計学 – Japanese" lang="ja" hreflang="ja" data-title="統計学" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-frr mw-list-item"><a href="https://frr.wikipedia.org/wiki/Statistik" title="Statistik – Northern Frisian" lang="frr" hreflang="frr" data-title="Statistik" data-language-autonym="Nordfriisk" data-language-local-name="Northern Frisian" class="interlanguage-link-target"><span>Nordfriisk</span></a></li><li class="interlanguage-link interwiki-pih mw-list-item"><a href="https://pih.wikipedia.org/wiki/Stetistiks" title="Stetistiks – Norfuk / Pitkern" lang="pih" hreflang="pih" data-title="Stetistiks" data-language-autonym="Norfuk / Pitkern" data-language-local-name="Norfuk / Pitkern" class="interlanguage-link-target"><span>Norfuk / Pitkern</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Statistikk" title="Statistikk – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Statistikk" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Statistikk" title="Statistikk – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Statistikk" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Estatistica" title="Estatistica – Occitan" lang="oc" hreflang="oc" data-title="Estatistica" data-language-autonym="Occitan" data-language-local-name="Occitan" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-or mw-list-item"><a href="https://or.wikipedia.org/wiki/%E0%AC%AA%E0%AC%B0%E0%AC%BF%E0%AC%B8%E0%AC%82%E0%AC%96%E0%AD%8D%E0%AD%9F%E0%AC%BE%E0%AC%A8" title="ପରିସଂଖ୍ୟାନ – Odia" lang="or" hreflang="or" data-title="ପରିସଂଖ୍ୟାନ" data-language-autonym="ଓଡ଼ିଆ" data-language-local-name="Odia" class="interlanguage-link-target"><span>ଓଡ଼ିଆ</span></a></li><li class="interlanguage-link interwiki-om mw-list-item"><a href="https://om.wikipedia.org/wiki/Xiinannoo" title="Xiinannoo – Oromo" lang="om" hreflang="om" data-title="Xiinannoo" data-language-autonym="Oromoo" data-language-local-name="Oromo" class="interlanguage-link-target"><span>Oromoo</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Statistika" title="Statistika – Uzbek" lang="uz" hreflang="uz" data-title="Statistika" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%85%E0%A9%B0%E0%A8%95%E0%A9%9C%E0%A8%BE_%E0%A8%B5%E0%A8%BF%E0%A8%97%E0%A8%BF%E0%A8%86%E0%A8%A8" title="ਅੰਕੜਾ ਵਿਗਿਆਨ – Punjabi" lang="pa" hreflang="pa" data-title="ਅੰਕੜਾ ਵਿਗਿਆਨ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Punjabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D8%B4%D9%85%D8%A7%D8%B1%DB%8C%D8%A7%D8%AA" title="شماریات – Western Punjabi" lang="pnb" hreflang="pnb" data-title="شماریات" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-ps mw-list-item"><a href="https://ps.wikipedia.org/wiki/%D8%B3%D8%B1%D8%B4%D9%85%DB%8C%D8%B1%D9%86%D9%87" title="سرشمیرنه – Pashto" lang="ps" hreflang="ps" data-title="سرشمیرنه" data-language-autonym="پښتو" data-language-local-name="Pashto" class="interlanguage-link-target"><span>پښتو</span></a></li><li class="interlanguage-link interwiki-jam mw-list-item"><a href="https://jam.wikipedia.org/wiki/Statistix" title="Statistix – Jamaican Creole English" lang="jam" hreflang="jam" data-title="Statistix" data-language-autonym="Patois" data-language-local-name="Jamaican Creole English" class="interlanguage-link-target"><span>Patois</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Stat%C3%ACstica" title="Statìstica – Piedmontese" lang="pms" hreflang="pms" data-title="Statìstica" data-language-autonym="Piemontèis" data-language-local-name="Piedmontese" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Statystyka" title="Statystyka – Polish" lang="pl" hreflang="pl" data-title="Statystyka" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Estat%C3%ADstica" title="Estatística – Portuguese" lang="pt" hreflang="pt" data-title="Estatística" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Statistic%C4%83" title="Statistică – Romanian" lang="ro" hreflang="ro" data-title="Statistică" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-qu mw-list-item"><a href="https://qu.wikipedia.org/wiki/Khipukamay" title="Khipukamay – Quechua" lang="qu" hreflang="qu" data-title="Khipukamay" data-language-autonym="Runa Simi" data-language-local-name="Quechua" class="interlanguage-link-target"><span>Runa Simi</span></a></li><li class="interlanguage-link interwiki-rue mw-list-item"><a href="https://rue.wikipedia.org/wiki/%D0%A8%D1%82%D0%B0%D1%82%D1%96%D1%81%D1%82%D1%96%D0%BA%D0%B0" title="Штатістіка – Rusyn" lang="rue" hreflang="rue" data-title="Штатістіка" data-language-autonym="Русиньскый" data-language-local-name="Rusyn" class="interlanguage-link-target"><span>Русиньскый</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A1%D1%82%D0%B0%D1%82%D0%B8%D1%81%D1%82%D0%B8%D0%BA%D0%B0" title="Статистика – Russian" lang="ru" hreflang="ru" data-title="Статистика" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Stateestics" title="Stateestics – Scots" lang="sco" hreflang="sco" data-title="Stateestics" data-language-autonym="Scots" data-language-local-name="Scots" class="interlanguage-link-target"><span>Scots</span></a></li><li class="interlanguage-link interwiki-stq mw-list-item"><a href="https://stq.wikipedia.org/wiki/Statistik" title="Statistik – Saterland Frisian" lang="stq" hreflang="stq" data-title="Statistik" data-language-autonym="Seeltersk" data-language-local-name="Saterland Frisian" class="interlanguage-link-target"><span>Seeltersk</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Statistika" title="Statistika – Albanian" lang="sq" hreflang="sq" data-title="Statistika" data-language-autonym="Shqip" data-language-local-name="Albanian" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Stat%C3%ACstica" title="Statìstica – Sicilian" lang="scn" hreflang="scn" data-title="Statìstica" data-language-autonym="Sicilianu" data-language-local-name="Sicilian" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B7%83%E0%B6%82%E0%B6%9B%E0%B7%8A%E2%80%8D%E0%B6%BA%E0%B7%8F%E0%B6%B1%E0%B6%BA" title="සංඛ්‍යානය – Sinhala" lang="si" hreflang="si" data-title="සංඛ්‍යානය" data-language-autonym="සිංහල" data-language-local-name="Sinhala" class="interlanguage-link-target"><span>සිංහල</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Statistics" title="Statistics – Simple English" lang="en-simple" hreflang="en-simple" data-title="Statistics" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sd mw-list-item"><a href="https://sd.wikipedia.org/wiki/%D8%B4%D9%85%D8%A7%D8%B1%D9%8A%D8%A7%D8%AA" title="شماريات – Sindhi" lang="sd" hreflang="sd" data-title="شماريات" data-language-autonym="سنڌي" data-language-local-name="Sindhi" class="interlanguage-link-target"><span>سنڌي</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/%C5%A0tatistika" title="Štatistika – Slovak" lang="sk" hreflang="sk" data-title="Štatistika" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Statistika" title="Statistika – Slovenian" lang="sl" hreflang="sl" data-title="Statistika" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D8%A6%D8%A7%D9%85%D8%A7%D8%B1" title="ئامار – Central Kurdish" lang="ckb" hreflang="ckb" data-title="ئامار" data-language-autonym="کوردی" data-language-local-name="Central Kurdish" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%A1%D1%82%D0%B0%D1%82%D0%B8%D1%81%D1%82%D0%B8%D0%BA%D0%B0" title="Статистика – Serbian" lang="sr" hreflang="sr" data-title="Статистика" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Statistika" title="Statistika – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Statistika" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-su mw-list-item"><a href="https://su.wikipedia.org/wiki/Statistika" title="Statistika – Sundanese" lang="su" hreflang="su" data-title="Statistika" data-language-autonym="Sunda" data-language-local-name="Sundanese" class="interlanguage-link-target"><span>Sunda</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Tilastotiede" title="Tilastotiede – Finnish" lang="fi" hreflang="fi" data-title="Tilastotiede" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Statistik" title="Statistik – Swedish" lang="sv" hreflang="sv" data-title="Statistik" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Estadistika" title="Estadistika – Tagalog" lang="tl" hreflang="tl" data-title="Estadistika" data-language-autonym="Tagalog" data-language-local-name="Tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%AA%E0%AF%81%E0%AE%B3%E0%AF%8D%E0%AE%B3%E0%AE%BF%E0%AE%AF%E0%AE%BF%E0%AE%AF%E0%AE%B2%E0%AF%8D" title="புள்ளியியல் – Tamil" lang="ta" hreflang="ta" data-title="புள்ளியியல்" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-kab mw-list-item"><a href="https://kab.wikipedia.org/wiki/Addadan_(tussna)" title="Addadan (tussna) – Kabyle" lang="kab" hreflang="kab" data-title="Addadan (tussna)" data-language-autonym="Taqbaylit" data-language-local-name="Kabyle" class="interlanguage-link-target"><span>Taqbaylit</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%A1%D1%82%D0%B0%D1%82%D0%B8%D1%81%D1%82%D0%B8%D0%BA%D0%B0" title="Статистика – Tatar" lang="tt" hreflang="tt" data-title="Статистика" data-language-autonym="Татарча / tatarça" data-language-local-name="Tatar" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-tet mw-list-item"><a href="https://tet.wikipedia.org/wiki/Estat%C3%ADstika" title="Estatístika – Tetum" lang="tet" hreflang="tet" data-title="Estatístika" data-language-autonym="Tetun" data-language-local-name="Tetum" class="interlanguage-link-target"><span>Tetun</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%AA%E0%B8%96%E0%B8%B4%E0%B8%95%E0%B8%B4%E0%B8%A8%E0%B8%B2%E0%B8%AA%E0%B8%95%E0%B8%A3%E0%B9%8C" title="สถิติศาสตร์ – Thai" lang="th" hreflang="th" data-title="สถิติศาสตร์" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/%D0%9E%D0%BC%D0%BE%D1%80" title="Омор – Tajik" lang="tg" hreflang="tg" data-title="Омор" data-language-autonym="Тоҷикӣ" data-language-local-name="Tajik" class="interlanguage-link-target"><span>Тоҷикӣ</span></a></li><li class="interlanguage-link interwiki-tcy mw-list-item"><a href="https://tcy.wikipedia.org/wiki/%E0%B2%B8%E0%B2%82%E0%B2%96%E0%B3%8D%E0%B2%AF%E0%B2%BE%E0%B2%B6%E0%B2%BE%E0%B2%B8%E0%B3%8D%E0%B2%A4%E0%B3%8D%E0%B2%B0" title="ಸಂಖ್ಯಾಶಾಸ್ತ್ರ – Tulu" lang="tcy" hreflang="tcy" data-title="ಸಂಖ್ಯಾಶಾಸ್ತ್ರ" data-language-autonym="ತುಳು" data-language-local-name="Tulu" class="interlanguage-link-target"><span>ತುಳು</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/%C4%B0statistik" title="İstatistik – Turkish" lang="tr" hreflang="tr" data-title="İstatistik" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-tk mw-list-item"><a href="https://tk.wikipedia.org/wiki/Statistika" title="Statistika – Turkmen" lang="tk" hreflang="tk" data-title="Statistika" data-language-autonym="Türkmençe" data-language-local-name="Turkmen" class="interlanguage-link-target"><span>Türkmençe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A1%D1%82%D0%B0%D1%82%D0%B8%D1%81%D1%82%D0%B8%D0%BA%D0%B0" title="Статистика – Ukrainian" lang="uk" hreflang="uk" data-title="Статистика" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D8%B4%D9%85%D8%A7%D8%B1%DB%8C%D8%A7%D8%AA" title="شماریات – Urdu" lang="ur" hreflang="ur" data-title="شماریات" data-language-autonym="اردو" data-language-local-name="Urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-vec mw-list-item"><a href="https://vec.wikipedia.org/wiki/Stat%C3%ACstega" title="Statìstega – Venetian" lang="vec" hreflang="vec" data-title="Statìstega" data-language-autonym="Vèneto" data-language-local-name="Venetian" class="interlanguage-link-target"><span>Vèneto</span></a></li><li class="interlanguage-link interwiki-vep mw-list-item"><a href="https://vep.wikipedia.org/wiki/Statistik" title="Statistik – Veps" lang="vep" hreflang="vep" data-title="Statistik" data-language-autonym="Vepsän kel’" data-language-local-name="Veps" class="interlanguage-link-target"><span>Vepsän kel’</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Th%E1%BB%91ng_k%C3%AA" title="Thống kê – Vietnamese" lang="vi" hreflang="vi" data-title="Thống kê" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-fiu-vro mw-list-item"><a href="https://fiu-vro.wikipedia.org/wiki/Statistiga" title="Statistiga – Võro" lang="vro" hreflang="vro" data-title="Statistiga" data-language-autonym="Võro" data-language-local-name="Võro" class="interlanguage-link-target"><span>Võro</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Estadistik%C3%A1" title="Estadistiká – Waray" lang="war" hreflang="war" data-title="Estadistiká" data-language-autonym="Winaray" data-language-local-name="Waray" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E7%BB%9F%E8%AE%A1%E5%AD%A6" title="统计学 – Wu" lang="wuu" hreflang="wuu" data-title="统计学" data-language-autonym="吴语" data-language-local-name="Wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%A1%D7%98%D7%90%D7%98%D7%99%D7%A1%D7%98%D7%99%D7%A7" title="סטאטיסטיק – Yiddish" lang="yi" hreflang="yi" data-title="סטאטיסטיק" data-language-autonym="ייִדיש" data-language-local-name="Yiddish" class="interlanguage-link-target"><span>ייִדיש</span></a></li><li class="interlanguage-link interwiki-yo mw-list-item"><a href="https://yo.wikipedia.org/wiki/%C3%8Csir%C3%B2_Statistiki" title="Ìsirò Statistiki – Yoruba" lang="yo" hreflang="yo" data-title="Ìsirò Statistiki" data-language-autonym="Yorùbá" data-language-local-name="Yoruba" class="interlanguage-link-target"><span>Yorùbá</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E7%B5%B1%E8%A8%88%E5%AD%B8" title="統計學 – Cantonese" lang="yue" hreflang="yue" data-title="統計學" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-diq mw-list-item"><a href="https://diq.wikipedia.org/wiki/%C4%B0statistik" title="İstatistik – Zazaki" lang="diq" hreflang="diq" data-title="İstatistik" data-language-autonym="Zazaki" data-language-local-name="Zazaki" class="interlanguage-link-target"><span>Zazaki</span></a></li><li class="interlanguage-link interwiki-bat-smg mw-list-item"><a href="https://bat-smg.wikipedia.org/wiki/Stat%C4%97st%C4%97ka" title="Statėstėka – Samogitian" lang="sgs" hreflang="sgs" data-title="Statėstėka" data-language-autonym="Žemaitėška" data-language-local-name="Samogitian" class="interlanguage-link-target"><span>Žemaitėška</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E7%BB%9F%E8%AE%A1%E5%AD%A6" title="统计学 – Chinese" lang="zh" hreflang="zh" data-title="统计学" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-bew mw-list-item"><a href="https://bew.wikipedia.org/wiki/Statistik" title="Statistik – Betawi" lang="bew" hreflang="bew" data-title="Statistik" data-language-autonym="Betawi" data-language-local-name="Betawi" class="interlanguage-link-target"><span>Betawi</span></a></li><li class="interlanguage-link interwiki-iba mw-list-item"><a href="https://iba.wikipedia.org/wiki/Statistik" title="Statistik – Iban" lang="iba" hreflang="iba" data-title="Statistik" data-language-autonym="Jaku Iban" data-language-local-name="Iban" class="interlanguage-link-target"><span>Jaku Iban</span></a></li><li class="interlanguage-link interwiki-zgh mw-list-item"><a href="https://zgh.wikipedia.org/wiki/%E2%B5%9C%E2%B4%B0%E2%B5%99%E2%B5%8F%E2%B5%8E%E2%B4%BD%E2%B5%9C%E2%B4%B0" title="ⵜⴰⵙⵏⵎⴽⵜⴰ – Standard Moroccan Tamazight" lang="zgh" hreflang="zgh" data-title="ⵜⴰⵙⵏⵎⴽⵜⴰ" data-language-autonym="ⵜⴰⵎⴰⵣⵉⵖⵜ ⵜⴰⵏⴰⵡⴰⵢⵜ" data-language-local-name="Standard Moroccan Tamazight" class="interlanguage-link-target"><span>ⵜⴰⵎⴰⵣⵉⵖⵜ ⵜⴰⵏⴰⵡⴰⵢⵜ</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q12483#sitelinks-wikipedia" title="Edit interlanguage links" class="wbc-editpage">Edit links</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Namespaces"> <div id="p-associated-pages" class="vector-menu 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class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Study of the collection and analysis of data</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">For other uses, see <a href="/wiki/Statistics_(disambiguation)" class="mw-disambig" title="Statistics (disambiguation)">Statistics (disambiguation)</a>.</div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Standard_Normal_Distribution.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/44/Standard_Normal_Distribution.png/290px-Standard_Normal_Distribution.png" decoding="async" width="290" height="179" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/44/Standard_Normal_Distribution.png/435px-Standard_Normal_Distribution.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/44/Standard_Normal_Distribution.png/580px-Standard_Normal_Distribution.png 2x" data-file-width="5986" data-file-height="3700" /></a><figcaption>The <a href="/wiki/Normal_distribution" title="Normal distribution">normal distribution</a>, a very common <a href="/wiki/Probability_density_function" title="Probability density function">probability density</a>, is used extensively in <a href="/wiki/Inferential_statistics" class="mw-redirect" title="Inferential statistics">inferential statistics</a>.</figcaption></figure> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Iris_Pairs_Plot.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2c/Iris_Pairs_Plot.svg/290px-Iris_Pairs_Plot.svg.png" decoding="async" width="290" height="283" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2c/Iris_Pairs_Plot.svg/435px-Iris_Pairs_Plot.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/2c/Iris_Pairs_Plot.svg/580px-Iris_Pairs_Plot.svg.png 2x" data-file-width="645" data-file-height="629" /></a><figcaption><a href="/wiki/Scatter_plot" title="Scatter plot">Scatter plots</a> and <a href="/wiki/Line_chart" title="Line chart">line charts</a> are used in <a href="/wiki/Descriptive_statistics" title="Descriptive statistics">descriptive statistics</a> to show the observed relationships between different variables, here using the <a href="/wiki/Iris_flower_data_set" 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typeof="mw:File/Frameless"><a href="/wiki/File:Fisher_iris_versicolor_sepalwidth.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/40/Fisher_iris_versicolor_sepalwidth.svg/100px-Fisher_iris_versicolor_sepalwidth.svg.png" decoding="async" width="100" height="69" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/40/Fisher_iris_versicolor_sepalwidth.svg/150px-Fisher_iris_versicolor_sepalwidth.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/40/Fisher_iris_versicolor_sepalwidth.svg/200px-Fisher_iris_versicolor_sepalwidth.svg.png 2x" data-file-width="822" data-file-height="567" /></a></span></td></tr><tr><td class="sidebar-content"> <ul><li><a href="/wiki/Outline_of_statistics" title="Outline of statistics">Outline</a></li> <li><a href="/wiki/List_of_statisticians" title="List of statisticians">Statisticians</a></li> <li><a href="/wiki/Glossary_of_probability_and_statistics" title="Glossary of probability and statistics">Glossary</a></li> <li><a href="/wiki/Notation_in_probability_and_statistics" title="Notation in probability and statistics">Notation</a></li> <li><a href="/wiki/List_of_statistics_journals" title="List of statistics journals">Journals</a></li> <li><a href="/wiki/Lists_of_statistics_topics" title="Lists of statistics topics">Lists of topics</a></li> <li><a href="/wiki/List_of_statistics_articles" title="List of statistics articles">Articles</a></li> <li><a href="/wiki/Category:Statistics" title="Category:Statistics">Category</a></li> <li><br /><span class="nowrap"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Nuvola_apps_edu_mathematics_blue-p.svg" class="mw-file-description"><img alt="icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/16px-Nuvola_apps_edu_mathematics_blue-p.svg.png" decoding="async" width="16" height="16" class="mw-file-element" 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class="sidebar-above" style="padding-bottom:0.35em;"> <ul><li><a href="/wiki/History_of_mathematics" title="History of mathematics">History</a></li> <li><a href="/wiki/Lists_of_mathematics_topics" title="Lists of mathematics topics">Index</a></li></ul></td></tr><tr><td class="sidebar-content-with-subgroup"> <table class="sidebar-subgroup"><tbody><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible"><div class="sidebar-list-title" style="border-top:1px solid #aaa;background:#ddddff;text-align:center;;color: var(--color-base)"><a href="/wiki/Areas_of_mathematics" class="mw-redirect" title="Areas of mathematics">Areas</a></div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/Number_theory" title="Number theory">Number theory</a></li> <li><a href="/wiki/Geometry" title="Geometry">Geometry</a></li> <li><a href="/wiki/Algebra" title="Algebra">Algebra</a></li> <li><a href="/wiki/Calculus" title="Calculus">Calculus</a> and <a href="/wiki/Mathematical_analysis" title="Mathematical analysis">Analysis</a></li> <li><a href="/wiki/Discrete_mathematics" title="Discrete mathematics">Discrete mathematics</a></li> <li><a href="/wiki/Mathematical_logic" title="Mathematical logic">Logic</a> and <a href="/wiki/Set_theory" title="Set theory">Set theory</a></li> <li><a href="/wiki/Probability" title="Probability">Probability</a></li> <li><a class="mw-selflink selflink">Statistics</a> and <a href="/wiki/Decision_theory" title="Decision theory">Decision theory</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible"><div class="sidebar-list-title" style="border-top:1px solid #aaa;background:#ddddff;text-align:center;;color: var(--color-base)">Relationship with sciences</div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/Mathematical_physics" title="Mathematical physics">Physics</a></li> <li><a href="/wiki/Mathematical_chemistry" title="Mathematical chemistry">Chemistry</a></li> <li><a href="/wiki/Geomathematics" title="Geomathematics">Geosciences</a></li> <li><a href="/wiki/Computational_mathematics" title="Computational mathematics">Computation</a></li> <li><a href="/wiki/Mathematical_and_theoretical_biology" title="Mathematical and theoretical biology">Biology</a></li> <li><a href="/wiki/Computational_linguistics" title="Computational linguistics">Linguistics</a></li> <li><a href="/wiki/Mathematical_economics" title="Mathematical economics">Economics</a></li> <li><a href="/wiki/Philosophy_of_mathematics" title="Philosophy of mathematics">Philosophy</a></li> <li><a href="/wiki/Mathematics_education" title="Mathematics education">Education</a></li></ul></div></div></td> </tr></tbody></table></td> </tr><tr><th class="sidebar-heading"> <span typeof="mw:File"><a href="/wiki/File:Nuvola_apps_edu_mathematics_blue-p.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/20px-Nuvola_apps_edu_mathematics_blue-p.svg.png" decoding="async" width="20" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/30px-Nuvola_apps_edu_mathematics_blue-p.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/40px-Nuvola_apps_edu_mathematics_blue-p.svg.png 2x" data-file-width="128" data-file-height="128" /></a></span> <a href="/wiki/Portal:Mathematics" title="Portal:Mathematics">Mathematics Portal</a></th></tr><tr><td class="sidebar-navbar"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Math_topics_sidebar" title="Template:Math topics sidebar"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Math_topics_sidebar" title="Template talk:Math topics sidebar"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Math_topics_sidebar" title="Special:EditPage/Template:Math topics sidebar"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table> <p><b>Statistics</b> (from <a href="/wiki/German_language" title="German language">German</a>: <i><span lang="de"><a href="https://en.wiktionary.org/wiki/Statistik#German" class="extiw" title="wikt:Statistik">Statistik</a></span></i>, <abbr title="originally">orig.</abbr> "description of a <a href="/wiki/State_(polity)" title="State (polity)">state</a>, a country"<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>) is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of <a href="/wiki/Data" title="Data">data</a>.<sup id="cite_ref-def_2-0" class="reference"><a href="#cite_note-def-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a <a href="/wiki/Statistical_population" title="Statistical population">statistical population</a> or a <a href="/wiki/Statistical_model" title="Statistical model">statistical model</a> to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of <a href="/wiki/Statistical_survey" class="mw-redirect" title="Statistical survey">surveys</a> and <a href="/wiki/Experimental_design" class="mw-redirect" title="Experimental design">experiments</a>.<sup id="cite_ref-Dodge_3-0" class="reference"><a href="#cite_note-Dodge-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p><p>When <a href="/wiki/Census" title="Census">census</a> data cannot be collected, <a href="/wiki/Statistician" title="Statistician">statisticians</a> collect data by developing specific experiment designs and survey <a href="/wiki/Sample_(statistics)" class="mw-redirect" title="Sample (statistics)">samples</a>. Representative sampling assures that inferences and conclusions can reasonably extend from the sample to the population as a whole. An <a href="/wiki/Experimental_study" class="mw-redirect" title="Experimental study">experimental study</a> involves taking measurements of the system under study, manipulating the system, and then taking additional measurements using the same procedure to determine if the manipulation has modified the values of the measurements. In contrast, an <a href="/wiki/Observational_study" title="Observational study">observational study</a> does not involve experimental manipulation. </p><p>Two main statistical methods are used in <a href="/wiki/Data_analysis" title="Data analysis">data analysis</a>: <a href="/wiki/Descriptive_statistics" title="Descriptive statistics">descriptive statistics</a>, which summarize data from a sample using <a href="/wiki/Index_(statistics)" title="Index (statistics)">indexes</a> such as the <a href="/wiki/Mean" title="Mean">mean</a> or <a href="/wiki/Standard_deviation" title="Standard deviation">standard deviation</a>, and <a href="/wiki/Statistical_inference" title="Statistical inference">inferential statistics</a>, which draw conclusions from data that are subject to random variation (e.g., observational errors, sampling variation).<sup id="cite_ref-LundResearchLtd_4-0" class="reference"><a href="#cite_note-LundResearchLtd-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> Descriptive statistics are most often concerned with two sets of properties of a <i>distribution</i> (sample or population): <i><a href="/wiki/Central_tendency" title="Central tendency">central tendency</a></i> (or <i>location</i>) seeks to characterize the distribution's central or typical value, while <i><a href="/wiki/Statistical_dispersion" title="Statistical dispersion">dispersion</a></i> (or <i>variability</i>) characterizes the extent to which members of the distribution depart from its center and each other. Inferences made using <a href="/wiki/Mathematical_statistics" title="Mathematical statistics">mathematical statistics</a> employ the framework of <a href="/wiki/Probability_theory" title="Probability theory">probability theory</a>, which deals with the analysis of random phenomena. </p><p>A standard statistical procedure involves the collection of data leading to a <a href="/wiki/Statistical_hypothesis_testing" class="mw-redirect" title="Statistical hypothesis testing">test of the relationship</a> between two statistical data sets, or a data set and synthetic data drawn from an idealized model. A hypothesis is proposed for the statistical relationship between the two data sets, an <a href="/wiki/Alternative_hypothesis" title="Alternative hypothesis">alternative</a> to an idealized <a href="/wiki/Null_hypothesis" title="Null hypothesis">null hypothesis</a> of no relationship between two data sets. Rejecting or disproving the null hypothesis is done using statistical tests that quantify the sense in which the null can be proven false, given the data that are used in the test. Working from a null hypothesis, two basic forms of error are recognized: <a href="/wiki/Type_I_error" class="mw-redirect" title="Type I error">Type I errors</a> (null hypothesis is rejected when it is in fact true, giving a "false positive") and <a href="/wiki/Type_II_error" class="mw-redirect" title="Type II error">Type II errors</a> (null hypothesis fails to be rejected when it is in fact false, giving a "false negative"). Multiple problems have come to be associated with this framework, ranging from obtaining a sufficient sample size to specifying an adequate null hypothesis.<sup id="cite_ref-LundResearchLtd_4-1" class="reference"><a href="#cite_note-LundResearchLtd-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p><p>Statistical measurement processes are also prone to error in regards to the data that they generate. Many of these errors are classified as random (noise) or systematic (<a href="/wiki/Bias_(statistics)" title="Bias (statistics)">bias</a>), but other types of errors (e.g., blunder, such as when an analyst reports incorrect units) can also occur. The presence of <a href="/wiki/Missing_data" title="Missing data">missing data</a> or <a href="/wiki/Censoring_(statistics)" title="Censoring (statistics)">censoring</a> may result in biased estimates and specific techniques have been developed to address these problems. </p> <style data-mw-deduplicate="TemplateStyles:r886046785">.mw-parser-output .toclimit-2 .toclevel-1 ul,.mw-parser-output .toclimit-3 .toclevel-2 ul,.mw-parser-output .toclimit-4 .toclevel-3 ul,.mw-parser-output .toclimit-5 .toclevel-4 ul,.mw-parser-output .toclimit-6 .toclevel-5 ul,.mw-parser-output .toclimit-7 .toclevel-6 ul{display:none}</style><div class="toclimit-3"><meta property="mw:PageProp/toc" /></div> <div class="mw-heading mw-heading2"><h2 id="Introduction">Introduction</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Statistics&action=edit&section=1" title="Edit section: Introduction"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Outline_of_statistics" title="Outline of statistics">Outline of statistics</a></div> <p>Statistics is a mathematical body of science that pertains to the collection, analysis, interpretation or explanation, and presentation of <a href="/wiki/Data" title="Data">data</a>,<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> or as a branch of <a href="/wiki/Mathematics" title="Mathematics">mathematics</a>.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> Some consider statistics to be a distinct <a href="/wiki/Mathematical_sciences" title="Mathematical sciences">mathematical science</a> rather than a branch of mathematics. While many scientific investigations make use of data, statistics is generally concerned with the use of data in the context of uncertainty and decision-making in the face of uncertainty.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p><p>In applying statistics to a problem, it is common practice to start with a <a href="/wiki/Statistical_population" title="Statistical population">population</a> or process to be studied. Populations can be diverse topics, such as "all people living in a country" or "every atom composing a crystal". Ideally, statisticians compile data about the entire population (an operation called a <a href="/wiki/Census" title="Census">census</a>). This may be organized by governmental statistical institutes. <i><a href="/wiki/Descriptive_statistics" title="Descriptive statistics">Descriptive statistics</a></i> can be used to summarize the population data. Numerical descriptors include <a href="/wiki/Mean" title="Mean">mean</a> and <a href="/wiki/Standard_deviation" title="Standard deviation">standard deviation</a> for <a href="/wiki/Continuous_probability_distribution" class="mw-redirect" title="Continuous probability distribution">continuous data</a> (like income), while frequency and percentage are more useful in terms of describing <a href="/wiki/Categorical_data" class="mw-redirect" title="Categorical data">categorical data</a> (like education). </p><p>When a census is not feasible, a chosen subset of the population called a <a href="/wiki/Sampling_(statistics)" title="Sampling (statistics)">sample</a> is studied. Once a sample that is representative of the population is determined, data is collected for the sample members in an observational or <a href="/wiki/Experiment" title="Experiment">experimental</a> setting. Again, descriptive statistics can be used to summarize the sample data. However, drawing the sample contains an element of randomness; hence, the numerical descriptors from the sample are also prone to uncertainty. To draw meaningful conclusions about the entire population, <i><a href="/wiki/Inferential_statistics" class="mw-redirect" title="Inferential statistics">inferential statistics</a></i> are needed. It uses patterns in the sample data to draw inferences about the population represented while accounting for randomness. These inferences may take the form of answering yes/no questions about the data (<a href="/wiki/Hypothesis_testing" class="mw-redirect" title="Hypothesis testing">hypothesis testing</a>), estimating numerical characteristics of the data (<a href="/wiki/Estimation_theory" title="Estimation theory">estimation</a>), describing <a href="/wiki/Association_(statistics)" class="mw-redirect" title="Association (statistics)">associations</a> within the data (<a href="/wiki/Correlation_and_dependence" class="mw-redirect" title="Correlation and dependence">correlation</a>), and modeling relationships within the data (for example, using <a href="/wiki/Regression_analysis" title="Regression analysis">regression analysis</a>). Inference can extend to the <a href="/wiki/Forecasting" title="Forecasting">forecasting</a>, <a href="/wiki/Prediction" title="Prediction">prediction</a>, and estimation of unobserved values either in or associated with the population being studied. It can include <a href="/wiki/Extrapolation" title="Extrapolation">extrapolation</a> and <a href="/wiki/Interpolation" title="Interpolation">interpolation</a> of <a href="/wiki/Time_series" title="Time series">time series</a> or <a href="/wiki/Spatial_statistics" title="Spatial statistics">spatial data</a>, as well as <a href="/wiki/Data_mining" title="Data mining">data mining</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Mathematical_statistics">Mathematical statistics</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Statistics&action=edit&section=2" title="Edit section: Mathematical statistics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Mathematical_statistics" title="Mathematical statistics">Mathematical statistics</a></div> <p>Mathematical statistics is the application of mathematics to statistics. Mathematical techniques used for this include <a href="/wiki/Mathematical_analysis" title="Mathematical analysis">mathematical analysis</a>, <a href="/wiki/Linear_algebra" title="Linear algebra">linear algebra</a>, <a href="/wiki/Stochastic_analysis" class="mw-redirect" title="Stochastic analysis">stochastic analysis</a>, <a href="/wiki/Differential_equations" class="mw-redirect" title="Differential equations">differential equations</a>, and <a href="/wiki/Measure-theoretic_probability_theory" class="mw-redirect" title="Measure-theoretic probability theory">measure-theoretic probability theory</a>.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="History">History</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Statistics&action=edit&section=3" title="Edit section: History"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main articles: <a href="/wiki/History_of_statistics" title="History of statistics">History of statistics</a> and <a href="/wiki/Founders_of_statistics" title="Founders of statistics">Founders of statistics</a></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Jakob_Bernoulli.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/19/Jakob_Bernoulli.jpg/220px-Jakob_Bernoulli.jpg" decoding="async" width="220" height="257" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/19/Jakob_Bernoulli.jpg/330px-Jakob_Bernoulli.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/19/Jakob_Bernoulli.jpg/440px-Jakob_Bernoulli.jpg 2x" data-file-width="2000" data-file-height="2338" /></a><figcaption>Bernoulli's <i><span title="Latin-language text"><span lang="la"><a href="/wiki/Ars_Conjectandi" title="Ars Conjectandi">Ars Conjectandi</a></span></span></i> was the first work that dealt with <a href="/wiki/Probability_theory" title="Probability theory">probability theory</a> as currently understood.</figcaption></figure> <p>Formal discussions on inference date back to the <a href="/wiki/Mathematics_in_medieval_Islam" class="mw-redirect" title="Mathematics in medieval Islam">mathematicians</a> and <a href="/wiki/Cryptographers" class="mw-redirect" title="Cryptographers">cryptographers</a> of the <a href="/wiki/Islamic_Golden_Age" title="Islamic Golden Age">Islamic Golden Age</a> between the 8th and 13th centuries. <a href="/wiki/Al-Khalil_ibn_Ahmad_al-Farahidi" title="Al-Khalil ibn Ahmad al-Farahidi">Al-Khalil</a> (717–786) wrote the <i>Book of Cryptographic Messages</i>, which contains one of the first uses of <a href="/wiki/Permutation" title="Permutation">permutations</a> and <a href="/wiki/Combination" title="Combination">combinations</a>, to list all possible Arabic words with and without vowels.<sup id="cite_ref-LB_11-0" class="reference"><a href="#cite_note-LB-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Al-Kindi" title="Al-Kindi">Al-Kindi</a>'s <i>Manuscript on Deciphering Cryptographic Messages</i> gave a detailed description of how to use <a href="/wiki/Frequency_analysis" title="Frequency analysis">frequency analysis</a> to decipher <a href="/wiki/Encrypted" class="mw-redirect" title="Encrypted">encrypted</a> messages, providing an early example of <a href="/wiki/Statistical_inference" title="Statistical inference">statistical inference</a> for <a href="/wiki/Code" title="Code">decoding</a>. <a href="/wiki/Ibn_Adlan" title="Ibn Adlan">Ibn Adlan</a> (1187–1268) later made an important contribution on the use of <a href="/wiki/Sample_size" class="mw-redirect" title="Sample size">sample size</a> in frequency analysis.<sup id="cite_ref-LB_11-1" class="reference"><a href="#cite_note-LB-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p><p>Although the term <i>statistic</i> was introduced by the Italian scholar <a href="/wiki/Girolamo_Ghilini" title="Girolamo Ghilini">Girolamo Ghilini</a> in 1589 with reference to a collection of facts and information about a state, it was the German <a href="/wiki/Gottfried_Achenwall" title="Gottfried Achenwall">Gottfried Achenwall</a> in 1749 who started using the term as a collection of quantitative information, in the modern use for this science.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> The earliest writing containing statistics in Europe dates back to 1663, with the publication of <i><a href="/wiki/Natural_and_Political_Observations_upon_the_Bills_of_Mortality" class="mw-redirect" title="Natural and Political Observations upon the Bills of Mortality">Natural and Political Observations upon the Bills of Mortality</a></i> by <a href="/wiki/John_Graunt" title="John Graunt">John Graunt</a>.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> Early applications of statistical thinking revolved around the needs of states to base policy on demographic and economic data, hence its <a href="/wiki/History_of_statistics#Etymology" title="History of statistics"><i>stat-</i> etymology</a>. The scope of the discipline of statistics broadened in the early 19th century to include the collection and analysis of data in general. Today, statistics is widely employed in government, business, and natural and social sciences. </p> <figure class="mw-default-size mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:Carl_Friedrich_Gauss_1840_by_Jensen.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ec/Carl_Friedrich_Gauss_1840_by_Jensen.jpg/220px-Carl_Friedrich_Gauss_1840_by_Jensen.jpg" decoding="async" width="220" height="280" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ec/Carl_Friedrich_Gauss_1840_by_Jensen.jpg/330px-Carl_Friedrich_Gauss_1840_by_Jensen.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ec/Carl_Friedrich_Gauss_1840_by_Jensen.jpg/440px-Carl_Friedrich_Gauss_1840_by_Jensen.jpg 2x" data-file-width="1639" data-file-height="2088" /></a><figcaption><a href="/wiki/Carl_Friedrich_Gauss" title="Carl Friedrich Gauss">Carl Friedrich Gauss</a> made major contributions to probabilistic methods leading to statistics.</figcaption></figure> <p>The mathematical foundations of statistics developed from discussions concerning <a href="/wiki/Game_of_chance" title="Game of chance">games of chance</a> among mathematicians such as <a href="/wiki/Gerolamo_Cardano" title="Gerolamo Cardano">Gerolamo Cardano</a>, <a href="/wiki/Blaise_Pascal" title="Blaise Pascal">Blaise Pascal</a>, <a href="/wiki/Pierre_de_Fermat" title="Pierre de Fermat">Pierre de Fermat</a>, and <a href="/wiki/Christiaan_Huygens" title="Christiaan Huygens">Christiaan Huygens</a>. Although the idea of probability was already examined in ancient and medieval law and philosophy (such as the work of <a href="/wiki/Juan_Caramuel" class="mw-redirect" title="Juan Caramuel">Juan Caramuel</a>), <a href="/wiki/Probability_theory" title="Probability theory">probability theory</a> as a mathematical discipline only took shape at the very end of the 17th century, particularly in <a href="/wiki/Jacob_Bernoulli" title="Jacob Bernoulli">Jacob Bernoulli</a>'s posthumous work <i><span title="Latin-language text"><span lang="la"><a href="/wiki/Ars_Conjectandi" title="Ars Conjectandi">Ars Conjectandi</a></span></span></i>.<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> This was the first book where the realm of games of chance and the realm of the probable (which concerned opinion, evidence, and argument) were combined and submitted to mathematical analysis.<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> The <a href="/wiki/Method_of_least_squares" class="mw-redirect" title="Method of least squares">method of least squares</a> was first described by <a href="/wiki/Adrien-Marie_Legendre" title="Adrien-Marie Legendre">Adrien-Marie Legendre</a> in 1805, though <a href="/wiki/Carl_Friedrich_Gauss" title="Carl Friedrich Gauss">Carl Friedrich Gauss</a> presumably made use of it a decade earlier in 1795.<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> </p> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Karl_Pearson,_1910.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/18/Karl_Pearson%2C_1910.jpg/220px-Karl_Pearson%2C_1910.jpg" decoding="async" width="220" height="160" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/18/Karl_Pearson%2C_1910.jpg/330px-Karl_Pearson%2C_1910.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/18/Karl_Pearson%2C_1910.jpg/440px-Karl_Pearson%2C_1910.jpg 2x" data-file-width="1177" data-file-height="856" /></a><figcaption><a href="/wiki/Karl_Pearson" title="Karl Pearson">Karl Pearson</a>, a founder of mathematical statistics</figcaption></figure> <p>The modern field of statistics emerged in the late 19th and early 20th century in three stages.<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> The first wave, at the turn of the century, was led by the work of <a href="/wiki/Francis_Galton" title="Francis Galton">Francis Galton</a> and <a href="/wiki/Karl_Pearson" title="Karl Pearson">Karl Pearson</a>, who transformed statistics into a rigorous mathematical discipline used for analysis, not just in science, but in industry and politics as well. Galton's contributions included introducing the concepts of <a href="/wiki/Standard_deviation" title="Standard deviation">standard deviation</a>, <a href="/wiki/Correlation" title="Correlation">correlation</a>, <a href="/wiki/Regression_analysis" title="Regression analysis">regression analysis</a> and the application of these methods to the study of the variety of human characteristics—height, weight and eyelash length among others.<sup id="cite_ref-Galton1877_19-0" class="reference"><a href="#cite_note-Galton1877-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> Pearson developed the <a href="/wiki/Pearson_product-moment_correlation_coefficient" class="mw-redirect" title="Pearson product-moment correlation coefficient">Pearson product-moment correlation coefficient</a>, defined as a product-moment,<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> the <a href="/wiki/Method_of_moments_(statistics)" title="Method of moments (statistics)">method of moments</a> for the fitting of distributions to samples and the <a href="/wiki/Pearson_distribution" title="Pearson distribution">Pearson distribution</a>, among many other things.<sup id="cite_ref-Pearson,_On_the_criterion_21-0" class="reference"><a href="#cite_note-Pearson,_On_the_criterion-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> Galton and Pearson founded <i><a href="/wiki/Biometrika" title="Biometrika">Biometrika</a></i> as the first journal of mathematical statistics and <a href="/wiki/Biostatistics" title="Biostatistics">biostatistics</a> (then called <i>biometry</i>), and the latter founded the world's first university statistics department at <a href="/wiki/University_College_London" title="University College London">University College London</a>.<sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> </p><p>The second wave of the 1910s and 20s was initiated by <a href="/wiki/William_Sealy_Gosset" title="William Sealy Gosset">William Sealy Gosset</a>, and reached its culmination in the insights of <a href="/wiki/Ronald_Fisher" title="Ronald Fisher">Ronald Fisher</a>, who wrote the textbooks that were to define the academic discipline in universities around the world. Fisher's most important publications were his 1918 seminal paper <i><a href="/wiki/The_Correlation_between_Relatives_on_the_Supposition_of_Mendelian_Inheritance" title="The Correlation between Relatives on the Supposition of Mendelian Inheritance">The Correlation between Relatives on the Supposition of Mendelian Inheritance</a></i> (which was the first to use the statistical term, <a href="/wiki/Variance" title="Variance">variance</a>), his classic 1925 work <i><a href="/wiki/Statistical_Methods_for_Research_Workers" title="Statistical Methods for Research Workers">Statistical Methods for Research Workers</a></i> and his 1935 <i><a href="/wiki/The_Design_of_Experiments" title="The Design of Experiments">The Design of Experiments</a></i>,<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> where he developed rigorous <a href="/wiki/Design_of_experiments" title="Design of experiments">design of experiments</a> models. He originated the concepts of <a href="/wiki/Sufficiency_(statistics)" class="mw-redirect" title="Sufficiency (statistics)">sufficiency</a>, <a href="/wiki/Ancillary_statistic" title="Ancillary statistic">ancillary statistics</a>, <a href="/wiki/Linear_discriminant_analysis" title="Linear discriminant analysis">Fisher's linear discriminator</a> and <a href="/wiki/Fisher_information" title="Fisher information">Fisher information</a>.<sup id="cite_ref-26" class="reference"><a href="#cite_note-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> He also coined the term <a href="/wiki/Null_hypothesis" title="Null hypothesis">null hypothesis</a> during the <a href="/wiki/Lady_tasting_tea" title="Lady tasting tea">Lady tasting tea</a> experiment, which "is never proved or established, but is possibly disproved, in the course of experimentation".<sup id="cite_ref-oed_27-0" class="reference"><a href="#cite_note-oed-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-28" class="reference"><a href="#cite_note-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> In his 1930 book <i><a href="/wiki/The_Genetical_Theory_of_Natural_Selection" title="The Genetical Theory of Natural Selection">The Genetical Theory of Natural Selection</a></i>, he applied statistics to various <a href="/wiki/Biology" title="Biology">biological</a> concepts such as <a href="/wiki/Fisher%27s_principle" title="Fisher's principle">Fisher's principle</a><sup id="cite_ref-Edwards98_29-0" class="reference"><a href="#cite_note-Edwards98-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup> (which <a href="/wiki/A._W._F._Edwards" title="A. W. F. Edwards">A. W. F. Edwards</a> called "probably the most celebrated argument in <a href="/wiki/Evolutionary_biology" title="Evolutionary biology">evolutionary biology</a>") and <a href="/wiki/Fisherian_runaway" title="Fisherian runaway">Fisherian runaway</a>,<sup id="cite_ref-fisher15_30-0" class="reference"><a href="#cite_note-fisher15-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-fisher30_31-0" class="reference"><a href="#cite_note-fisher30-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-pers00_32-0" class="reference"><a href="#cite_note-pers00-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-ander94_33-0" class="reference"><a href="#cite_note-ander94-33"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-ander06_34-0" class="reference"><a href="#cite_note-ander06-34"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-gayon10_35-0" class="reference"><a href="#cite_note-gayon10-35"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup> a concept in <a href="/wiki/Sexual_selection" title="Sexual selection">sexual selection</a> about a positive feedback runaway effect found in <a href="/wiki/Evolution" title="Evolution">evolution</a>. </p><p>The final wave, which mainly saw the refinement and expansion of earlier developments, emerged from the collaborative work between <a href="/wiki/Egon_Pearson" title="Egon Pearson">Egon Pearson</a> and <a href="/wiki/Jerzy_Neyman" title="Jerzy Neyman">Jerzy Neyman</a> in the 1930s. They introduced the concepts of "<a href="/wiki/Type_I_and_type_II_errors" title="Type I and type II errors">Type II</a>" error, <a href="/wiki/Power_of_a_test" class="mw-redirect" title="Power of a test">power of a test</a> and <a href="/wiki/Confidence_interval" title="Confidence interval">confidence intervals</a>. Jerzy Neyman in 1934 showed that stratified random sampling was in general a better method of estimation than purposive (quota) sampling.<sup id="cite_ref-36" class="reference"><a href="#cite_note-36"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup> </p><p>Today, statistical methods are applied in all fields that involve decision making, for making accurate inferences from a collated body of data and for making decisions in the face of uncertainty based on statistical methodology. The use of modern <a href="/wiki/Computer" title="Computer">computers</a> has expedited large-scale statistical computations and has also made possible new methods that are impractical to perform manually. Statistics continues to be an area of active research, for example on the problem of how to analyze <a href="/wiki/Big_data" title="Big data">big data</a>.<sup id="cite_ref-37" class="reference"><a href="#cite_note-37"><span class="cite-bracket">[</span>37<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Statistical_data">Statistical data</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Statistics&action=edit&section=4" title="Edit section: Statistical data"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Statistical_data" class="mw-redirect" title="Statistical data">Statistical data</a></div> <div class="mw-heading mw-heading3"><h3 id="Data_collection">Data collection</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Statistics&action=edit&section=5" title="Edit section: Data collection"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading4"><h4 id="Sampling">Sampling</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Statistics&action=edit&section=6" title="Edit section: Sampling"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>When full census data cannot be collected, statisticians collect sample data by developing specific <a href="/wiki/Design_of_experiments" title="Design of experiments">experiment designs</a> and <a href="/wiki/Survey_sampling" title="Survey sampling">survey samples</a>. Statistics itself also provides tools for prediction and forecasting through <a href="/wiki/Statistical_model" title="Statistical model">statistical models</a>. </p><p>To use a sample as a guide to an entire population, it is important that it truly represents the overall population. Representative <a href="/wiki/Sampling_(statistics)" title="Sampling (statistics)">sampling</a> assures that inferences and conclusions can safely extend from the sample to the population as a whole. A major problem lies in determining the extent that the sample chosen is actually representative. Statistics offers methods to estimate and correct for any bias within the sample and data collection procedures. There are also methods of experimental design that can lessen these issues at the outset of a study, strengthening its capability to discern truths about the population. </p><p>Sampling theory is part of the <a href="/wiki/Mathematics" title="Mathematics">mathematical discipline</a> of <a href="/wiki/Probability_theory" title="Probability theory">probability theory</a>. Probability is used in <a href="/wiki/Statistical_theory" title="Statistical theory">mathematical statistics</a> to study the <a href="/wiki/Sampling_distribution" title="Sampling distribution">sampling distributions</a> of <a href="/wiki/Sample_statistic" class="mw-redirect" title="Sample statistic">sample statistics</a> and, more generally, the properties of <a href="/wiki/Statistical_decision_theory" class="mw-redirect" title="Statistical decision theory">statistical procedures</a>. The use of any statistical method is valid when the system or population under consideration satisfies the assumptions of the method. The difference in point of view between classic probability theory and sampling theory is, roughly, that probability theory starts from the given parameters of a total population to <a href="/wiki/Deductive_reasoning" title="Deductive reasoning">deduce</a> probabilities that pertain to samples. Statistical inference, however, moves in the opposite direction—<a href="/wiki/Inductive_reasoning" title="Inductive reasoning">inductively inferring</a> from samples to the parameters of a larger or total population. </p> <div class="mw-heading mw-heading4"><h4 id="Experimental_and_observational_studies">Experimental and observational studies</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Statistics&action=edit&section=7" title="Edit section: Experimental and observational studies"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A common goal for a statistical research project is to investigate <a href="/wiki/Causality" title="Causality">causality</a>, and in particular to draw a conclusion on the effect of changes in the values of predictors or <a href="/wiki/Dependent_and_independent_variables" title="Dependent and independent variables">independent variables on dependent variables</a>. There are two major types of causal statistical studies: <a href="/wiki/Experiment" title="Experiment">experimental studies</a> and <a href="/wiki/Observational_study" title="Observational study">observational studies</a>. In both types of studies, the effect of differences of an independent variable (or variables) on the behavior of the dependent variable are observed. The difference between the two types lies in how the study is actually conducted. Each can be very effective. An experimental study involves taking measurements of the system under study, manipulating the system, and then taking additional <a href="/wiki/Level_of_measurement" title="Level of measurement">measurements with different levels</a> using the same procedure to determine if the manipulation has modified the values of the measurements. In contrast, an observational study does not involve <a href="/wiki/Scientific_control" title="Scientific control">experimental manipulation</a>. Instead, data are gathered and correlations between predictors and response are investigated. While the tools of data analysis work best on data from <a href="/wiki/Randomized_controlled_trial" title="Randomized controlled trial">randomized studies</a>, they are also applied to other kinds of data—like <a href="/wiki/Natural_experiment" title="Natural experiment">natural experiments</a> and <a href="/wiki/Observational_study" title="Observational study">observational studies</a><sup id="cite_ref-38" class="reference"><a href="#cite_note-38"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup>—for which a statistician would use a modified, more structured estimation method (e.g., <a href="/wiki/Difference_in_differences" title="Difference in differences">difference in differences estimation</a> and <a href="/wiki/Instrumental_variable" class="mw-redirect" title="Instrumental variable">instrumental variables</a>, among many others) that produce <a href="/wiki/Consistent_estimator" title="Consistent estimator">consistent estimators</a>. </p> <div class="mw-heading mw-heading5"><h5 id="Experiments">Experiments</h5><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Statistics&action=edit&section=8" title="Edit section: Experiments"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The basic steps of a statistical experiment are: </p> <ol><li>Planning the research, including finding the number of replicates of the study, using the following information: preliminary estimates regarding the size of <a href="/wiki/Average_treatment_effect" title="Average treatment effect">treatment effects</a>, <a href="/wiki/Alternative_hypothesis" title="Alternative hypothesis">alternative hypotheses</a>, and the estimated <a href="/wiki/Experimental_error" class="mw-redirect" title="Experimental error">experimental variability</a>. Consideration of the selection of experimental subjects and the ethics of research is necessary. Statisticians recommend that experiments compare (at least) one new treatment with a standard treatment or control, to allow an unbiased estimate of the difference in treatment effects.</li> <li><a href="/wiki/Design_of_experiments" title="Design of experiments">Design of experiments</a>, using <a href="/wiki/Blocking_(statistics)" title="Blocking (statistics)">blocking</a> to reduce the influence of <a href="/wiki/Confounding_variable" class="mw-redirect" title="Confounding variable">confounding variables</a>, and <a href="/wiki/Randomized_assignment" class="mw-redirect" title="Randomized assignment">randomized assignment</a> of treatments to subjects to allow <a href="/wiki/Bias_of_an_estimator" title="Bias of an estimator">unbiased estimates</a> of treatment effects and experimental error. At this stage, the experimenters and statisticians write the <i><a href="/wiki/Protocol_(natural_sciences)" class="mw-redirect" title="Protocol (natural sciences)">experimental protocol</a></i> that will guide the performance of the experiment and which specifies the<i> primary analysis</i> of the experimental data.</li> <li>Performing the experiment following the <a href="/wiki/Protocol_(natural_sciences)" class="mw-redirect" title="Protocol (natural sciences)">experimental protocol</a> and <a href="/wiki/Analysis_of_variance" title="Analysis of variance">analyzing the data</a> following the experimental protocol.</li> <li>Further examining the data set in secondary analyses, to suggest new hypotheses for future study.</li> <li>Documenting and presenting the results of the study.</li></ol> <p>Experiments on human behavior have special concerns. The famous <a href="/wiki/Hawthorne_study" class="mw-redirect" title="Hawthorne study">Hawthorne study</a> examined changes to the working environment at the Hawthorne plant of the <a href="/wiki/Western_Electric_Company" class="mw-redirect" title="Western Electric Company">Western Electric Company</a>. The researchers were interested in determining whether increased illumination would increase the productivity of the <a href="/wiki/Assembly_line" title="Assembly line">assembly line</a> workers. The researchers first measured the productivity in the plant, then modified the illumination in an area of the plant and checked if the changes in illumination affected productivity. It turned out that productivity indeed improved (under the experimental conditions). However, the study is heavily criticized today for errors in experimental procedures, specifically for the lack of a <a href="/wiki/Control_group" class="mw-redirect" title="Control group">control group</a> and <a href="/wiki/Double-blind" class="mw-redirect" title="Double-blind">blindness</a>. The <a href="/wiki/Hawthorne_effect" title="Hawthorne effect">Hawthorne effect</a> refers to finding that an outcome (in this case, worker productivity) changed due to observation itself. Those in the Hawthorne study became more productive not because the lighting was changed but because they were being observed.<sup id="cite_ref-pmid17608932_39-0" class="reference"><a href="#cite_note-pmid17608932-39"><span class="cite-bracket">[</span>39<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading5"><h5 id="Observational_study">Observational study</h5><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Statistics&action=edit&section=9" title="Edit section: Observational study"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>An example of an observational study is one that explores the association between smoking and lung cancer. This type of study typically uses a survey to collect observations about the area of interest and then performs statistical analysis. In this case, the researchers would collect observations of both smokers and non-smokers, perhaps through a <a href="/wiki/Cohort_study" title="Cohort study">cohort study</a>, and then look for the number of cases of lung cancer in each group.<sup id="cite_ref-40" class="reference"><a href="#cite_note-40"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup> A <a href="/wiki/Case-control_study" class="mw-redirect" title="Case-control study">case-control study</a> is another type of observational study in which people with and without the outcome of interest (e.g. lung cancer) are invited to participate and their exposure histories are collected. </p> <div class="mw-heading mw-heading3"><h3 id="Types_of_data">Types of data</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Statistics&action=edit&section=10" title="Edit section: Types of data"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main articles: <a href="/wiki/Statistical_data_type" title="Statistical data type">Statistical data type</a> and <a href="/wiki/Levels_of_measurement" class="mw-redirect" title="Levels of measurement">Levels of measurement</a></div> <p>Various attempts have been made to produce a taxonomy of <a href="/wiki/Level_of_measurement" title="Level of measurement">levels of measurement</a>. The psychophysicist <a href="/wiki/Stanley_Smith_Stevens" title="Stanley Smith Stevens">Stanley Smith Stevens</a> defined nominal, ordinal, interval, and ratio scales. Nominal measurements do not have meaningful rank order among values, and permit any one-to-one (injective) transformation. Ordinal measurements have imprecise differences between consecutive values, but have a meaningful order to those values, and permit any order-preserving transformation. Interval measurements have meaningful distances between measurements defined, but the zero value is arbitrary (as in the case with <a href="/wiki/Longitude" title="Longitude">longitude</a> and <a href="/wiki/Temperature" title="Temperature">temperature</a> measurements in <a href="/wiki/Celsius" title="Celsius">Celsius</a> or <a href="/wiki/Fahrenheit" title="Fahrenheit">Fahrenheit</a>), and permit any linear transformation. Ratio measurements have both a meaningful zero value and the distances between different measurements defined, and permit any rescaling transformation. </p><p>Because variables conforming only to nominal or ordinal measurements cannot be reasonably measured numerically, sometimes they are grouped together as <a href="/wiki/Categorical_variable" title="Categorical variable">categorical variables</a>, whereas ratio and interval measurements are grouped together as <a href="/wiki/Variable_(mathematics)#Applied_statistics" title="Variable (mathematics)">quantitative variables</a>, which can be either <a href="/wiki/Probability_distribution#Discrete_probability_distribution" title="Probability distribution">discrete</a> or <a href="/wiki/Probability_distribution#Continuous_probability_distribution" title="Probability distribution">continuous</a>, due to their numerical nature. Such distinctions can often be loosely correlated with <a href="/wiki/Data_type" title="Data type">data type</a> in computer science, in that dichotomous categorical variables may be represented with the <a href="/wiki/Boolean_data_type" title="Boolean data type">Boolean data type</a>, polytomous categorical variables with arbitrarily assigned <a href="/wiki/Integer" title="Integer">integers</a> in the <a href="/wiki/Integer_(computer_science)" title="Integer (computer science)">integral data type</a>, and continuous variables with the <a href="/wiki/Real_data_type" title="Real data type">real data type</a> involving <a href="/wiki/Floating-point_arithmetic" title="Floating-point arithmetic">floating-point arithmetic</a>. But the mapping of computer science data types to statistical data types depends on which categorization of the latter is being implemented. </p><p>Other categorizations have been proposed. For example, Mosteller and Tukey (1977)<sup id="cite_ref-41" class="reference"><a href="#cite_note-41"><span class="cite-bracket">[</span>41<span class="cite-bracket">]</span></a></sup> distinguished grades, ranks, counted fractions, counts, amounts, and balances. Nelder (1990)<sup id="cite_ref-42" class="reference"><a href="#cite_note-42"><span class="cite-bracket">[</span>42<span class="cite-bracket">]</span></a></sup> described continuous counts, continuous ratios, count ratios, and categorical modes of data. (See also: Chrisman (1998),<sup id="cite_ref-43" class="reference"><a href="#cite_note-43"><span class="cite-bracket">[</span>43<span class="cite-bracket">]</span></a></sup> van den Berg (1991).<sup id="cite_ref-44" class="reference"><a href="#cite_note-44"><span class="cite-bracket">[</span>44<span class="cite-bracket">]</span></a></sup>) </p><p>The issue of whether or not it is appropriate to apply different kinds of statistical methods to data obtained from different kinds of measurement procedures is complicated by issues concerning the transformation of variables and the precise interpretation of research questions. "The relationship between the data and what they describe merely reflects the fact that certain kinds of statistical statements may have truth values which are not invariant under some transformations. Whether or not a transformation is sensible to contemplate depends on the question one is trying to answer."<sup id="cite_ref-45" class="reference"><a href="#cite_note-45"><span class="cite-bracket">[</span>45<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 82">: 82 </span></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Methods">Methods</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Statistics&action=edit&section=11" title="Edit section: Methods"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1251242444">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}</style><table class="box-More_citations_needed_section plainlinks metadata ambox ambox-content ambox-Refimprove" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><a href="/wiki/File:Question_book-new.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">This section <b>needs additional citations for <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">verification</a></b>.<span class="hide-when-compact"> Please help <a href="/wiki/Special:EditPage/Statistics" title="Special:EditPage/Statistics">improve this article</a> by <a href="/wiki/Help:Referencing_for_beginners" title="Help:Referencing for beginners">adding citations to reliable sources</a> in this section. Unsourced material may be challenged and removed.</span> <span class="date-container"><i>(<span class="date">December 2020</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="Descriptive_statistics">Descriptive statistics</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Statistics&action=edit&section=12" title="Edit section: Descriptive statistics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Descriptive_statistics" title="Descriptive statistics">Descriptive statistics</a></div> <p>A <b>descriptive statistic</b> (in the <a href="/wiki/Count_noun" title="Count noun">count noun</a> sense) is a <a href="/wiki/Summary_statistic" class="mw-redirect" title="Summary statistic">summary statistic</a> that quantitatively describes or summarizes features of a collection of <a href="/wiki/Information" title="Information">information</a>,<sup id="cite_ref-46" class="reference"><a href="#cite_note-46"><span class="cite-bracket">[</span>46<span class="cite-bracket">]</span></a></sup> while <b>descriptive statistics</b> in the <a href="/wiki/Mass_noun" title="Mass noun">mass noun</a> sense is the process of using and analyzing those statistics. Descriptive statistics is distinguished from <a href="/wiki/Statistical_inference" title="Statistical inference">inferential statistics</a> (or inductive statistics), in that descriptive statistics aims to summarize a <a href="/wiki/Sample_(statistics)" class="mw-redirect" title="Sample (statistics)">sample</a>, rather than use the data to learn about the <a href="/wiki/Statistical_population" title="Statistical population">population</a> that the sample of data is thought to represent.<sup id="cite_ref-47" class="reference"><a href="#cite_note-47"><span class="cite-bracket">[</span>47<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Inferential_statistics">Inferential statistics</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Statistics&action=edit&section=13" title="Edit section: Inferential statistics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Statistical_inference" title="Statistical inference">Statistical inference</a></div> <p><b>Statistical inference</b> is the process of using <a href="/wiki/Data_analysis" title="Data analysis">data analysis</a> to deduce properties of an underlying <a href="/wiki/Probability_distribution" title="Probability distribution">probability distribution</a>.<sup id="cite_ref-Oxford_48-0" class="reference"><a href="#cite_note-Oxford-48"><span class="cite-bracket">[</span>48<span class="cite-bracket">]</span></a></sup> Inferential statistical analysis infers properties of a <a href="/wiki/Statistical_population" title="Statistical population">population</a>, for example by testing hypotheses and deriving estimates. It is assumed that the observed data set is <a href="/wiki/Sampling_(statistics)" title="Sampling (statistics)">sampled</a> from a larger population. Inferential statistics can be contrasted with <a href="/wiki/Descriptive_statistics" title="Descriptive statistics">descriptive statistics</a>. Descriptive statistics is solely concerned with properties of the observed data, and it does not rest on the assumption that the data come from a larger population.<sup id="cite_ref-49" class="reference"><a href="#cite_note-49"><span class="cite-bracket">[</span>49<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Terminology_and_theory_of_inferential_statistics">Terminology and theory of inferential statistics</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Statistics&action=edit&section=14" title="Edit section: Terminology and theory of inferential statistics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading5"><h5 id="Statistics,_estimators_and_pivotal_quantities"><span id="Statistics.2C_estimators_and_pivotal_quantities"></span>Statistics, estimators and pivotal quantities</h5><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Statistics&action=edit&section=15" title="Edit section: Statistics, estimators and pivotal quantities"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Consider <a href="/wiki/Independent_identically_distributed" class="mw-redirect" title="Independent identically distributed">independent identically distributed (IID) random variables</a> with a given <a href="/wiki/Probability_distribution" title="Probability distribution">probability distribution</a>: standard <a href="/wiki/Statistical_inference" title="Statistical inference">statistical inference</a> and <a href="/wiki/Estimation_theory" title="Estimation theory">estimation theory</a> defines a <a href="/wiki/Random_sample" class="mw-redirect" title="Random sample">random sample</a> as the <a href="/wiki/Random_vector" class="mw-redirect" title="Random vector">random vector</a> given by the <a href="/wiki/Column_vector" class="mw-redirect" title="Column vector">column vector</a> of these IID variables.<sup id="cite_ref-Piazza_50-0" class="reference"><a href="#cite_note-Piazza-50"><span class="cite-bracket">[</span>50<span class="cite-bracket">]</span></a></sup> The <a href="/wiki/Statistical_population" title="Statistical population">population</a> being examined is described by a probability distribution that may have unknown parameters. </p><p>A statistic is a random variable that is a function of the random sample, but <em>not a function of unknown parameters</em>. The probability distribution of the statistic, though, may have unknown parameters. Consider now a function of the unknown parameter: an <a href="/wiki/Estimator" title="Estimator">estimator</a> is a statistic used to estimate such function. Commonly used estimators include <a href="/wiki/Sample_mean" class="mw-redirect" title="Sample mean">sample mean</a>, unbiased <a href="/wiki/Sample_variance" class="mw-redirect" title="Sample variance">sample variance</a> and <a href="/wiki/Sample_covariance" class="mw-redirect" title="Sample covariance">sample covariance</a>. </p><p>A random variable that is a function of the random sample and of the unknown parameter, but whose probability distribution <i>does not depend on the unknown parameter</i> is called a <a href="/wiki/Pivotal_quantity" title="Pivotal quantity">pivotal quantity</a> or pivot. Widely used pivots include the <a href="/wiki/Z-score" class="mw-redirect" title="Z-score">z-score</a>, the <a href="/wiki/Chi-squared_distribution#Applications" title="Chi-squared distribution">chi square statistic</a> and Student's <a href="/wiki/Student%27s_t-distribution#How_the_t-distribution_arises" title="Student's t-distribution">t-value</a>. </p><p>Between two estimators of a given parameter, the one with lower <a href="/wiki/Mean_squared_error" title="Mean squared error">mean squared error</a> is said to be more <a href="/wiki/Efficient_estimator" class="mw-redirect" title="Efficient estimator">efficient</a>. Furthermore, an estimator is said to be <a href="/wiki/Unbiased_estimator" class="mw-redirect" title="Unbiased estimator">unbiased</a> if its <a href="/wiki/Expected_value" title="Expected value">expected value</a> is equal to the <a href="/wiki/True_value" class="mw-redirect" title="True value">true value</a> of the unknown parameter being estimated, and asymptotically unbiased if its expected value converges at the <a href="/wiki/Limit_(mathematics)" title="Limit (mathematics)">limit</a> to the true value of such parameter. </p><p>Other desirable properties for estimators include: <a href="/wiki/UMVUE" class="mw-redirect" title="UMVUE">UMVUE</a> estimators that have the lowest variance for all possible values of the parameter to be estimated (this is usually an easier property to verify than efficiency) and <a href="/wiki/Consistent_estimator" title="Consistent estimator">consistent estimators</a> which <a href="/wiki/Converges_in_probability" class="mw-redirect" title="Converges in probability">converges in probability</a> to the true value of such parameter. </p><p>This still leaves the question of how to obtain estimators in a given situation and carry the computation, several methods have been proposed: the <a href="/wiki/Method_of_moments_(statistics)" title="Method of moments (statistics)">method of moments</a>, the <a href="/wiki/Maximum_likelihood" class="mw-redirect" title="Maximum likelihood">maximum likelihood</a> method, the <a href="/wiki/Least_squares" title="Least squares">least squares</a> method and the more recent method of <a href="/wiki/Estimating_equations" title="Estimating equations">estimating equations</a>. </p> <div class="mw-heading mw-heading5"><h5 id="Null_hypothesis_and_alternative_hypothesis">Null hypothesis and alternative hypothesis</h5><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Statistics&action=edit&section=16" title="Edit section: Null hypothesis and alternative hypothesis"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Interpretation of statistical information can often involve the development of a <a href="/wiki/Null_hypothesis" title="Null hypothesis">null hypothesis</a> which is usually (but not necessarily) that no relationship exists among variables or that no change occurred over time.<sup id="cite_ref-51" class="reference"><a href="#cite_note-51"><span class="cite-bracket">[</span>51<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-52" class="reference"><a href="#cite_note-52"><span class="cite-bracket">[</span>52<span class="cite-bracket">]</span></a></sup> </p><p>The best illustration for a novice is the predicament encountered by a criminal trial. The null hypothesis, H<sub>0</sub>, asserts that the defendant is innocent, whereas the alternative hypothesis, H<sub>1</sub>, asserts that the defendant is guilty. The indictment comes because of suspicion of the guilt. The H<sub>0</sub> (status quo) stands in opposition to H<sub>1</sub> and is maintained unless H<sub>1</sub> is supported by evidence "beyond a reasonable doubt". However, "failure to reject H<sub>0</sub>" in this case does not imply innocence, but merely that the evidence was insufficient to convict. So the jury does not necessarily <i>accept</i> H<sub>0</sub> but <i>fails to reject</i> H<sub>0</sub>. While one can not "prove" a null hypothesis, one can test how close it is to being true with a <a href="/wiki/Statistical_power" class="mw-redirect" title="Statistical power">power test</a>, which tests for <a href="/wiki/Type_II_error" class="mw-redirect" title="Type II error">type II errors</a>. </p><p>What <a href="/wiki/Statisticians" class="mw-redirect" title="Statisticians">statisticians</a> call an <a href="/wiki/Alternative_hypothesis" title="Alternative hypothesis">alternative hypothesis</a> is simply a hypothesis that contradicts the null hypothesis. </p> <div class="mw-heading mw-heading5"><h5 id="Error">Error</h5><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Statistics&action=edit&section=17" title="Edit section: Error"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Working from a <a href="/wiki/Null_hypothesis" title="Null hypothesis">null hypothesis</a>, two broad categories of error are recognized: </p> <ul><li><a href="/wiki/Type_I_and_type_II_errors#Type_I_error" title="Type I and type II errors">Type I errors</a> where the null hypothesis is falsely rejected, giving a "false positive".</li> <li><a href="/wiki/Type_I_and_type_II_errors#Type_II_error" title="Type I and type II errors">Type II errors</a> where the null hypothesis fails to be rejected and an actual difference between populations is missed, giving a "false negative".</li></ul> <p><a href="/wiki/Standard_deviation" title="Standard deviation">Standard deviation</a> refers to the extent to which individual observations in a sample differ from a central value, such as the sample or population mean, while <a href="/wiki/Standard_error_(statistics)#Standard_error_of_the_mean" class="mw-redirect" title="Standard error (statistics)">Standard error</a> refers to an estimate of difference between sample mean and population mean. </p><p>A <a href="/wiki/Errors_and_residuals_in_statistics#Introduction" class="mw-redirect" title="Errors and residuals in statistics">statistical error</a> is the amount by which an observation differs from its <a href="/wiki/Expected_value" title="Expected value">expected value</a>. A <a href="/wiki/Errors_and_residuals_in_statistics#Introduction" class="mw-redirect" title="Errors and residuals in statistics">residual</a> is the amount an observation differs from the value the estimator of the expected value assumes on a given sample (also called prediction). </p><p><a href="/wiki/Mean_squared_error" title="Mean squared error">Mean squared error</a> is used for obtaining <a href="/wiki/Efficient_estimators" class="mw-redirect" title="Efficient estimators">efficient estimators</a>, a widely used class of estimators. <a href="/wiki/Root_mean_square_error" class="mw-redirect" title="Root mean square error">Root mean square error</a> is simply the square root of mean squared error. </p> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Linear_least_squares(2).svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/75/Linear_least_squares%282%29.svg/220px-Linear_least_squares%282%29.svg.png" decoding="async" width="220" height="199" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/75/Linear_least_squares%282%29.svg/330px-Linear_least_squares%282%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/75/Linear_least_squares%282%29.svg/440px-Linear_least_squares%282%29.svg.png 2x" data-file-width="502" data-file-height="454" /></a><figcaption>A least squares fit: in red the points to be fitted, in blue the fitted line.</figcaption></figure> <p>Many statistical methods seek to minimize the <a href="/wiki/Residual_sum_of_squares" title="Residual sum of squares">residual sum of squares</a>, and these are called "<a href="/wiki/Least_squares" title="Least squares">methods of least squares</a>" in contrast to <a href="/wiki/Least_absolute_deviations" title="Least absolute deviations">Least absolute deviations</a>. The latter gives equal weight to small and big errors, while the former gives more weight to large errors. Residual sum of squares is also <a href="/wiki/Differentiable_function" title="Differentiable function">differentiable</a>, which provides a handy property for doing <a href="/wiki/Regression_analysis" title="Regression analysis">regression</a>. Least squares applied to <a href="/wiki/Linear_regression" title="Linear regression">linear regression</a> is called <a href="/wiki/Ordinary_least_squares" title="Ordinary least squares">ordinary least squares</a> method and least squares applied to <a href="/wiki/Nonlinear_regression" title="Nonlinear regression">nonlinear regression</a> is called <a href="/wiki/Non-linear_least_squares" title="Non-linear least squares">non-linear least squares</a>. Also in a linear regression model the non deterministic part of the model is called error term, disturbance or more simply noise. Both linear regression and non-linear regression are addressed in <a href="/wiki/Polynomial_least_squares" class="mw-redirect" title="Polynomial least squares">polynomial least squares</a>, which also describes the variance in a prediction of the dependent variable (y axis) as a function of the independent variable (x axis) and the deviations (errors, noise, disturbances) from the estimated (fitted) curve. </p><p>Measurement processes that generate statistical data are also subject to error. Many of these errors are classified as <a href="/wiki/Random_error" class="mw-redirect" title="Random error">random</a> (noise) or <a href="/wiki/Systematic_error" class="mw-redirect" title="Systematic error">systematic</a> (<a href="/wiki/Bias" title="Bias">bias</a>), but other types of errors (e.g., blunder, such as when an analyst reports incorrect units) can also be important. The presence of <a href="/wiki/Missing_data" title="Missing data">missing data</a> or <a href="/wiki/Censoring_(statistics)" title="Censoring (statistics)">censoring</a> may result in <a href="/wiki/Bias_(statistics)" title="Bias (statistics)">biased estimates</a> and specific techniques have been developed to address these problems.<sup id="cite_ref-53" class="reference"><a href="#cite_note-53"><span class="cite-bracket">[</span>53<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading5"><h5 id="Interval_estimation">Interval estimation</h5><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Statistics&action=edit&section=18" title="Edit section: Interval estimation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Interval_estimation" title="Interval estimation">Interval estimation</a></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:NYW-confidence-interval.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8f/NYW-confidence-interval.svg/220px-NYW-confidence-interval.svg.png" decoding="async" width="220" height="90" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8f/NYW-confidence-interval.svg/330px-NYW-confidence-interval.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8f/NYW-confidence-interval.svg/440px-NYW-confidence-interval.svg.png 2x" data-file-width="222" data-file-height="91" /></a><figcaption><a href="/wiki/Confidence_intervals" class="mw-redirect" title="Confidence intervals">Confidence intervals</a>: the red line is true value for the mean in this example, the blue lines are random confidence intervals for 100 realizations.</figcaption></figure> <p>Most studies only sample part of a population, so results do not fully represent the whole population. Any estimates obtained from the sample only approximate the population value. <a href="/wiki/Confidence_intervals" class="mw-redirect" title="Confidence intervals">Confidence intervals</a> allow statisticians to express how closely the sample estimate matches the true value in the whole population. Often they are expressed as 95% confidence intervals. Formally, a 95% confidence interval for a value is a range where, if the sampling and analysis were repeated under the same conditions (yielding a different dataset), the interval would include the true (population) value in 95% of all possible cases. This does <i>not</i> imply that the probability that the true value is in the confidence interval is 95%. From the <a href="/wiki/Frequentist_inference" title="Frequentist inference">frequentist</a> perspective, such a claim does not even make sense, as the true value is not a <a href="/wiki/Random_variable" title="Random variable">random variable</a>. Either the true value is or is not within the given interval. However, it is true that, before any data are sampled and given a plan for how to construct the confidence interval, the probability is 95% that the yet-to-be-calculated interval will cover the true value: at this point, the limits of the interval are yet-to-be-observed <a href="/wiki/Random_variable" title="Random variable">random variables</a>. One approach that does yield an interval that can be interpreted as having a given probability of containing the true value is to use a <a href="/wiki/Credible_interval" title="Credible interval">credible interval</a> from <a href="/wiki/Bayesian_statistics" title="Bayesian statistics">Bayesian statistics</a>: this approach depends on a different way of <a href="/wiki/Probability_interpretations" title="Probability interpretations">interpreting what is meant by "probability"</a>, that is as a <a href="/wiki/Bayesian_probability" title="Bayesian probability">Bayesian probability</a>. </p><p>In principle confidence intervals can be symmetrical or asymmetrical. An interval can be asymmetrical because it works as lower or upper bound for a parameter (left-sided interval or right sided interval), but it can also be asymmetrical because the two sided interval is built violating symmetry around the estimate. Sometimes the bounds for a confidence interval are reached asymptotically and these are used to approximate the true bounds. </p> <div class="mw-heading mw-heading5"><h5 id="Significance">Significance</h5><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Statistics&action=edit&section=19" title="Edit section: Significance"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Statistical_significance" title="Statistical significance">Statistical significance</a></div> <p>Statistics rarely give a simple Yes/No type answer to the question under analysis. Interpretation often comes down to the level of statistical significance applied to the numbers and often refers to the probability of a value accurately rejecting the null hypothesis (sometimes referred to as the <a href="/wiki/P-value" title="P-value">p-value</a>). </p> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:P-value_in_statistical_significance_testing.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3a/P-value_in_statistical_significance_testing.svg/400px-P-value_in_statistical_significance_testing.svg.png" decoding="async" width="400" height="405" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3a/P-value_in_statistical_significance_testing.svg/600px-P-value_in_statistical_significance_testing.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3a/P-value_in_statistical_significance_testing.svg/800px-P-value_in_statistical_significance_testing.svg.png 2x" data-file-width="1224" data-file-height="1239" /></a><figcaption>In this graph the black line is probability distribution for the <a href="/wiki/Test_statistic" title="Test statistic">test statistic</a>, the <a href="/wiki/Critical_region#Definition_of_terms" class="mw-redirect" title="Critical region">critical region</a> is the set of values to the right of the observed data point (observed value of the test statistic) and the <a href="/wiki/P-value" title="P-value">p-value</a> is represented by the green area.</figcaption></figure> <p>The standard approach<sup id="cite_ref-Piazza_50-1" class="reference"><a href="#cite_note-Piazza-50"><span class="cite-bracket">[</span>50<span class="cite-bracket">]</span></a></sup> is to test a null hypothesis against an alternative hypothesis. A <a href="/wiki/Critical_region#Definition_of_terms" class="mw-redirect" title="Critical region">critical region</a> is the set of values of the estimator that leads to refuting the null hypothesis. The probability of type I error is therefore the probability that the estimator belongs to the critical region given that null hypothesis is true (<a href="/wiki/Statistical_significance" title="Statistical significance">statistical significance</a>) and the probability of type II error is the probability that the estimator does not belong to the critical region given that the alternative hypothesis is true. The <a href="/wiki/Statistical_power" class="mw-redirect" title="Statistical power">statistical power</a> of a test is the probability that it correctly rejects the null hypothesis when the null hypothesis is false. </p><p>Referring to statistical significance does not necessarily mean that the overall result is significant in real world terms. For example, in a large study of a drug it may be shown that the drug has a statistically significant but very small beneficial effect, such that the drug is unlikely to help the patient noticeably. </p><p>Although in principle the acceptable level of statistical significance may be subject to debate, the <a href="/wiki/Significance_level" class="mw-redirect" title="Significance level">significance level</a> is the largest p-value that allows the test to reject the null hypothesis. This test is logically equivalent to saying that the p-value is the probability, assuming the null hypothesis is true, of observing a result at least as extreme as the <a href="/wiki/Test_statistic" title="Test statistic">test statistic</a>. Therefore, the smaller the significance level, the lower the probability of committing type I error. </p><p>Some problems are usually associated with this framework (See <a href="/wiki/Statistical_hypothesis_testing#Criticism" class="mw-redirect" title="Statistical hypothesis testing">criticism of hypothesis testing</a>): </p> <ul><li>A difference that is highly statistically significant can still be of no practical significance, but it is possible to properly formulate tests to account for this. One response involves going beyond reporting only the <a href="/wiki/Significance_level" class="mw-redirect" title="Significance level">significance level</a> to include the <a href="/wiki/P-value" title="P-value"><i>p</i>-value</a> when reporting whether a hypothesis is rejected or accepted. The p-value, however, does not indicate the <a href="/wiki/Effect_size" title="Effect size">size</a> or importance of the observed effect and can also seem to exaggerate the importance of minor differences in large studies. A better and increasingly common approach is to report <a href="/wiki/Confidence_interval" title="Confidence interval">confidence intervals</a>. Although these are produced from the same calculations as those of hypothesis tests or <i>p</i>-values, they describe both the size of the effect and the uncertainty surrounding it.</li> <li>Fallacy of the transposed conditional, aka <a href="/wiki/Prosecutor%27s_fallacy" class="mw-redirect" title="Prosecutor's fallacy">prosecutor's fallacy</a>: criticisms arise because the hypothesis testing approach forces one hypothesis (the <a href="/wiki/Null_hypothesis" title="Null hypothesis">null hypothesis</a>) to be favored, since what is being evaluated is the probability of the observed result given the null hypothesis and not probability of the null hypothesis given the observed result. An alternative to this approach is offered by <a href="/wiki/Bayesian_inference" title="Bayesian inference">Bayesian inference</a>, although it requires establishing a <a href="/wiki/Prior_probability" title="Prior probability">prior probability</a>.<sup id="cite_ref-Ioannidis2005_54-0" class="reference"><a href="#cite_note-Ioannidis2005-54"><span class="cite-bracket">[</span>54<span class="cite-bracket">]</span></a></sup></li> <li>Rejecting the null hypothesis does not automatically prove the alternative hypothesis.</li> <li>As everything in <a href="/wiki/Inferential_statistics" class="mw-redirect" title="Inferential statistics">inferential statistics</a> it relies on sample size, and therefore under <a href="/wiki/Fat_tails" class="mw-redirect" title="Fat tails">fat tails</a> p-values may be seriously mis-computed.<sup class="noprint Inline-Template" style="margin-left:0.1em; white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Please_clarify" title="Wikipedia:Please clarify"><span title="The text near this tag may need clarification or removal of jargon. (October 2016)">clarification needed</span></a></i>]</sup></li></ul> <div class="mw-heading mw-heading5"><h5 id="Examples">Examples</h5><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Statistics&action=edit&section=20" title="Edit section: Examples"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Some well-known statistical <a href="/wiki/Statistical_hypothesis_testing" class="mw-redirect" title="Statistical hypothesis testing">tests</a> and procedures are: </p> <style data-mw-deduplicate="TemplateStyles:r1184024115">.mw-parser-output .div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}</style><div class="div-col" style="column-width: 22em;"> <ul><li><a href="/wiki/Analysis_of_variance" title="Analysis of variance">Analysis of variance</a> (ANOVA)</li> <li><a href="/wiki/Chi-squared_test" title="Chi-squared test">Chi-squared test</a></li> <li><a href="/wiki/Correlation" title="Correlation">Correlation</a></li> <li><a href="/wiki/Factor_analysis" title="Factor analysis">Factor analysis</a></li> <li><a href="/wiki/Mann%E2%80%93Whitney_(U)" class="mw-redirect" title="Mann–Whitney (U)">Mann–Whitney <i>U</i></a></li> <li><a href="/wiki/Mean_square_weighted_deviation" class="mw-redirect" title="Mean square weighted deviation">Mean square weighted deviation</a> (MSWD)</li> <li><a href="/wiki/Pearson_product-moment_correlation_coefficient" class="mw-redirect" title="Pearson product-moment correlation coefficient">Pearson product-moment correlation coefficient</a></li> <li><a href="/wiki/Regression_analysis" title="Regression analysis">Regression analysis</a></li> <li><a href="/wiki/Spearman%27s_rank_correlation_coefficient" title="Spearman's rank correlation coefficient">Spearman's rank correlation coefficient</a></li> <li><a href="/wiki/Student%27s_t-test" title="Student's t-test">Student's <i>t</i>-test</a></li> <li><a href="/wiki/Time_series_analysis" class="mw-redirect" title="Time series analysis">Time series analysis</a></li> <li><a href="/wiki/Conjoint_Analysis" class="mw-redirect" title="Conjoint Analysis">Conjoint Analysis</a></li></ul></div> <div class="mw-heading mw-heading3"><h3 id="Exploratory_data_analysis">Exploratory data analysis</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Statistics&action=edit&section=21" title="Edit section: Exploratory data analysis"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Exploratory_data_analysis" title="Exploratory data analysis">Exploratory data analysis</a></div> <p><b>Exploratory data analysis</b> (<b>EDA</b>) is an approach to <a href="/wiki/Data_analysis" title="Data analysis">analyzing</a> <a href="/wiki/Data_set" title="Data set">data sets</a> to summarize their main characteristics, often with visual methods. A <a href="/wiki/Statistical_model" title="Statistical model">statistical model</a> can be used or not, but primarily EDA is for seeing what the data can tell us beyond the formal modeling or hypothesis testing task. </p> <div class="mw-heading mw-heading2"><h2 id="Misuse">Misuse</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Statistics&action=edit&section=22" title="Edit section: Misuse"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Misuse_of_statistics" title="Misuse of statistics">Misuse of statistics</a></div> <p><a href="/wiki/Misuse_of_statistics" title="Misuse of statistics">Misuse of statistics</a> can produce subtle but serious errors in description and interpretation—subtle in the sense that even experienced professionals make such errors, and serious in the sense that they can lead to devastating decision errors. For instance, social policy, medical practice, and the reliability of structures like bridges all rely on the proper use of statistics. </p><p>Even when statistical techniques are correctly applied, the results can be difficult to interpret for those lacking expertise. The <a href="/wiki/Statistical_significance" title="Statistical significance">statistical significance</a> of a trend in the data—which measures the extent to which a trend could be caused by random variation in the sample—may or may not agree with an intuitive sense of its significance. The set of basic statistical skills (and skepticism) that people need to deal with information in their everyday lives properly is referred to as <a href="/wiki/Statistical_literacy" title="Statistical literacy">statistical literacy</a>. </p><p>There is a general perception that statistical knowledge is all-too-frequently intentionally <a href="/wiki/Misuse_of_statistics" title="Misuse of statistics">misused</a> by finding ways to interpret only the data that are favorable to the presenter.<sup id="cite_ref-Huff_55-0" class="reference"><a href="#cite_note-Huff-55"><span class="cite-bracket">[</span>55<span class="cite-bracket">]</span></a></sup> A mistrust and misunderstanding of statistics is associated with the quotation, "<a href="/wiki/Lies,_damned_lies,_and_statistics" title="Lies, damned lies, and statistics">There are three kinds of lies: lies, damned lies, and statistics</a>". Misuse of statistics can be both inadvertent and intentional, and the book <i><a href="/wiki/How_to_Lie_with_Statistics" title="How to Lie with Statistics">How to Lie with Statistics</a></i>,<sup id="cite_ref-Huff_55-1" class="reference"><a href="#cite_note-Huff-55"><span class="cite-bracket">[</span>55<span class="cite-bracket">]</span></a></sup> by <a href="/wiki/Darrell_Huff" title="Darrell Huff">Darrell Huff</a>, outlines a range of considerations. In an attempt to shed light on the use and misuse of statistics, reviews of statistical techniques used in particular fields are conducted (e.g. Warne, Lazo, Ramos, and Ritter (2012)).<sup id="cite_ref-56" class="reference"><a href="#cite_note-56"><span class="cite-bracket">[</span>56<span class="cite-bracket">]</span></a></sup> </p><p>Ways to avoid misuse of statistics include using proper diagrams and avoiding <a href="/wiki/Bias_(statistics)" title="Bias (statistics)">bias</a>.<sup id="cite_ref-Statistics_in_Archaeology_57-0" class="reference"><a href="#cite_note-Statistics_in_Archaeology-57"><span class="cite-bracket">[</span>57<span class="cite-bracket">]</span></a></sup> Misuse can occur when conclusions are <a href="/wiki/Hasty_generalization" class="mw-redirect" title="Hasty generalization">overgeneralized</a> and claimed to be representative of more than they really are, often by either deliberately or unconsciously overlooking sampling bias.<sup id="cite_ref-Misuse_of_Statistics_58-0" class="reference"><a href="#cite_note-Misuse_of_Statistics-58"><span class="cite-bracket">[</span>58<span class="cite-bracket">]</span></a></sup> Bar graphs are arguably the easiest diagrams to use and understand, and they can be made either by hand or with simple computer programs.<sup id="cite_ref-Statistics_in_Archaeology_57-1" class="reference"><a href="#cite_note-Statistics_in_Archaeology-57"><span class="cite-bracket">[</span>57<span class="cite-bracket">]</span></a></sup> Most people do not look for bias or errors, so they are not noticed. Thus, people may often believe that something is true even if it is not well <a href="/wiki/Sampling_(statistics)" title="Sampling (statistics)">represented</a>.<sup id="cite_ref-Misuse_of_Statistics_58-1" class="reference"><a href="#cite_note-Misuse_of_Statistics-58"><span class="cite-bracket">[</span>58<span class="cite-bracket">]</span></a></sup> To make data gathered from statistics believable and accurate, the sample taken must be representative of the whole.<sup id="cite_ref-Modern_Elementary_Statistics_59-0" class="reference"><a href="#cite_note-Modern_Elementary_Statistics-59"><span class="cite-bracket">[</span>59<span class="cite-bracket">]</span></a></sup> According to Huff, "The dependability of a sample can be destroyed by [bias]... allow yourself some degree of skepticism."<sup id="cite_ref-60" class="reference"><a href="#cite_note-60"><span class="cite-bracket">[</span>60<span class="cite-bracket">]</span></a></sup> </p><p>To assist in the understanding of statistics Huff proposed a series of questions to be asked in each case:<sup id="cite_ref-Huff_55-2" class="reference"><a href="#cite_note-Huff-55"><span class="cite-bracket">[</span>55<span class="cite-bracket">]</span></a></sup> </p> <ul><li>Who says so? (Does he/she have an axe to grind?)</li> <li>How does he/she know? (Does he/she have the resources to know the facts?)</li> <li>What's missing? (Does he/she give us a complete picture?)</li> <li>Did someone change the subject? (Does he/she offer us the right answer to the wrong problem?)</li> <li>Does it make sense? (Is his/her conclusion logical and consistent with what we already know?)</li></ul> <div class="mw-heading mw-heading3"><h3 id="Misinterpretation:_correlation">Misinterpretation: correlation</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Statistics&action=edit&section=23" title="Edit section: Misinterpretation: correlation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Correlation_does_not_imply_causation" title="Correlation does not imply causation">Correlation does not imply causation</a></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Simple_Confounding_Case.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b8/Simple_Confounding_Case.svg/200px-Simple_Confounding_Case.svg.png" decoding="async" width="200" height="186" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b8/Simple_Confounding_Case.svg/300px-Simple_Confounding_Case.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b8/Simple_Confounding_Case.svg/400px-Simple_Confounding_Case.svg.png 2x" data-file-width="152" data-file-height="141" /></a><figcaption>The <a href="/wiki/Confounding_variable" class="mw-redirect" title="Confounding variable">confounding variable</a> problem: <i>X</i> and <i>Y</i> may be correlated, not because there is causal relationship between them, but because both depend on a third variable <i>Z</i>. <i>Z</i> is called a confounding factor.</figcaption></figure> <p>The concept of <a href="/wiki/Correlation" title="Correlation">correlation</a> is particularly noteworthy for the potential confusion it can cause. Statistical analysis of a <a href="/wiki/Data_set" title="Data set">data set</a> often reveals that two variables (properties) of the population under consideration tend to vary together, as if they were connected. For example, a study of annual income that also looks at age of death, might find that poor people tend to have shorter lives than affluent people. The two variables are said to be correlated; however, they may or may not be the cause of one another. The correlation phenomena could be caused by a third, previously unconsidered phenomenon, called a lurking variable or <a href="/wiki/Confounding_variable" class="mw-redirect" title="Confounding variable">confounding variable</a>. For this reason, there is no way to immediately infer the existence of a causal relationship between the two variables. </p> <div class="mw-heading mw-heading2"><h2 id="Applications">Applications</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Statistics&action=edit&section=24" title="Edit section: Applications"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Applied_statistics,_theoretical_statistics_and_mathematical_statistics"><span id="Applied_statistics.2C_theoretical_statistics_and_mathematical_statistics"></span>Applied statistics, theoretical statistics and mathematical statistics</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Statistics&action=edit&section=25" title="Edit section: Applied statistics, theoretical statistics and mathematical statistics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><i>Applied statistics,</i> sometimes referred to as <i>Statistical science,</i><sup id="cite_ref-61" class="reference"><a href="#cite_note-61"><span class="cite-bracket">[</span>61<span class="cite-bracket">]</span></a></sup> comprises descriptive statistics and the application of inferential statistics.<sup id="cite_ref-62" class="reference"><a href="#cite_note-62"><span class="cite-bracket">[</span>62<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-63" class="reference"><a href="#cite_note-63"><span class="cite-bracket">[</span>63<span class="cite-bracket">]</span></a></sup> <i>Theoretical statistics</i> concerns the logical arguments underlying justification of approaches to <a href="/wiki/Statistical_inference" title="Statistical inference">statistical inference</a>, as well as encompassing <i>mathematical statistics</i>. Mathematical statistics includes not only the manipulation of <a href="/wiki/Probability_distribution" title="Probability distribution">probability distributions</a> necessary for deriving results related to methods of estimation and inference, but also various aspects of <a href="/wiki/Computational_statistics" title="Computational statistics">computational statistics</a> and the <a href="/wiki/Design_of_experiments" title="Design of experiments">design of experiments</a>. </p><p><a href="/wiki/Statistical_consultant" class="mw-redirect" title="Statistical consultant">Statistical consultants</a> can help organizations and companies that do not have in-house expertise relevant to their particular questions. </p> <div class="mw-heading mw-heading3"><h3 id="Machine_learning_and_data_mining">Machine learning and data mining</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Statistics&action=edit&section=26" title="Edit section: Machine learning and data mining"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Machine_learning" title="Machine learning">Machine learning</a> models are statistical and probabilistic models that capture patterns in the data through use of computational algorithms. </p> <div class="mw-heading mw-heading3"><h3 id="Statistics_in_academia">Statistics in academia</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Statistics&action=edit&section=27" title="Edit section: Statistics in academia"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Statistics is applicable to a wide variety of <a href="/wiki/Academic_discipline" title="Academic discipline">academic disciplines</a>, including <a href="/wiki/Natural_science" title="Natural science">natural</a> and <a href="/wiki/Social_science" title="Social science">social sciences</a>, government, and business. Business statistics applies statistical methods in <a href="/wiki/Econometrics" title="Econometrics">econometrics</a>, <a href="/wiki/Auditing" class="mw-redirect" title="Auditing">auditing</a> and production and operations, including services improvement and marketing research.<sup id="cite_ref-64" class="reference"><a href="#cite_note-64"><span class="cite-bracket">[</span>64<span class="cite-bracket">]</span></a></sup> A study of two journals in tropical biology found that the 12 most frequent statistical tests are: <a href="/wiki/Analysis_of_variance" title="Analysis of variance">analysis of variance</a> (ANOVA), <a href="/wiki/Chi-squared_test" title="Chi-squared test">chi-squared test</a>, <a href="/wiki/Student%27s_t-test" title="Student's t-test">Student's t-test</a>, <a href="/wiki/Linear_regression" title="Linear regression">linear regression</a>, <a href="/wiki/Pearson%27s_correlation_coefficient" class="mw-redirect" title="Pearson's correlation coefficient">Pearson's correlation coefficient</a>, <a href="/wiki/Mann-Whitney_U_test" class="mw-redirect" title="Mann-Whitney U test">Mann-Whitney U test</a>, <a href="/wiki/Kruskal-Wallis_test" class="mw-redirect" title="Kruskal-Wallis test">Kruskal-Wallis test</a>, <a href="/wiki/Diversity_index#Shannon_index" title="Diversity index">Shannon's diversity index</a>, <a href="/wiki/Tukey%27s_range_test" title="Tukey's range test">Tukey's range test</a>, <a href="/wiki/Cluster_analysis" title="Cluster analysis">cluster analysis</a>, <a href="/wiki/Spearman%27s_rank_correlation_coefficient" title="Spearman's rank correlation coefficient">Spearman's rank correlation coefficient</a> and <a href="/wiki/Principal_component_analysis" title="Principal component analysis">principal component analysis</a>.<sup id="cite_ref-:0_65-0" class="reference"><a href="#cite_note-:0-65"><span class="cite-bracket">[</span>65<span class="cite-bracket">]</span></a></sup> </p><p>A typical statistics course covers descriptive statistics, probability, binomial and <a href="/wiki/Normal_distribution" title="Normal distribution">normal distributions</a>, test of hypotheses and confidence intervals, <a href="/wiki/Linear_regression" title="Linear regression">linear regression</a>, and correlation.<sup id="cite_ref-66" class="reference"><a href="#cite_note-66"><span class="cite-bracket">[</span>66<span class="cite-bracket">]</span></a></sup> Modern fundamental statistical courses for undergraduate students focus on correct test selection, results interpretation, and use of <a href="/wiki/Free_statistics_software" class="mw-redirect" title="Free statistics software">free statistics software</a>.<sup id="cite_ref-:0_65-1" class="reference"><a href="#cite_note-:0-65"><span class="cite-bracket">[</span>65<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Statistical_computing">Statistical computing</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Statistics&action=edit&section=28" title="Edit section: Statistical computing"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Computational_statistics" title="Computational statistics">Computational statistics</a></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Gretl_screenshot.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b9/Gretl_screenshot.png/250px-Gretl_screenshot.png" decoding="async" width="250" height="213" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b9/Gretl_screenshot.png/375px-Gretl_screenshot.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b9/Gretl_screenshot.png/500px-Gretl_screenshot.png 2x" data-file-width="990" data-file-height="844" /></a><figcaption><a href="/wiki/Gretl" title="Gretl">gretl</a>, an example of an <a href="/wiki/List_of_open_source_statistical_packages" class="mw-redirect" title="List of open source statistical packages">open source statistical package</a></figcaption></figure> <p>The rapid and sustained increases in computing power starting from the second half of the 20th century have had a substantial impact on the practice of statistical science. Early statistical models were almost always from the class of <a href="/wiki/Linear_model" title="Linear model">linear models</a>, but powerful computers, coupled with suitable numerical <a href="/wiki/Algorithms" class="mw-redirect" title="Algorithms">algorithms</a>, caused an increased interest in <a href="/wiki/Nonlinear_regression" title="Nonlinear regression">nonlinear models</a> (such as <a href="/wiki/Artificial_neural_network" class="mw-redirect" title="Artificial neural network">neural networks</a>) as well as the creation of new types, such as <a href="/wiki/Generalized_linear_model" title="Generalized linear model">generalized linear models</a> and <a href="/wiki/Multilevel_model" title="Multilevel model">multilevel models</a>. </p><p>Increased computing power has also led to the growing popularity of computationally intensive methods based on <a href="/wiki/Resampling_(statistics)" title="Resampling (statistics)">resampling</a>, such as <a href="/wiki/Permutation_test" title="Permutation test">permutation tests</a> and the <a href="/wiki/Bootstrapping_(statistics)" title="Bootstrapping (statistics)">bootstrap</a>, while techniques such as <a href="/wiki/Gibbs_sampling" title="Gibbs sampling">Gibbs sampling</a> have made use of <a href="/wiki/Bayesian_model" class="mw-redirect" title="Bayesian model">Bayesian models</a> more feasible. The computer revolution has implications for the future of statistics with a new emphasis on "experimental" and "empirical" statistics. A large number of both general and special purpose <a href="/wiki/List_of_statistical_packages" class="mw-redirect" title="List of statistical packages">statistical software</a> are now available. Examples of available software capable of complex statistical computation include programs such as <a href="/wiki/Mathematica" class="mw-redirect" title="Mathematica">Mathematica</a>, <a href="/wiki/SAS_(software)" title="SAS (software)">SAS</a>, <a href="/wiki/SPSS" title="SPSS">SPSS</a>, and <a href="/wiki/R_(programming_language)" title="R (programming language)">R</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Business_statistics">Business statistics</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Statistics&action=edit&section=29" title="Edit section: Business statistics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Business_mathematics#University_level" title="Business mathematics">Business mathematics § University level</a></div> <p>In business, "statistics" is a widely used <a href="/wiki/Management#Nature_of_work" title="Management">management-</a> and <a href="/wiki/Decision_support" class="mw-redirect" title="Decision support">decision support</a> tool. It is particularly applied in <a href="/wiki/Financial_management" title="Financial management">financial management</a>, <a href="/wiki/Marketing_management" title="Marketing management">marketing management</a>, and <a href="/wiki/Manufacturing_process_management" title="Manufacturing process management">production</a>, <a href="/wiki/Operations_management_for_services" title="Operations management for services">services</a> and <a href="/wiki/Operations_management" title="Operations management">operations management</a>.<sup id="cite_ref-67" class="reference"><a href="#cite_note-67"><span class="cite-bracket">[</span>67<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-68" class="reference"><a href="#cite_note-68"><span class="cite-bracket">[</span>68<span class="cite-bracket">]</span></a></sup> Statistics is also heavily used in <a href="/wiki/Management_accounting" title="Management accounting">management accounting</a> and <a href="/wiki/Auditing" class="mw-redirect" title="Auditing">auditing</a>. The discipline of <a href="/wiki/Management_Science" class="mw-redirect" title="Management Science">Management Science</a> formalizes the use of statistics, and other mathematics, in business. (<a href="/wiki/Econometrics" title="Econometrics">Econometrics</a> is the application of statistical methods to <a href="/wiki/Economic_data" title="Economic data">economic data</a> in order to give empirical content to <a href="/wiki/Economic_theory" class="mw-redirect" title="Economic theory">economic relationships</a>.) </p><p>A typical "Business Statistics" course is intended for <a href="/wiki/Business_education#Undergraduate_education" title="Business education">business majors</a>, and covers<sup id="cite_ref-69" class="reference"><a href="#cite_note-69"><span class="cite-bracket">[</span>69<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Descriptive_statistics" title="Descriptive statistics">descriptive statistics</a> (<a href="/wiki/Data_collection" title="Data collection">collection</a>, description, analysis, and summary of data), probability (typically the <a href="/wiki/Binomial_distribution" title="Binomial distribution">binomial</a> and <a href="/wiki/Normal_distribution" title="Normal distribution">normal distributions</a>), test of hypotheses and confidence intervals, <a href="/wiki/Linear_regression" title="Linear regression">linear regression</a>, and correlation; (follow-on) courses may include <a href="/wiki/Forecasting" title="Forecasting">forecasting</a>, <a href="/wiki/Time_series" title="Time series">time series</a>, <a href="/wiki/Decision_trees" class="mw-redirect" title="Decision trees">decision trees</a>, <a href="/wiki/Multiple_linear_regression" class="mw-redirect" title="Multiple linear regression">multiple linear regression</a>, and other topics from <a href="/wiki/Business_analytics" title="Business analytics">business analytics</a> more generally. <a href="/wiki/Professional_certification_in_financial_services" title="Professional certification in financial services">Professional certification programs</a>, such as the <a href="/wiki/Chartered_Financial_Analyst" title="Chartered Financial Analyst">CFA</a>, often include topics in statistics. </p> <div class="mw-heading mw-heading3"><h3 id="Statistics_applied_to_mathematics_or_the_arts">Statistics applied to mathematics or the arts</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Statistics&action=edit&section=30" title="Edit section: Statistics applied to mathematics or the arts"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Traditionally, statistics was concerned with drawing inferences using a semi-standardized methodology that was "required learning" in most sciences. This tradition has changed with the use of statistics in non-inferential contexts. What was once considered a dry subject, taken in many fields as a degree-requirement, is now viewed enthusiastically.<sup class="noprint Inline-Template" style="margin-left:0.1em; white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Manual_of_Style/Words_to_watch#Unsupported_attributions" title="Wikipedia:Manual of Style/Words to watch"><span title="The material near this tag may use weasel words or too-vague attribution. (April 2014)">according to whom?</span></a></i>]</sup> Initially derided by some mathematical purists, it is now considered essential methodology in certain areas. </p> <ul><li>In <a href="/wiki/Number_theory" title="Number theory">number theory</a>, <a href="/wiki/Scatter_plot" title="Scatter plot">scatter plots</a> of data generated by a distribution function may be transformed with familiar tools used in statistics to reveal underlying patterns, which may then lead to hypotheses.</li> <li>Predictive methods of statistics in <a href="/wiki/Forecasting" title="Forecasting">forecasting</a> combining <a href="/wiki/Chaos_theory" title="Chaos theory">chaos theory</a> and <a href="/wiki/Fractal_geometry" class="mw-redirect" title="Fractal geometry">fractal geometry</a> can be used to create video works.<sup id="cite_ref-70" class="reference"><a href="#cite_note-70"><span class="cite-bracket">[</span>70<span class="cite-bracket">]</span></a></sup></li> <li>The <a href="/wiki/Process_art" title="Process art">process art</a> of <a href="/wiki/Jackson_Pollock" title="Jackson Pollock">Jackson Pollock</a> relied on artistic experiments whereby underlying distributions in nature were artistically revealed.<sup id="cite_ref-71" class="reference"><a href="#cite_note-71"><span class="cite-bracket">[</span>71<span class="cite-bracket">]</span></a></sup> With the advent of computers, statistical methods were applied to formalize such distribution-driven natural processes to make and analyze moving video art.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (March 2013)">citation needed</span></a></i>]</sup></li> <li>Methods of statistics may be used predicatively in <a href="/wiki/Performance_art" title="Performance art">performance art</a>, as in a card trick based on a <a href="/wiki/Markov_process" class="mw-redirect" title="Markov process">Markov process</a> that only works some of the time, the occasion of which can be predicted using statistical methodology.</li> <li>Statistics can be used to predicatively create art, as in the statistical or <a href="/wiki/Stochastic_music" class="mw-redirect" title="Stochastic music">stochastic music</a> invented by <a href="/wiki/Iannis_Xenakis" title="Iannis Xenakis">Iannis Xenakis</a>, where the music is performance-specific. Though this type of artistry does not always come out as expected, it does behave in ways that are predictable and tunable using statistics.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Specialized_disciplines">Specialized disciplines</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Statistics&action=edit&section=31" title="Edit section: Specialized disciplines"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/List_of_fields_of_application_of_statistics" title="List of fields of application of statistics">List of fields of application of statistics</a></div> <p>Statistical techniques are used in a wide range of types of scientific and social research, including: <a href="/wiki/Biostatistics" title="Biostatistics">biostatistics</a>, <a href="/wiki/Computational_biology" title="Computational biology">computational biology</a>, <a href="/wiki/Computational_sociology" title="Computational sociology">computational sociology</a>, <a href="/wiki/Network_biology" class="mw-redirect" title="Network biology">network biology</a>, <a href="/wiki/Social_science" title="Social science">social science</a>, <a href="/wiki/Sociology" title="Sociology">sociology</a> and <a href="/wiki/Social_research" title="Social research">social research</a>. Some fields of inquiry use applied statistics so extensively that they have <a href="/wiki/Specialized_terminology" class="mw-redirect" title="Specialized terminology">specialized terminology</a>. These disciplines include: </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1184024115"><div class="div-col" style="column-width: 30em;"> <ul><li><a href="/wiki/Actuarial_science" title="Actuarial science">Actuarial science</a> (assesses risk in the insurance and finance industries)</li> <li>Applied information economics</li> <li><a href="/wiki/Astrostatistics" title="Astrostatistics">Astrostatistics</a> (statistical evaluation of astronomical data)</li> <li><a href="/wiki/Biostatistics" title="Biostatistics">Biostatistics</a></li> <li><a href="/wiki/Chemometrics" title="Chemometrics">Chemometrics</a> (for analysis of data from <a href="/wiki/Chemistry" title="Chemistry">chemistry</a>)</li> <li><a href="/wiki/Data_mining" title="Data mining">Data mining</a> (applying statistics and <a href="/wiki/Pattern_recognition" title="Pattern recognition">pattern recognition</a> to discover knowledge from data)</li> <li><a href="/wiki/Data_science" title="Data science">Data science</a> (<style data-mw-deduplicate="TemplateStyles:r1033199720">.mw-parser-output div.crossreference{padding-left:0}</style><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><span role="note" class="hatnote navigation-not-searchable crossreference">see also: <a href="/wiki/Data_science#Relationship_to_statistics" title="Data science">Data science#Relationship to statistics</a></span>)</li> <li><a href="/wiki/Demography" title="Demography">Demography</a> (statistical study of populations)</li> <li><a href="/wiki/Econometrics" title="Econometrics">Econometrics</a> (statistical analysis of economic data)</li> <li><a href="/wiki/Statistical_study_of_energy_data" title="Statistical study of energy data">Energy statistics</a></li> <li><a href="/wiki/Engineering_statistics" title="Engineering statistics">Engineering statistics</a></li> <li><a href="/wiki/Epidemiology" title="Epidemiology">Epidemiology</a> (statistical analysis of disease)</li> <li><a href="/wiki/Geography" title="Geography">Geography</a> and <a href="/wiki/Geographic_information_system" title="Geographic information system">geographic information systems</a>, specifically in <a href="/wiki/Spatial_analysis" title="Spatial analysis">spatial analysis</a></li> <li><a href="/wiki/Image_processing" class="mw-redirect" title="Image processing">Image processing</a></li> <li><a href="/wiki/Jurimetrics" title="Jurimetrics">Jurimetrics</a> (<a href="/wiki/Law" title="Law">law</a>)</li> <li><a href="/wiki/Medical_statistics" title="Medical statistics">Medical statistics</a></li> <li><a href="/wiki/Political_science" title="Political science">Political science</a></li> <li><a href="/wiki/Psychological_statistics" title="Psychological statistics">Psychological statistics</a></li> <li><a href="/wiki/Reliability_engineering" title="Reliability engineering">Reliability engineering</a></li> <li><a href="/wiki/Social_statistics" title="Social statistics">Social statistics</a></li> <li><a href="/wiki/Statistical_mechanics" title="Statistical mechanics">Statistical mechanics</a></li></ul></div> <p>In addition, there are particular types of statistical analysis that have also developed their own specialised terminology and methodology: </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1184024115"><div class="div-col" style="column-width: 30em;"> <ul><li><a href="/wiki/Bootstrapping_(statistics)" title="Bootstrapping (statistics)">Bootstrap</a> / <a href="/wiki/Jackknife_resampling" title="Jackknife resampling">jackknife resampling</a></li> <li><a href="/wiki/Multivariate_statistics" title="Multivariate statistics">Multivariate statistics</a></li> <li><a href="/wiki/Statistical_classification" title="Statistical classification">Statistical classification</a></li> <li><a href="/wiki/Structured_data_analysis_(statistics)" title="Structured data analysis (statistics)">Structured data analysis</a></li> <li><a href="/wiki/Structural_equation_modelling" class="mw-redirect" title="Structural equation modelling">Structural equation modelling</a></li> <li><a href="/wiki/Survey_methodology" title="Survey methodology">Survey methodology</a></li> <li><a href="/wiki/Survival_analysis" title="Survival analysis">Survival analysis</a></li> <li>Statistics in various sports, particularly <a href="/wiki/Baseball_statistics" title="Baseball statistics">baseball</a> – known as <a href="/wiki/Sabermetrics" title="Sabermetrics">sabermetrics</a> – and <a href="/wiki/Cricket_statistics" title="Cricket statistics">cricket</a></li></ul></div> <p>Statistics form a key basis tool in business and manufacturing as well. It is used to understand measurement systems variability, control processes (as in <a href="/wiki/Statistical_process_control" title="Statistical process control">statistical process control</a> or SPC), for summarizing data, and to make data-driven decisions. </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Statistics&action=edit&section=32" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Outline_of_statistics" title="Outline of statistics">Outline of statistics</a></div> <style data-mw-deduplicate="TemplateStyles:r1239009302">.mw-parser-output .portalbox{padding:0;margin:0.5em 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estimation">Abundance estimation</a></li> <li><a href="/wiki/Glossary_of_probability_and_statistics" title="Glossary of probability and statistics">Glossary of probability and statistics</a></li> <li><a href="/wiki/List_of_academic_statistical_associations" title="List of academic statistical associations">List of academic statistical associations</a></li> <li><a href="/wiki/List_of_important_publications_in_statistics" title="List of important publications in statistics">List of important publications in statistics</a></li> <li><a href="/wiki/List_of_national_and_international_statistical_services" title="List of national and international statistical services">List of national and international statistical services</a></li> <li><a href="/wiki/List_of_statistical_software" title="List of statistical software">List of statistical software</a></li> <li><a href="/wiki/List_of_statistics_articles" title="List of statistics articles">List of statistics articles</a></li> <li><a href="/wiki/List_of_university_statistical_consulting_centers" title="List of university statistical consulting centers">List of university statistical consulting centers</a></li> <li><a href="/wiki/Notation_in_probability_and_statistics" title="Notation in probability and statistics">Notation in probability and statistics</a></li> <li><a href="/wiki/Statistics_education" title="Statistics education">Statistics education</a></li> <li><a href="/wiki/World_Statistics_Day" title="World Statistics Day">World Statistics Day</a></li> <li><a href="/wiki/Robust_statistics" title="Robust statistics">Robust statistics</a></li></ul></div> <dl><dt>Foundations and major areas of statistics</dt></dl> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1184024115"><div class="div-col" style="column-width: 22em;"> <ul><li><a href="/wiki/Philosophy_of_statistics" title="Philosophy of statistics">Philosophy of statistics</a></li> <li><a href="/wiki/Probability_interpretations" title="Probability interpretations">Probability interpretations</a></li> <li><a href="/wiki/Foundations_of_statistics" title="Foundations of statistics">Foundations of statistics</a></li> <li><a href="/wiki/List_of_statisticians" title="List of statisticians">List of statisticians</a></li> <li><a href="/wiki/Official_statistics" title="Official statistics">Official statistics</a></li> <li><a href="/wiki/Multivariate_analysis_of_variance" title="Multivariate analysis of variance">Multivariate analysis of variance</a></li></ul> <dl><dd></dd> <dd></dd></dl></div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Statistics&action=edit&section=33" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><span 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.cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFReference-OED-statistics" class="citation encyclopaedia cs1"><span class="id-lock-subscription" title="Paid subscription required"><a rel="nofollow" class="external text" href="https://www.oed.com/search/dictionary/?q=statistics">"statistics"</a></span>. <i><a href="/wiki/Oxford_English_Dictionary" title="Oxford English Dictionary">Oxford English Dictionary</a></i> (Online ed.). <a href="/wiki/Oxford_University_Press" title="Oxford University Press">Oxford University Press</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=statistics&rft.btitle=Oxford+English+Dictionary&rft.edition=Online&rft.pub=Oxford+University+Press&rft_id=https%3A%2F%2Fwww.oed.com%2Fsearch%2Fdictionary%2F%3Fq%3Dstatistics&rfr_id=info%3Asid%2Fen.wikipedia.org%3AStatistics" class="Z3988"></span> <span style="font-size:0.95em; font-size:95%; color: var( --color-subtle, #555 )">(Subscription or <a rel="nofollow" class="external text" href="https://www.oed.com/public/login/loggingin#withyourlibrary">participating institution membership</a> required.)</span></li><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation encyclopaedia cs1 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Berlin-Brandenburgischen Akademie der Wissenschaften. 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(2005). <a rel="nofollow" class="external text" href="http://www.stat.ufl.edu/~aa/articles/agresti_hitchcock_2005.pdf">"Bayesian Inference for Categorical Data Analysis"</a> <span class="cs1-format">(PDF)</span>. <i>Statistical Methods & Applications</i>. <b>14</b> (3): 298. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2Fs10260-005-0121-y">10.1007/s10260-005-0121-y</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:18896230">18896230</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20131219212926/http://www.stat.ufl.edu/~aa/articles/agresti_hitchcock_2005.pdf">Archived</a> <span class="cs1-format">(PDF)</span> from the original on 2013-12-19<span class="reference-accessdate">. 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Fisher, <i><a href="/wiki/The_Design_of_Experiments" title="The Design of Experiments">The Design of Experiments</a></i> ii. 19, "We may speak of this hypothesis as the 'null hypothesis', and the null hypothesis is never proved or established, but is possibly disproved, in the course of experimentation."</span> </li> <li id="cite_note-28"><span class="mw-cite-backlink"><b><a href="#cite_ref-28">^</a></b></span> <span class="reference-text">Fisher 1971. Chapter II: The Principles of Experimentation, Illustrated by a Psycho-physical Experiment, Section 8. The Null Hypothesis</span> </li> <li id="cite_note-Edwards98-29"><span class="mw-cite-backlink"><b><a href="#cite_ref-Edwards98_29-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEdwards1998" class="citation journal cs1">Edwards, A. W. F. (1998). 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Ioannidis">Ioannidis, J.P.A.</a> (2005). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1182327">"Why Most Published Research Findings Are False"</a>. <i>PLOS Medicine</i>. <b>2</b> (8): e124. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1371%2Fjournal.pmed.0020124">10.1371/journal.pmed.0020124</a></span>. <a href="/wiki/PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1182327">1182327</a></span>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/16060722">16060722</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=PLOS+Medicine&rft.atitle=Why+Most+Published+Research+Findings+Are+False&rft.volume=2&rft.issue=8&rft.pages=e124&rft.date=2005&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC1182327%23id-name%3DPMC&rft_id=info%3Apmid%2F16060722&rft_id=info%3Adoi%2F10.1371%2Fjournal.pmed.0020124&rft.aulast=Ioannidis&rft.aufirst=J.P.A.&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC1182327&rfr_id=info%3Asid%2Fen.wikipedia.org%3AStatistics" class="Z3988"></span></span> </li> <li id="cite_note-Huff-55"><span class="mw-cite-backlink">^ <a href="#cite_ref-Huff_55-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Huff_55-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Huff_55-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text">Huff, Darrell (1954) <i><a href="/wiki/How_to_Lie_with_Statistics" title="How to Lie with Statistics">How to Lie with Statistics</a></i>, WW Norton & Company, Inc. New York. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-393-31072-8" title="Special:BookSources/0-393-31072-8">0-393-31072-8</a></span> </li> <li id="cite_note-56"><span class="mw-cite-backlink"><b><a href="#cite_ref-56">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWarneRamosRitter2012" class="citation journal cs1">Warne, R. Lazo; Ramos, T.; Ritter, N. (2012). "Statistical Methods Used in Gifted Education Journals, 2006–2010". <i>Gifted Child Quarterly</i>. <b>56</b> (3): 134–149. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1177%2F0016986212444122">10.1177/0016986212444122</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:144168910">144168910</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Gifted+Child+Quarterly&rft.atitle=Statistical+Methods+Used+in+Gifted+Education+Journals%2C+2006%E2%80%932010&rft.volume=56&rft.issue=3&rft.pages=134-149&rft.date=2012&rft_id=info%3Adoi%2F10.1177%2F0016986212444122&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A144168910%23id-name%3DS2CID&rft.aulast=Warne&rft.aufirst=R.+Lazo&rft.au=Ramos%2C+T.&rft.au=Ritter%2C+N.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AStatistics" class="Z3988"></span></span> </li> <li id="cite_note-Statistics_in_Archaeology-57"><span class="mw-cite-backlink">^ <a href="#cite_ref-Statistics_in_Archaeology_57-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Statistics_in_Archaeology_57-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDrennan2008" class="citation book cs1">Drennan, Robert D. (2008). "Statistics in archaeology". In Pearsall, Deborah M. (ed.). <span class="id-lock-limited" title="Free access subject to limited trial, subscription normally required"><a rel="nofollow" class="external text" href="https://archive.org/details/encyclopediaarch00pear"><i>Encyclopedia of Archaeology</i></a></span>. Elsevier Inc. pp. <a rel="nofollow" class="external text" href="https://archive.org/details/encyclopediaarch00pear/page/n2072">2093</a>–2100. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-12-373962-9" title="Special:BookSources/978-0-12-373962-9"><bdi>978-0-12-373962-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Statistics+in+archaeology&rft.btitle=Encyclopedia+of+Archaeology&rft.pages=2093-2100&rft.pub=Elsevier+Inc.&rft.date=2008&rft.isbn=978-0-12-373962-9&rft.aulast=Drennan&rft.aufirst=Robert+D.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fencyclopediaarch00pear&rfr_id=info%3Asid%2Fen.wikipedia.org%3AStatistics" class="Z3988"></span></span> </li> <li id="cite_note-Misuse_of_Statistics-58"><span class="mw-cite-backlink">^ <a href="#cite_ref-Misuse_of_Statistics_58-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Misuse_of_Statistics_58-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCohen1938" class="citation journal cs1">Cohen, Jerome B. (December 1938). "Misuse of Statistics". <i>Journal of the American Statistical Association</i>. <b>33</b> (204). JSTOR: 657–674. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1080%2F01621459.1938.10502344">10.1080/01621459.1938.10502344</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+the+American+Statistical+Association&rft.atitle=Misuse+of+Statistics&rft.volume=33&rft.issue=204&rft.pages=657-674&rft.date=1938-12&rft_id=info%3Adoi%2F10.1080%2F01621459.1938.10502344&rft.aulast=Cohen&rft.aufirst=Jerome+B.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AStatistics" class="Z3988"></span></span> </li> <li id="cite_note-Modern_Elementary_Statistics-59"><span class="mw-cite-backlink"><b><a href="#cite_ref-Modern_Elementary_Statistics_59-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFreund1988" class="citation journal cs1"><a href="/wiki/John_E._Freund" title="John E. Freund">Freund, J.E.</a> (1988). "Modern Elementary Statistics". <i>Credo Reference</i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Credo+Reference&rft.atitle=Modern+Elementary+Statistics&rft.date=1988&rft.aulast=Freund&rft.aufirst=J.E.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AStatistics" class="Z3988"></span></span> </li> <li id="cite_note-60"><span class="mw-cite-backlink"><b><a href="#cite_ref-60">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHuffIrving_Geis1954" class="citation book cs1">Huff, Darrell; Irving Geis (1954). <i>How to Lie with Statistics</i>. New York: Norton. <q>The dependability of a sample can be destroyed by [bias]... allow yourself some degree of skepticism.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=How+to+Lie+with+Statistics&rft.place=New+York&rft.pub=Norton&rft.date=1954&rft.aulast=Huff&rft.aufirst=Darrell&rft.au=Irving+Geis&rfr_id=info%3Asid%2Fen.wikipedia.org%3AStatistics" class="Z3988"></span></span> </li> <li id="cite_note-61"><span class="mw-cite-backlink"><b><a href="#cite_ref-61">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNelder1999" class="citation journal cs1">Nelder, John A. (1999). <span class="id-lock-subscription" title="Paid subscription required"><a rel="nofollow" class="external text" href="https://www.jstor.org/stable/2681191">"From Statistics to Statistical Science"</a></span>. <i>Journal of the Royal Statistical Society. Series D (The Statistician)</i>. <b>48</b> (2): 257–269. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1111%2F1467-9884.00187">10.1111/1467-9884.00187</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0039-0526">0039-0526</a>. <a href="/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/2681191">2681191</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20220115160959/https://www.jstor.org/stable/2681191">Archived</a> from the original on 2022-01-15<span class="reference-accessdate">. Retrieved <span class="nowrap">2022-01-15</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+the+Royal+Statistical+Society.+Series+D+%28The+Statistician%29&rft.atitle=From+Statistics+to+Statistical+Science&rft.volume=48&rft.issue=2&rft.pages=257-269&rft.date=1999&rft.issn=0039-0526&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F2681191%23id-name%3DJSTOR&rft_id=info%3Adoi%2F10.1111%2F1467-9884.00187&rft.aulast=Nelder&rft.aufirst=John+A.&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F2681191&rfr_id=info%3Asid%2Fen.wikipedia.org%3AStatistics" class="Z3988"></span></span> </li> <li id="cite_note-62"><span class="mw-cite-backlink"><b><a href="#cite_ref-62">^</a></b></span> <span class="reference-text">Nikoletseas, M.M. (2014) "Statistics: Concepts and Examples." <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1500815684" title="Special:BookSources/978-1500815684">978-1500815684</a></span> </li> <li id="cite_note-63"><span class="mw-cite-backlink"><b><a href="#cite_ref-63">^</a></b></span> <span class="reference-text">Anderson, D.R.; Sweeney, D.J.; Williams, T.A. (1994) <i>Introduction to Statistics: Concepts and Applications</i>, pp. 5–9. West Group. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-314-03309-3" title="Special:BookSources/978-0-314-03309-3">978-0-314-03309-3</a></span> </li> <li id="cite_note-64"><span class="mw-cite-backlink"><b><a href="#cite_ref-64">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://amstat.tandfonline.com/loi/jbes">"Journal of Business & Economic Statistics"</a>. <i>Journal of Business & Economic Statistics</i>. Taylor & Francis. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20200727052958/https://amstat.tandfonline.com/loi/jbes">Archived</a> from the original on 27 July 2020<span class="reference-accessdate">. Retrieved <span class="nowrap">16 March</span> 2020</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Journal+of+Business+%26+Economic+Statistics&rft.atitle=Journal+of+Business+%26+Economic+Statistics&rft_id=https%3A%2F%2Famstat.tandfonline.com%2Floi%2Fjbes&rfr_id=info%3Asid%2Fen.wikipedia.org%3AStatistics" class="Z3988"></span></span> </li> <li id="cite_note-:0-65"><span class="mw-cite-backlink">^ <a href="#cite_ref-:0_65-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:0_65-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNatalia_Loaiza_Velásquez,_María_Isabel_González_Lutz_&_Julián_Monge-Nájera2011" class="citation journal cs1">Natalia Loaiza Velásquez, María Isabel González Lutz & Julián Monge-Nájera (2011). <a rel="nofollow" class="external text" href="https://investiga.uned.ac.cr/ecologiaurbana/wp-content/uploads/sites/30/2017/09/JMN-2011-statistics-should-learn.pdf">"Which statistics should tropical biologists learn?"</a> <span class="cs1-format">(PDF)</span>. <i>Revista de Biología Tropical</i>. <b>59</b> (3): 983–992. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/22017105">22017105</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20201019160957/https://investiga.uned.ac.cr/ecologiaurbana/wp-content/uploads/sites/30/2017/09/JMN-2011-statistics-should-learn.pdf">Archived</a> <span class="cs1-format">(PDF)</span> from the original on 2020-10-19<span class="reference-accessdate">. Retrieved <span class="nowrap">2020-04-26</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Revista+de+Biolog%C3%ADa+Tropical&rft.atitle=Which+statistics+should+tropical+biologists+learn%3F&rft.volume=59&rft.issue=3&rft.pages=983-992&rft.date=2011&rft_id=info%3Apmid%2F22017105&rft.au=Natalia+Loaiza+Vel%C3%A1squez%2C+Mar%C3%ADa+Isabel+Gonz%C3%A1lez+Lutz+%26+Juli%C3%A1n+Monge-N%C3%A1jera&rft_id=https%3A%2F%2Finvestiga.uned.ac.cr%2Fecologiaurbana%2Fwp-content%2Fuploads%2Fsites%2F30%2F2017%2F09%2FJMN-2011-statistics-should-learn.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AStatistics" class="Z3988"></span></span> </li> <li id="cite_note-66"><span class="mw-cite-backlink"><b><a href="#cite_ref-66">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPekoz2009" class="citation book cs1">Pekoz, Erol (2009). <i>The Manager's Guide to Statistics</i>. Erol Pekoz. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0979570438" title="Special:BookSources/978-0979570438"><bdi>978-0979570438</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Manager%27s+Guide+to+Statistics&rft.pub=Erol+Pekoz&rft.date=2009&rft.isbn=978-0979570438&rft.aulast=Pekoz&rft.aufirst=Erol&rfr_id=info%3Asid%2Fen.wikipedia.org%3AStatistics" class="Z3988"></span></span> </li> <li id="cite_note-67"><span class="mw-cite-backlink"><b><a href="#cite_ref-67">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://amstat.tandfonline.com/action/journalInformation?show=aimsScope&journalCode=ubes20">"Aims and scope"</a>. <i>Journal of Business & Economic Statistics</i>. Taylor & Francis. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210623194835/https://amstat.tandfonline.com/action/journalInformation?show=aimsScope&journalCode=ubes20">Archived</a> from the original on 23 June 2021<span class="reference-accessdate">. Retrieved <span class="nowrap">16 March</span> 2020</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Journal+of+Business+%26+Economic+Statistics&rft.atitle=Aims+and+scope&rft_id=https%3A%2F%2Famstat.tandfonline.com%2Faction%2FjournalInformation%3Fshow%3DaimsScope%26journalCode%3Dubes20&rfr_id=info%3Asid%2Fen.wikipedia.org%3AStatistics" class="Z3988"></span></span> </li> <li id="cite_note-68"><span class="mw-cite-backlink"><b><a href="#cite_ref-68">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://amstat.tandfonline.com/loi/jbes">"Journal of Business & Economic Statistics"</a>. <i>Journal of Business & Economic Statistics</i>. Taylor & Francis. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20200727052958/https://amstat.tandfonline.com/loi/jbes">Archived</a> from the original on 27 July 2020<span class="reference-accessdate">. Retrieved <span class="nowrap">16 March</span> 2020</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Journal+of+Business+%26+Economic+Statistics&rft.atitle=Journal+of+Business+%26+Economic+Statistics&rft_id=https%3A%2F%2Famstat.tandfonline.com%2Floi%2Fjbes&rfr_id=info%3Asid%2Fen.wikipedia.org%3AStatistics" class="Z3988"></span></span> </li> <li id="cite_note-69"><span class="mw-cite-backlink"><b><a href="#cite_ref-69">^</a></b></span> <span class="reference-text">Numerous texts are available, reflecting the scope and reach of the discipline in the business world: <ul><li>Sharpe, N. (2014). <i>Business Statistics</i>, Pearson. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0134705217" title="Special:BookSources/978-0134705217">978-0134705217</a></li> <li>Wegner, T. (2010). <i>Applied Business Statistics: Methods and Excel-Based Applications,</i> Juta Academic. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0702172863" title="Special:BookSources/0702172863">0702172863</a></li></ul> Two <a href="/wiki/Open_textbook" title="Open textbook">open textbooks</a> are: <ul><li>Holmes, L., Illowsky, B., Dean, S. (2017). <a rel="nofollow" class="external text" href="https://open.umn.edu/opentextbooks/textbooks/509"><i>Introductory Business Statistics</i></a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210616084059/https://open.umn.edu/opentextbooks/textbooks/509">Archived</a> 2021-06-16 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></li> <li>Nica, M. (2013). <a rel="nofollow" class="external text" href="https://open.umn.edu/opentextbooks/textbooks/384"><i>Principles of Business Statistics</i></a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210518151122/https://open.umn.edu/opentextbooks/textbooks/384">Archived</a> 2021-05-18 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></li></ul> </span></li> <li id="cite_note-70"><span class="mw-cite-backlink"><b><a href="#cite_ref-70">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCline2019" class="citation book cs1">Cline, Graysen (2019). <a rel="nofollow" class="external text" href="https://www.worldcat.org/oclc/1132348139"><i>Nonparametric Statistical Methods Using R</i></a>. EDTECH. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-83947-325-8" title="Special:BookSources/978-1-83947-325-8"><bdi>978-1-83947-325-8</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/1132348139">1132348139</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20220515012840/https://www.worldcat.org/title/nonparametric-statistical-methods-using-r/oclc/1132348139">Archived</a> from the original on 2022-05-15<span class="reference-accessdate">. Retrieved <span class="nowrap">2021-09-16</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Nonparametric+Statistical+Methods+Using+R&rft.pub=EDTECH&rft.date=2019&rft_id=info%3Aoclcnum%2F1132348139&rft.isbn=978-1-83947-325-8&rft.aulast=Cline&rft.aufirst=Graysen&rft_id=https%3A%2F%2Fwww.worldcat.org%2Foclc%2F1132348139&rfr_id=info%3Asid%2Fen.wikipedia.org%3AStatistics" class="Z3988"></span></span> </li> <li id="cite_note-71"><span class="mw-cite-backlink"><b><a href="#cite_ref-71">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPalaciosRosarioWilhelmusZetina2019" class="citation journal cs1">Palacios, Bernardo; Rosario, Alfonso; Wilhelmus, Monica M.; Zetina, Sandra; Zenit, Roberto (2019-10-30). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6821064">"Pollock avoided hydrodynamic instabilities to paint with his dripping technique"</a>. <i>PLOS ONE</i>. <b>14</b> (10): e0223706. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2019PLoSO..1423706P">2019PLoSO..1423706P</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1371%2Fjournal.pone.0223706">10.1371/journal.pone.0223706</a></span>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/1932-6203">1932-6203</a>. <a href="/wiki/PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6821064">6821064</a></span>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/31665191">31665191</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=PLOS+ONE&rft.atitle=Pollock+avoided+hydrodynamic+instabilities+to+paint+with+his+dripping+technique&rft.volume=14&rft.issue=10&rft.pages=e0223706&rft.date=2019-10-30&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC6821064%23id-name%3DPMC&rft_id=info%3Abibcode%2F2019PLoSO..1423706P&rft_id=info%3Apmid%2F31665191&rft_id=info%3Adoi%2F10.1371%2Fjournal.pone.0223706&rft.issn=1932-6203&rft.aulast=Palacios&rft.aufirst=Bernardo&rft.au=Rosario%2C+Alfonso&rft.au=Wilhelmus%2C+Monica+M.&rft.au=Zetina%2C+Sandra&rft.au=Zenit%2C+Roberto&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC6821064&rfr_id=info%3Asid%2Fen.wikipedia.org%3AStatistics" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Statistics&action=edit&section=34" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><div class="side-box metadata side-box-right"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"> <div class="side-box-abovebelow"> <a href="/wiki/Wikipedia:The_Wikipedia_Library" title="Wikipedia:The Wikipedia Library">Library resources</a> about <br /> <b>Statistics</b> <hr /></div> <div class="side-box-flex"> <div class="side-box-text plainlist"><ul><li><a class="external text" href="https://ftl.toolforge.org/cgi-bin/ftl?st=wp&su=Statistics">Resources in your library</a></li> </ul></div></div> </div> <ul><li>Lydia Denworth, "A Significant Problem: Standard scientific methods are under fire. Will anything change?", <i><a href="/wiki/Scientific_American" title="Scientific American">Scientific American</a></i>, vol. 321, no. 4 (October 2019), pp. 62–67. "The use of <a href="/wiki/P_value" class="mw-redirect" title="P value"><i>p</i> values</a> for nearly a century [since 1925] to determine <a href="/wiki/Statistical_significance" title="Statistical significance">statistical significance</a> of <a href="/wiki/Experiment" title="Experiment">experimental</a> results has contributed to an illusion of <a href="/wiki/Certainty" title="Certainty">certainty</a> and [to] <a href="/wiki/Replication_crisis" title="Replication crisis">reproducibility crises</a> in many <a href="/wiki/Science" title="Science">scientific fields</a>. There is growing determination to reform statistical analysis... Some [researchers] suggest changing statistical methods, whereas others would do away with a threshold for defining "significant" results." (p. 63.)</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBarbara_IllowskySusan_Dean2014" class="citation book cs1">Barbara Illowsky; Susan Dean (2014). <a rel="nofollow" class="external text" href="https://openstax.org/details/introductory-statistics"><i>Introductory Statistics</i></a>. OpenStax CNX. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1938168208" title="Special:BookSources/978-1938168208"><bdi>978-1938168208</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Introductory+Statistics&rft.pub=OpenStax+CNX&rft.date=2014&rft.isbn=978-1938168208&rft.au=Barbara+Illowsky&rft.au=Susan+Dean&rft_id=https%3A%2F%2Fopenstax.org%2Fdetails%2Fintroductory-statistics&rfr_id=info%3Asid%2Fen.wikipedia.org%3AStatistics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFStockburger" class="citation web cs1">Stockburger, David W. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20200528093101/http://psychstat3.missouristate.edu/Documents/IntroBook3/sbk.htm">"Introductory Statistics: Concepts, Models, and Applications"</a>. <i><a href="/wiki/Missouri_State_University" title="Missouri State University">Missouri State University</a></i> (3rd Web ed.). Archived from <a rel="nofollow" class="external text" href="http://psychstat3.missouristate.edu/Documents/IntroBook3/sbk.htm">the original</a> on 28 May 2020.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Missouri+State+University&rft.atitle=Introductory+Statistics%3A+Concepts%2C+Models%2C+and+Applications&rft.aulast=Stockburger&rft.aufirst=David+W.&rft_id=http%3A%2F%2Fpsychstat3.missouristate.edu%2FDocuments%2FIntroBook3%2Fsbk.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3AStatistics" class="Z3988"></span></li> <li><a rel="nofollow" class="external text" href="https://www.openintro.org/stat/textbook.php?stat_book=os"><i>OpenIntro Statistics</i></a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20190616110442/https://www.openintro.org/stat/textbook.php?stat_book=os">Archived</a> 2019-06-16 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>, 3rd edition by Diez, Barr, and Cetinkaya-Rundel</li> <li>Stephen Jones, 2010. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20170215092220/https://books.google.com/books?id=mywdBQAAQBAJ"><i>Statistics in Psychology: Explanations without Equations</i></a>. Palgrave Macmillan. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1137282392" title="Special:BookSources/978-1137282392">978-1137282392</a>.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCohen1990" class="citation journal cs1">Cohen, J (1990). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20171018181831/http://moityca.com.br/pdfs/Cohen_1990.pdf">"Things I have learned (so far)"</a> <span class="cs1-format">(PDF)</span>. <i>American Psychologist</i>. <b>45</b> (12): 1304–1312. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1037%2F0003-066x.45.12.1304">10.1037/0003-066x.45.12.1304</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:7180431">7180431</a>. Archived from <a rel="nofollow" class="external text" href="http://moityca.com.br/pdfs/Cohen_1990.pdf">the original</a> <span class="cs1-format">(PDF)</span> on 2017-10-18.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=American+Psychologist&rft.atitle=Things+I+have+learned+%28so+far%29&rft.volume=45&rft.issue=12&rft.pages=1304-1312&rft.date=1990&rft_id=info%3Adoi%2F10.1037%2F0003-066x.45.12.1304&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A7180431%23id-name%3DS2CID&rft.aulast=Cohen&rft.aufirst=J&rft_id=http%3A%2F%2Fmoityca.com.br%2Fpdfs%2FCohen_1990.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AStatistics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGigerenzer2004" class="citation journal cs1">Gigerenzer, G (2004). "Mindless statistics". <i>Journal of Socio-Economics</i>. <b>33</b> (5): 587–606. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.socec.2004.09.033">10.1016/j.socec.2004.09.033</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Socio-Economics&rft.atitle=Mindless+statistics&rft.volume=33&rft.issue=5&rft.pages=587-606&rft.date=2004&rft_id=info%3Adoi%2F10.1016%2Fj.socec.2004.09.033&rft.aulast=Gigerenzer&rft.aufirst=G&rfr_id=info%3Asid%2Fen.wikipedia.org%3AStatistics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFIoannidis2005" class="citation journal cs1">Ioannidis, J.P.A. (2005). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1855693">"Why most published research findings are false"</a>. <i>PLOS Medicine</i>. <b>2</b> (4): 696–701. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1371%2Fjournal.pmed.0040168">10.1371/journal.pmed.0040168</a></span>. <a href="/wiki/PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1855693">1855693</a></span>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/17456002">17456002</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=PLOS+Medicine&rft.atitle=Why+most+published+research+findings+are+false&rft.volume=2&rft.issue=4&rft.pages=696-701&rft.date=2005&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC1855693%23id-name%3DPMC&rft_id=info%3Apmid%2F17456002&rft_id=info%3Adoi%2F10.1371%2Fjournal.pmed.0040168&rft.aulast=Ioannidis&rft.aufirst=J.P.A.&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC1855693&rfr_id=info%3Asid%2Fen.wikipedia.org%3AStatistics" class="Z3988"></span></li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Statistics&action=edit&section=35" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1235681985"><style data-mw-deduplicate="TemplateStyles:r1250146164">.mw-parser-output .sister-box .side-box-abovebelow{padding:0.75em 0;text-align:center}.mw-parser-output .sister-box .side-box-abovebelow>b{display:block}.mw-parser-output .sister-box .side-box-text>ul{border-top:1px solid #aaa;padding:0.75em 0;width:217px;margin:0 auto}.mw-parser-output .sister-box .side-box-text>ul>li{min-height:31px}.mw-parser-output .sister-logo{display:inline-block;width:31px;line-height:31px;vertical-align:middle;text-align:center}.mw-parser-output .sister-link{display:inline-block;margin-left:4px;width:182px;vertical-align:middle}@media print{body.ns-0 .mw-parser-output .sistersitebox{display:none!important}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-v2.svg"]{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-v2.svg"]{background-color:white}}</style><div role="navigation" aria-labelledby="sister-projects" class="side-box metadata side-box-right sister-box sistersitebox plainlinks"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"> <div class="side-box-abovebelow"> <b>Statistics</b> at Wikipedia's <a href="/wiki/Wikipedia:Wikimedia_sister_projects" title="Wikipedia:Wikimedia sister projects"><span id="sister-projects">sister projects</span></a></div> <div class="side-box-flex"> <div class="side-box-text plainlist"><ul><li><span class="sister-logo"><span class="mw-valign-middle" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/0/06/Wiktionary-logo-v2.svg/27px-Wiktionary-logo-v2.svg.png" decoding="async" width="27" height="27" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/0/06/Wiktionary-logo-v2.svg/41px-Wiktionary-logo-v2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/0/06/Wiktionary-logo-v2.svg/54px-Wiktionary-logo-v2.svg.png 2x" data-file-width="391" data-file-height="391" /></span></span></span><span class="sister-link"><a href="https://en.wiktionary.org/wiki/Special:Search/Statistics" class="extiw" title="wikt:Special:Search/Statistics">Definitions</a> from Wiktionary</span></li><li><span class="sister-logo"><span class="mw-valign-middle" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/20px-Commons-logo.svg.png" decoding="async" width="20" height="27" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/40px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span></span><span class="sister-link"><a href="https://commons.wikimedia.org/wiki/Category:Statistics" class="extiw" title="c:Category:Statistics">Media</a> from Commons</span></li><li><span class="sister-logo"><span class="mw-valign-middle" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/2/24/Wikinews-logo.svg/27px-Wikinews-logo.svg.png" decoding="async" width="27" height="15" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/24/Wikinews-logo.svg/41px-Wikinews-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/24/Wikinews-logo.svg/54px-Wikinews-logo.svg.png 2x" data-file-width="759" data-file-height="415" /></span></span></span><span class="sister-link"><a href="https://en.wikinews.org/wiki/Special:Search/Statistics" class="extiw" title="n:Special:Search/Statistics">News</a> from Wikinews</span></li><li><span class="sister-logo"><span class="mw-valign-middle" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/23px-Wikiquote-logo.svg.png" decoding="async" width="23" height="27" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/35px-Wikiquote-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/46px-Wikiquote-logo.svg.png 2x" data-file-width="300" data-file-height="355" /></span></span></span><span class="sister-link"><a href="https://en.wikiquote.org/wiki/Statistics" class="extiw" title="q:Statistics">Quotations</a> from Wikiquote</span></li><li><span class="sister-logo"><span class="mw-valign-middle" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/26px-Wikisource-logo.svg.png" decoding="async" width="26" height="27" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/39px-Wikisource-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/51px-Wikisource-logo.svg.png 2x" data-file-width="410" data-file-height="430" /></span></span></span><span class="sister-link"><a href="https://en.wikisource.org/wiki/Special:Search/Statistics" class="extiw" title="s:Special:Search/Statistics">Texts</a> from Wikisource</span></li><li><span class="sister-logo"><span class="mw-valign-middle" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikibooks-logo.svg/27px-Wikibooks-logo.svg.png" decoding="async" width="27" height="27" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikibooks-logo.svg/41px-Wikibooks-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikibooks-logo.svg/54px-Wikibooks-logo.svg.png 2x" data-file-width="300" data-file-height="300" /></span></span></span><span class="sister-link"><a href="https://en.wikibooks.org/wiki/Statistics" class="extiw" title="b:Statistics">Textbooks</a> from Wikibooks</span></li><li><span class="sister-logo"><span class="mw-valign-middle" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0b/Wikiversity_logo_2017.svg/27px-Wikiversity_logo_2017.svg.png" decoding="async" width="27" height="22" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0b/Wikiversity_logo_2017.svg/41px-Wikiversity_logo_2017.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0b/Wikiversity_logo_2017.svg/54px-Wikiversity_logo_2017.svg.png 2x" data-file-width="626" data-file-height="512" /></span></span></span><span class="sister-link"><a href="https://en.wikiversity.org/wiki/Statistics/Introduction" class="extiw" title="v:Statistics/Introduction">Resources</a> from Wikiversity</span></li></ul></div></div> </div> <ul><li>(Electronic Version): TIBCO Software Inc. (2020). <a rel="nofollow" class="external text" href="https://docs.tibco.com/data-science/textbook">Data Science Textbook</a>.</li> <li><a rel="nofollow" class="external text" href="http://onlinestatbook.com/index.html"><i>Online Statistics Education: An Interactive Multimedia Course of Study</i></a>. Developed by Rice University (Lead Developer), University of Houston Clear Lake, Tufts University, and National Science Foundation.</li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20060717201702/http://www.ats.ucla.edu/stat/">UCLA Statistical Computing Resources</a> (archived 17 July 2006)</li> <li><a rel="nofollow" class="external text" href="https://plato.stanford.edu/entries/statistics/">Philosophy of Statistics</a> from the <a href="/wiki/Stanford_Encyclopedia_of_Philosophy" title="Stanford Encyclopedia of Philosophy">Stanford Encyclopedia of Philosophy</a></li></ul> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1236075235">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output 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.navbox-title{background-color:#ddf}.mw-parser-output .navbox-subgroup .navbox-group,.mw-parser-output .navbox-subgroup .navbox-abovebelow{background-color:#e6e6ff}.mw-parser-output .navbox-even{background-color:#f7f7f7}.mw-parser-output .navbox-odd{background-color:transparent}.mw-parser-output .navbox .hlist td dl,.mw-parser-output .navbox .hlist td ol,.mw-parser-output .navbox .hlist td ul,.mw-parser-output .navbox td.hlist dl,.mw-parser-output .navbox td.hlist ol,.mw-parser-output .navbox td.hlist ul{padding:0.125em 0}.mw-parser-output .navbox .navbar{display:block;font-size:100%}.mw-parser-output .navbox-title .navbar{float:left;text-align:left;margin-right:0.5em}body.skin--responsive .mw-parser-output .navbox-image img{max-width:none!important}@media print{body.ns-0 .mw-parser-output .navbox{display:none!important}}</style></div><div role="navigation" class="navbox" aria-labelledby="Statistics" style="padding:3px"><table class="nowraplinks hlist mw-collapsible expanded navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Statistics" title="Template:Statistics"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Statistics" title="Template talk:Statistics"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Statistics" title="Special:EditPage/Template:Statistics"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Statistics" style="font-size:114%;margin:0 4em"><a class="mw-selflink selflink">Statistics</a></div></th></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><a href="/wiki/Outline_of_statistics" title="Outline of statistics">Outline</a></li> <li><a href="/wiki/List_of_statistics_articles" title="List of statistics articles">Index</a></li></ul> </div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Descriptive_statistics" style="font-size:114%;margin:0 4em"><a href="/wiki/Descriptive_statistics" title="Descriptive statistics">Descriptive statistics</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Continuous_probability_distribution" class="mw-redirect" title="Continuous probability distribution">Continuous data</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/wiki/Central_tendency" title="Central tendency">Center</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Mean" title="Mean">Mean</a> <ul><li><a href="/wiki/Arithmetic_mean" title="Arithmetic mean">Arithmetic</a></li> <li><a href="/wiki/Arithmetic%E2%80%93geometric_mean" title="Arithmetic–geometric mean">Arithmetic-Geometric</a></li> <li><a href="/wiki/Contraharmonic_mean" title="Contraharmonic mean">Contraharmonic</a></li> <li><a href="/wiki/Cubic_mean" title="Cubic mean">Cubic</a></li> <li><a href="/wiki/Generalized_mean" title="Generalized mean">Generalized/power</a></li> <li><a href="/wiki/Geometric_mean" title="Geometric mean">Geometric</a></li> <li><a href="/wiki/Harmonic_mean" title="Harmonic mean">Harmonic</a></li> <li><a href="/wiki/Heronian_mean" title="Heronian mean">Heronian</a></li> <li><a href="/wiki/Heinz_mean" title="Heinz mean">Heinz</a></li> <li><a href="/wiki/Lehmer_mean" title="Lehmer mean">Lehmer</a></li></ul></li> <li><a href="/wiki/Median" title="Median">Median</a></li> <li><a href="/wiki/Mode_(statistics)" title="Mode (statistics)">Mode</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/wiki/Statistical_dispersion" title="Statistical dispersion">Dispersion</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Average_absolute_deviation" title="Average absolute deviation">Average absolute deviation</a></li> <li><a href="/wiki/Coefficient_of_variation" title="Coefficient of variation">Coefficient of variation</a></li> <li><a href="/wiki/Interquartile_range" title="Interquartile range">Interquartile range</a></li> <li><a href="/wiki/Percentile" title="Percentile">Percentile</a></li> <li><a href="/wiki/Range_(statistics)" title="Range (statistics)">Range</a></li> <li><a href="/wiki/Standard_deviation" title="Standard deviation">Standard deviation</a></li> <li><a href="/wiki/Variance#Sample_variance" title="Variance">Variance</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/wiki/Shape_of_the_distribution" class="mw-redirect" title="Shape of the distribution">Shape</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Central_limit_theorem" title="Central limit theorem">Central limit theorem</a></li> <li><a href="/wiki/Moment_(mathematics)" title="Moment (mathematics)">Moments</a> <ul><li><a href="/wiki/Kurtosis" title="Kurtosis">Kurtosis</a></li> <li><a href="/wiki/L-moment" title="L-moment">L-moments</a></li> <li><a href="/wiki/Skewness" title="Skewness">Skewness</a></li></ul></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Count_data" title="Count data">Count data</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Index_of_dispersion" title="Index of dispersion">Index of dispersion</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em">Summary tables</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Contingency_table" title="Contingency table">Contingency table</a></li> <li><a href="/wiki/Frequency_distribution" class="mw-redirect" title="Frequency distribution">Frequency distribution</a></li> <li><a href="/wiki/Grouped_data" title="Grouped data">Grouped data</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Correlation_and_dependence" class="mw-redirect" title="Correlation and dependence">Dependence</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Partial_correlation" title="Partial correlation">Partial correlation</a></li> <li><a href="/wiki/Pearson_correlation_coefficient" title="Pearson correlation coefficient">Pearson product-moment correlation</a></li> <li><a href="/wiki/Rank_correlation" title="Rank correlation">Rank correlation</a> <ul><li><a href="/wiki/Kendall_rank_correlation_coefficient" title="Kendall rank correlation coefficient">Kendall's τ</a></li> <li><a href="/wiki/Spearman%27s_rank_correlation_coefficient" title="Spearman's rank correlation coefficient">Spearman's ρ</a></li></ul></li> <li><a href="/wiki/Scatter_plot" title="Scatter plot">Scatter plot</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Statistical_graphics" title="Statistical graphics">Graphics</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bar_chart" title="Bar chart">Bar chart</a></li> <li><a href="/wiki/Biplot" title="Biplot">Biplot</a></li> <li><a href="/wiki/Box_plot" title="Box plot">Box plot</a></li> <li><a href="/wiki/Control_chart" title="Control chart">Control chart</a></li> <li><a href="/wiki/Correlogram" title="Correlogram">Correlogram</a></li> <li><a href="/wiki/Fan_chart_(statistics)" title="Fan chart (statistics)">Fan chart</a></li> <li><a href="/wiki/Forest_plot" title="Forest plot">Forest plot</a></li> <li><a href="/wiki/Histogram" title="Histogram">Histogram</a></li> <li><a href="/wiki/Pie_chart" title="Pie chart">Pie chart</a></li> <li><a href="/wiki/Q%E2%80%93Q_plot" title="Q–Q plot">Q–Q plot</a></li> <li><a href="/wiki/Radar_chart" title="Radar chart">Radar chart</a></li> <li><a href="/wiki/Run_chart" title="Run chart">Run chart</a></li> <li><a href="/wiki/Scatter_plot" title="Scatter plot">Scatter plot</a></li> <li><a href="/wiki/Stem-and-leaf_display" title="Stem-and-leaf display">Stem-and-leaf display</a></li> <li><a href="/wiki/Violin_plot" title="Violin plot">Violin plot</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Data_collection" style="font-size:114%;margin:0 4em"><a href="/wiki/Data_collection" title="Data collection">Data collection</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Design_of_experiments" title="Design of experiments">Study design</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Effect_size" title="Effect size">Effect size</a></li> <li><a href="/wiki/Missing_data" title="Missing data">Missing data</a></li> <li><a href="/wiki/Optimal_design" class="mw-redirect" title="Optimal design">Optimal design</a></li> <li><a href="/wiki/Statistical_population" title="Statistical population">Population</a></li> <li><a href="/wiki/Replication_(statistics)" title="Replication (statistics)">Replication</a></li> <li><a href="/wiki/Sample_size_determination" title="Sample size determination">Sample size determination</a></li> <li><a href="/wiki/Statistic" title="Statistic">Statistic</a></li> <li><a href="/wiki/Statistical_power" class="mw-redirect" title="Statistical power">Statistical power</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Survey_methodology" title="Survey methodology">Survey methodology</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Sampling_(statistics)" title="Sampling (statistics)">Sampling</a> <ul><li><a href="/wiki/Cluster_sampling" title="Cluster sampling">Cluster</a></li> <li><a href="/wiki/Stratified_sampling" title="Stratified sampling">Stratified</a></li></ul></li> <li><a href="/wiki/Opinion_poll" title="Opinion poll">Opinion poll</a></li> <li><a href="/wiki/Questionnaire" title="Questionnaire">Questionnaire</a></li> <li><a href="/wiki/Standard_error" title="Standard error">Standard error</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Experiment" title="Experiment">Controlled experiments</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Blocking_(statistics)" title="Blocking (statistics)">Blocking</a></li> <li><a href="/wiki/Factorial_experiment" title="Factorial experiment">Factorial experiment</a></li> <li><a href="/wiki/Interaction_(statistics)" title="Interaction (statistics)">Interaction</a></li> <li><a href="/wiki/Random_assignment" title="Random assignment">Random assignment</a></li> <li><a href="/wiki/Randomized_controlled_trial" title="Randomized controlled trial">Randomized controlled trial</a></li> <li><a href="/wiki/Randomized_experiment" title="Randomized experiment">Randomized experiment</a></li> <li><a href="/wiki/Scientific_control" title="Scientific control">Scientific control</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em">Adaptive designs</th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Adaptive_clinical_trial" class="mw-redirect" title="Adaptive clinical trial">Adaptive clinical trial</a></li> <li><a href="/wiki/Stochastic_approximation" title="Stochastic approximation">Stochastic approximation</a></li> <li><a href="/wiki/Up-and-Down_Designs" class="mw-redirect" title="Up-and-Down Designs">Up-and-down designs</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Observational_study" title="Observational study">Observational studies</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Cohort_study" title="Cohort study">Cohort study</a></li> <li><a href="/wiki/Cross-sectional_study" title="Cross-sectional study">Cross-sectional study</a></li> <li><a href="/wiki/Natural_experiment" title="Natural experiment">Natural experiment</a></li> <li><a href="/wiki/Quasi-experiment" title="Quasi-experiment">Quasi-experiment</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Statistical_inference" style="font-size:114%;margin:0 4em"><a href="/wiki/Statistical_inference" title="Statistical inference">Statistical inference</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Statistical_theory" title="Statistical theory">Statistical theory</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Population_(statistics)" class="mw-redirect" title="Population (statistics)">Population</a></li> <li><a href="/wiki/Statistic" title="Statistic">Statistic</a></li> <li><a href="/wiki/Probability_distribution" title="Probability distribution">Probability distribution</a></li> <li><a href="/wiki/Sampling_distribution" title="Sampling distribution">Sampling distribution</a> <ul><li><a href="/wiki/Order_statistic" title="Order statistic">Order statistic</a></li></ul></li> <li><a href="/wiki/Empirical_distribution_function" title="Empirical distribution function">Empirical distribution</a> <ul><li><a href="/wiki/Density_estimation" title="Density estimation">Density estimation</a></li></ul></li> <li><a href="/wiki/Statistical_model" title="Statistical model">Statistical model</a> <ul><li><a href="/wiki/Model_specification" class="mw-redirect" title="Model specification">Model specification</a></li> <li><a href="/wiki/Lp_space" title="Lp space">L<sup><i>p</i></sup> space</a></li></ul></li> <li><a href="/wiki/Statistical_parameter" title="Statistical parameter">Parameter</a> <ul><li><a href="/wiki/Location_parameter" title="Location parameter">location</a></li> <li><a href="/wiki/Scale_parameter" title="Scale parameter">scale</a></li> <li><a href="/wiki/Shape_parameter" title="Shape parameter">shape</a></li></ul></li> <li><a href="/wiki/Parametric_statistics" title="Parametric statistics">Parametric family</a> <ul><li><a href="/wiki/Likelihood_function" title="Likelihood function">Likelihood</a> <a href="/wiki/Monotone_likelihood_ratio" title="Monotone likelihood ratio"><span style="font-size:85%;">(monotone)</span></a></li> <li><a href="/wiki/Location%E2%80%93scale_family" title="Location–scale family">Location–scale family</a></li> <li><a href="/wiki/Exponential_family" title="Exponential family">Exponential family</a></li></ul></li> <li><a href="/wiki/Completeness_(statistics)" title="Completeness (statistics)">Completeness</a></li> <li><a href="/wiki/Sufficient_statistic" title="Sufficient statistic">Sufficiency</a></li> <li><a href="/wiki/Plug-in_principle" class="mw-redirect" title="Plug-in principle">Statistical functional</a> <ul><li><a href="/wiki/Bootstrapping_(statistics)" title="Bootstrapping (statistics)">Bootstrap</a></li> <li><a href="/wiki/U-statistic" title="U-statistic">U</a></li> <li><a href="/wiki/V-statistic" title="V-statistic">V</a></li></ul></li> <li><a href="/wiki/Optimal_decision" title="Optimal decision">Optimal decision</a> <ul><li><a href="/wiki/Loss_function" title="Loss function">loss function</a></li></ul></li> <li><a href="/wiki/Efficiency_(statistics)" title="Efficiency (statistics)">Efficiency</a></li> <li><a href="/wiki/Statistical_distance" title="Statistical distance">Statistical distance</a> <ul><li><a href="/wiki/Divergence_(statistics)" title="Divergence (statistics)">divergence</a></li></ul></li> <li><a href="/wiki/Asymptotic_theory_(statistics)" title="Asymptotic theory (statistics)">Asymptotics</a></li> <li><a href="/wiki/Robust_statistics" title="Robust statistics">Robustness</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Frequentist_inference" title="Frequentist inference">Frequentist inference</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/wiki/Point_estimation" title="Point estimation">Point estimation</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Estimating_equations" title="Estimating equations">Estimating equations</a> <ul><li><a href="/wiki/Maximum_likelihood" class="mw-redirect" title="Maximum likelihood">Maximum likelihood</a></li> <li><a href="/wiki/Method_of_moments_(statistics)" title="Method of moments (statistics)">Method of moments</a></li> <li><a href="/wiki/M-estimator" title="M-estimator">M-estimator</a></li> <li><a href="/wiki/Minimum_distance_estimation" class="mw-redirect" title="Minimum distance estimation">Minimum distance</a></li></ul></li> <li><a href="/wiki/Bias_of_an_estimator" title="Bias of an estimator">Unbiased estimators</a> <ul><li><a href="/wiki/Minimum-variance_unbiased_estimator" title="Minimum-variance unbiased estimator">Mean-unbiased minimum-variance</a> <ul><li><a href="/wiki/Rao%E2%80%93Blackwell_theorem" title="Rao–Blackwell theorem">Rao–Blackwellization</a></li> <li><a href="/wiki/Lehmann%E2%80%93Scheff%C3%A9_theorem" title="Lehmann–Scheffé theorem">Lehmann–Scheffé theorem</a></li></ul></li> <li><a href="/wiki/Median-unbiased_estimator" class="mw-redirect" title="Median-unbiased estimator">Median unbiased</a></li></ul></li> <li><a href="/wiki/Plug-in_principle" class="mw-redirect" title="Plug-in principle">Plug-in</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/wiki/Interval_estimation" title="Interval estimation">Interval estimation</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Confidence_interval" title="Confidence interval">Confidence interval</a></li> <li><a href="/wiki/Pivotal_quantity" title="Pivotal quantity">Pivot</a></li> <li><a href="/wiki/Likelihood_interval" class="mw-redirect" title="Likelihood interval">Likelihood interval</a></li> <li><a href="/wiki/Prediction_interval" title="Prediction interval">Prediction interval</a></li> <li><a href="/wiki/Tolerance_interval" title="Tolerance interval">Tolerance interval</a></li> <li><a href="/wiki/Resampling_(statistics)" title="Resampling (statistics)">Resampling</a> <ul><li><a href="/wiki/Bootstrapping_(statistics)" title="Bootstrapping (statistics)">Bootstrap</a></li> <li><a href="/wiki/Jackknife_resampling" title="Jackknife resampling">Jackknife</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/wiki/Statistical_hypothesis_testing" class="mw-redirect" title="Statistical hypothesis testing">Testing hypotheses</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/One-_and_two-tailed_tests" title="One- and two-tailed tests">1- & 2-tails</a></li> <li><a href="/wiki/Power_(statistics)" title="Power (statistics)">Power</a> <ul><li><a href="/wiki/Uniformly_most_powerful_test" title="Uniformly most powerful test">Uniformly most powerful test</a></li></ul></li> <li><a href="/wiki/Permutation_test" title="Permutation test">Permutation test</a> <ul><li><a href="/wiki/Randomization_test" class="mw-redirect" title="Randomization test">Randomization test</a></li></ul></li> <li><a href="/wiki/Multiple_comparisons" class="mw-redirect" title="Multiple comparisons">Multiple comparisons</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/wiki/Parametric_statistics" title="Parametric statistics">Parametric tests</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Likelihood-ratio_test" title="Likelihood-ratio test">Likelihood-ratio</a></li> <li><a href="/wiki/Score_test" title="Score test">Score/Lagrange multiplier</a></li> <li><a href="/wiki/Wald_test" title="Wald test">Wald</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/List_of_statistical_tests" title="List of statistical tests">Specific tests</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><td colspan="2" class="navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Z-test" title="Z-test"><i>Z</i>-test <span style="font-size:85%;">(normal)</span></a></li> <li><a href="/wiki/Student%27s_t-test" title="Student's t-test">Student's <i>t</i>-test</a></li> <li><a href="/wiki/F-test" title="F-test"><i>F</i>-test</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/wiki/Goodness_of_fit" title="Goodness of fit">Goodness of fit</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Chi-squared_test" title="Chi-squared test">Chi-squared</a></li> <li><a href="/wiki/G-test" title="G-test"><i>G</i>-test</a></li> <li><a href="/wiki/Kolmogorov%E2%80%93Smirnov_test" title="Kolmogorov–Smirnov test">Kolmogorov–Smirnov</a></li> <li><a href="/wiki/Anderson%E2%80%93Darling_test" title="Anderson–Darling test">Anderson–Darling</a></li> <li><a href="/wiki/Lilliefors_test" title="Lilliefors test">Lilliefors</a></li> <li><a href="/wiki/Jarque%E2%80%93Bera_test" title="Jarque–Bera test">Jarque–Bera</a></li> <li><a href="/wiki/Shapiro%E2%80%93Wilk_test" title="Shapiro–Wilk test">Normality <span style="font-size:85%;">(Shapiro–Wilk)</span></a></li> <li><a href="/wiki/Likelihood-ratio_test" title="Likelihood-ratio test">Likelihood-ratio test</a></li> <li><a href="/wiki/Model_selection" title="Model selection">Model selection</a> <ul><li><a href="/wiki/Cross-validation_(statistics)" title="Cross-validation (statistics)">Cross validation</a></li> <li><a href="/wiki/Akaike_information_criterion" title="Akaike information criterion">AIC</a></li> <li><a href="/wiki/Bayesian_information_criterion" title="Bayesian information criterion">BIC</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/wiki/Rank_statistics" class="mw-redirect" title="Rank statistics">Rank statistics</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Sign_test" title="Sign test">Sign</a> <ul><li><a href="/wiki/Sample_median" class="mw-redirect" title="Sample median">Sample median</a></li></ul></li> <li><a href="/wiki/Wilcoxon_signed-rank_test" title="Wilcoxon signed-rank test">Signed rank <span style="font-size:85%;">(Wilcoxon)</span></a> <ul><li><a href="/wiki/Hodges%E2%80%93Lehmann_estimator" title="Hodges–Lehmann estimator">Hodges–Lehmann estimator</a></li></ul></li> <li><a href="/wiki/Mann%E2%80%93Whitney_U_test" title="Mann–Whitney U test">Rank sum <span style="font-size:85%;">(Mann–Whitney)</span></a></li> <li><a href="/wiki/Nonparametric_statistics" title="Nonparametric statistics">Nonparametric</a> <a href="/wiki/Analysis_of_variance" title="Analysis of variance">anova</a> <ul><li><a href="/wiki/Kruskal%E2%80%93Wallis_test" title="Kruskal–Wallis test">1-way <span style="font-size:85%;">(Kruskal–Wallis)</span></a></li> <li><a href="/wiki/Friedman_test" title="Friedman test">2-way <span style="font-size:85%;">(Friedman)</span></a></li> <li><a href="/wiki/Jonckheere%27s_trend_test" title="Jonckheere's trend test">Ordered alternative <span style="font-size:85%;">(Jonckheere–Terpstra)</span></a></li></ul></li> <li><a href="/wiki/Van_der_Waerden_test" title="Van der Waerden test">Van der Waerden test</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Bayesian_inference" title="Bayesian inference">Bayesian inference</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bayesian_probability" title="Bayesian probability">Bayesian probability</a> <ul><li><a href="/wiki/Prior_probability" title="Prior probability">prior</a></li> <li><a href="/wiki/Posterior_probability" title="Posterior probability">posterior</a></li></ul></li> <li><a href="/wiki/Credible_interval" title="Credible interval">Credible interval</a></li> <li><a href="/wiki/Bayes_factor" title="Bayes factor">Bayes factor</a></li> <li><a href="/wiki/Bayes_estimator" title="Bayes estimator">Bayesian estimator</a> <ul><li><a href="/wiki/Maximum_a_posteriori_estimation" title="Maximum a posteriori estimation">Maximum posterior estimator</a></li></ul></li></ul> </div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="CorrelationRegression_analysis" style="font-size:114%;margin:0 4em"><div class="hlist"><ul><li><a href="/wiki/Correlation_and_dependence" class="mw-redirect" title="Correlation and dependence">Correlation</a></li><li><a href="/wiki/Regression_analysis" title="Regression analysis">Regression analysis</a></li></ul></div></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Correlation_and_dependence" class="mw-redirect" title="Correlation and dependence">Correlation</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Pearson_product-moment_correlation_coefficient" class="mw-redirect" title="Pearson product-moment correlation coefficient">Pearson product-moment</a></li> <li><a href="/wiki/Partial_correlation" title="Partial correlation">Partial correlation</a></li> <li><a href="/wiki/Confounding" title="Confounding">Confounding variable</a></li> <li><a href="/wiki/Coefficient_of_determination" title="Coefficient of determination">Coefficient of determination</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Regression_analysis" title="Regression analysis">Regression analysis</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Errors_and_residuals" title="Errors and residuals">Errors and residuals</a></li> <li><a href="/wiki/Regression_validation" title="Regression validation">Regression validation</a></li> <li><a href="/wiki/Mixed_model" title="Mixed model">Mixed effects models</a></li> <li><a href="/wiki/Simultaneous_equations_model" title="Simultaneous equations model">Simultaneous equations models</a></li> <li><a href="/wiki/Multivariate_adaptive_regression_splines" class="mw-redirect" title="Multivariate adaptive regression splines">Multivariate adaptive regression splines (MARS)</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Linear_regression" title="Linear regression">Linear regression</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Simple_linear_regression" title="Simple linear regression">Simple linear regression</a></li> <li><a href="/wiki/Ordinary_least_squares" title="Ordinary least squares">Ordinary least squares</a></li> <li><a href="/wiki/General_linear_model" title="General linear model">General linear model</a></li> <li><a href="/wiki/Bayesian_linear_regression" title="Bayesian linear regression">Bayesian regression</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em">Non-standard predictors</th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Nonlinear_regression" title="Nonlinear regression">Nonlinear regression</a></li> <li><a href="/wiki/Nonparametric_regression" title="Nonparametric regression">Nonparametric</a></li> <li><a href="/wiki/Semiparametric_regression" title="Semiparametric regression">Semiparametric</a></li> <li><a href="/wiki/Isotonic_regression" title="Isotonic regression">Isotonic</a></li> <li><a href="/wiki/Robust_regression" title="Robust regression">Robust</a></li> <li><a href="/wiki/Heteroscedasticity" class="mw-redirect" title="Heteroscedasticity">Heteroscedasticity</a></li> <li><a href="/wiki/Homoscedasticity" class="mw-redirect" title="Homoscedasticity">Homoscedasticity</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Generalized_linear_model" title="Generalized linear model">Generalized linear model</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Exponential_family" title="Exponential family">Exponential families</a></li> <li><a href="/wiki/Logistic_regression" title="Logistic regression">Logistic <span style="font-size:85%;">(Bernoulli)</span></a> / <a href="/wiki/Binomial_regression" title="Binomial regression">Binomial</a> / <a href="/wiki/Poisson_regression" title="Poisson regression">Poisson regressions</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Partition_of_sums_of_squares" title="Partition of sums of squares">Partition of variance</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Analysis_of_variance" title="Analysis of variance">Analysis of variance (ANOVA, anova)</a></li> <li><a href="/wiki/Analysis_of_covariance" title="Analysis of covariance">Analysis of covariance</a></li> <li><a href="/wiki/Multivariate_analysis_of_variance" title="Multivariate analysis of variance">Multivariate ANOVA</a></li> <li><a href="/wiki/Degrees_of_freedom_(statistics)" title="Degrees of freedom (statistics)">Degrees of freedom</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Categorical_/_Multivariate_/_Time-series_/_Survival_analysis" style="font-size:114%;margin:0 4em"><a href="/wiki/Categorical_variable" title="Categorical variable">Categorical</a> / <a href="/wiki/Multivariate_statistics" title="Multivariate statistics">Multivariate</a> / <a href="/wiki/Time_series" title="Time series">Time-series</a> / <a href="/wiki/Survival_analysis" title="Survival analysis">Survival analysis</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Categorical_variable" title="Categorical variable">Categorical</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Cohen%27s_kappa" title="Cohen's kappa">Cohen's kappa</a></li> <li><a href="/wiki/Contingency_table" title="Contingency table">Contingency table</a></li> <li><a href="/wiki/Graphical_model" title="Graphical model">Graphical model</a></li> <li><a href="/wiki/Poisson_regression" title="Poisson regression">Log-linear model</a></li> <li><a href="/wiki/McNemar%27s_test" title="McNemar's test">McNemar's test</a></li> <li><a href="/wiki/Cochran%E2%80%93Mantel%E2%80%93Haenszel_statistics" title="Cochran–Mantel–Haenszel statistics">Cochran–Mantel–Haenszel statistics</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Multivariate_statistics" title="Multivariate statistics">Multivariate</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/General_linear_model" title="General linear model">Regression</a></li> <li><a href="/wiki/Multivariate_analysis_of_variance" title="Multivariate analysis of variance">Manova</a></li> <li><a href="/wiki/Principal_component_analysis" title="Principal component analysis">Principal components</a></li> <li><a href="/wiki/Canonical_correlation" title="Canonical correlation">Canonical correlation</a></li> <li><a href="/wiki/Linear_discriminant_analysis" title="Linear discriminant analysis">Discriminant analysis</a></li> <li><a href="/wiki/Cluster_analysis" title="Cluster analysis">Cluster analysis</a></li> <li><a href="/wiki/Statistical_classification" title="Statistical classification">Classification</a></li> <li><a href="/wiki/Structural_equation_modeling" title="Structural equation modeling">Structural equation model</a> <ul><li><a href="/wiki/Factor_analysis" title="Factor analysis">Factor analysis</a></li></ul></li> <li><a href="/wiki/Multivariate_distribution" class="mw-redirect" title="Multivariate distribution">Multivariate distributions</a> <ul><li><a href="/wiki/Elliptical_distribution" title="Elliptical distribution">Elliptical distributions</a> <ul><li><a href="/wiki/Multivariate_normal_distribution" title="Multivariate normal distribution">Normal</a></li></ul></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Time_series" title="Time series">Time-series</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;">General</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Decomposition_of_time_series" title="Decomposition of time series">Decomposition</a></li> <li><a href="/wiki/Trend_estimation" class="mw-redirect" title="Trend estimation">Trend</a></li> <li><a href="/wiki/Stationary_process" title="Stationary process">Stationarity</a></li> <li><a href="/wiki/Seasonal_adjustment" title="Seasonal adjustment">Seasonal adjustment</a></li> <li><a href="/wiki/Exponential_smoothing" title="Exponential smoothing">Exponential smoothing</a></li> <li><a href="/wiki/Cointegration" title="Cointegration">Cointegration</a></li> <li><a href="/wiki/Structural_break" title="Structural break">Structural break</a></li> <li><a href="/wiki/Granger_causality" title="Granger causality">Granger causality</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;">Specific tests</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Dickey%E2%80%93Fuller_test" title="Dickey–Fuller test">Dickey–Fuller</a></li> <li><a href="/wiki/Johansen_test" title="Johansen test">Johansen</a></li> <li><a href="/wiki/Ljung%E2%80%93Box_test" title="Ljung–Box test">Q-statistic <span style="font-size:85%;">(Ljung–Box)</span></a></li> <li><a href="/wiki/Durbin%E2%80%93Watson_statistic" title="Durbin–Watson statistic">Durbin–Watson</a></li> <li><a href="/wiki/Breusch%E2%80%93Godfrey_test" title="Breusch–Godfrey test">Breusch–Godfrey</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/wiki/Time_domain" title="Time domain">Time domain</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Autocorrelation" title="Autocorrelation">Autocorrelation (ACF)</a> <ul><li><a href="/wiki/Partial_autocorrelation_function" title="Partial autocorrelation function">partial (PACF)</a></li></ul></li> <li><a href="/wiki/Cross-correlation" title="Cross-correlation">Cross-correlation (XCF)</a></li> <li><a href="/wiki/Autoregressive%E2%80%93moving-average_model" class="mw-redirect" title="Autoregressive–moving-average model">ARMA model</a></li> <li><a href="/wiki/Box%E2%80%93Jenkins_method" title="Box–Jenkins method">ARIMA model <span style="font-size:85%;">(Box–Jenkins)</span></a></li> <li><a href="/wiki/Autoregressive_conditional_heteroskedasticity" title="Autoregressive conditional heteroskedasticity">Autoregressive conditional heteroskedasticity (ARCH)</a></li> <li><a href="/wiki/Vector_autoregression" title="Vector autoregression">Vector autoregression (VAR)</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/wiki/Frequency_domain" title="Frequency domain">Frequency domain</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Spectral_density_estimation" title="Spectral density estimation">Spectral density estimation</a></li> <li><a href="/wiki/Fourier_analysis" title="Fourier analysis">Fourier analysis</a></li> <li><a href="/wiki/Least-squares_spectral_analysis" title="Least-squares spectral analysis">Least-squares spectral analysis</a></li> <li><a href="/wiki/Wavelet" title="Wavelet">Wavelet</a></li> <li><a href="/wiki/Whittle_likelihood" title="Whittle likelihood">Whittle likelihood</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:12.5em"><a href="/wiki/Survival_analysis" title="Survival analysis">Survival</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/wiki/Survival_function" title="Survival function">Survival function</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Kaplan%E2%80%93Meier_estimator" title="Kaplan–Meier estimator">Kaplan–Meier estimator (product limit)</a></li> <li><a href="/wiki/Proportional_hazards_model" title="Proportional hazards model">Proportional hazards models</a></li> <li><a href="/wiki/Accelerated_failure_time_model" title="Accelerated failure time model">Accelerated failure time (AFT) model</a></li> <li><a href="/wiki/First-hitting-time_model" title="First-hitting-time model">First hitting time</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/wiki/Failure_rate" title="Failure rate">Hazard function</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Nelson%E2%80%93Aalen_estimator" title="Nelson–Aalen estimator">Nelson–Aalen estimator</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;">Test</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Log-rank_test" class="mw-redirect" title="Log-rank test">Log-rank test</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Applications" style="font-size:114%;margin:0 4em"><a href="/wiki/List_of_fields_of_application_of_statistics" title="List of fields of application of statistics">Applications</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table 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style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Areas_of_mathematics" title="Template:Areas of mathematics"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Areas_of_mathematics" title="Template talk:Areas of mathematics"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Areas_of_mathematics" title="Special:EditPage/Template:Areas of mathematics"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Major_mathematics_areas" style="font-size:114%;margin:0 4em">Major <a href="/wiki/Mathematics" title="Mathematics">mathematics</a> areas</div></th></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><a href="/wiki/History_of_mathematics" title="History of mathematics">History</a> <ul><li><a href="/wiki/Timeline_of_mathematics" title="Timeline of mathematics">Timeline</a></li> <li><a href="/wiki/Future_of_mathematics" title="Future of mathematics">Future</a></li></ul></li> <li><a href="/wiki/Lists_of_mathematics_topics" title="Lists of mathematics topics">Lists</a></li> <li><a href="/wiki/Glossary_of_mathematical_symbols" title="Glossary of mathematical symbols">Glossary</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Foundations_of_mathematics" title="Foundations of mathematics">Foundations</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Category_theory" title="Category theory">Category theory</a></li> <li><a href="/wiki/Information_theory" title="Information theory">Information theory</a></li> <li><a href="/wiki/Mathematical_logic" title="Mathematical logic">Mathematical logic</a></li> <li><a href="/wiki/Philosophy_of_mathematics" title="Philosophy of mathematics">Philosophy of mathematics</a></li> <li><a href="/wiki/Set_theory" title="Set theory">Set theory</a></li> <li><a href="/wiki/Type_theory" title="Type theory">Type theory</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Algebra" title="Algebra">Algebra</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Abstract_algebra" title="Abstract algebra">Abstract</a></li> <li><a href="/wiki/Commutative_algebra" title="Commutative algebra">Commutative</a></li> <li><a href="/wiki/Elementary_algebra" title="Elementary algebra">Elementary</a></li> <li><a href="/wiki/Group_theory" title="Group theory">Group theory</a></li> <li><a href="/wiki/Linear_algebra" title="Linear algebra">Linear</a></li> <li><a href="/wiki/Multilinear_algebra" title="Multilinear algebra">Multilinear</a></li> <li><a href="/wiki/Universal_algebra" title="Universal algebra">Universal</a></li> <li><a href="/wiki/Homological_algebra" title="Homological algebra">Homological</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Mathematical_analysis" title="Mathematical analysis">Analysis</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Calculus" title="Calculus">Calculus</a></li> <li><a href="/wiki/Real_analysis" title="Real analysis">Real analysis</a></li> <li><a href="/wiki/Complex_analysis" title="Complex analysis">Complex analysis</a></li> <li><a href="/wiki/Hypercomplex_analysis" title="Hypercomplex analysis">Hypercomplex analysis</a></li> <li><a href="/wiki/Differential_equation" title="Differential equation">Differential equations</a></li> <li><a href="/wiki/Functional_analysis" title="Functional analysis">Functional analysis</a></li> <li><a href="/wiki/Harmonic_analysis" title="Harmonic analysis">Harmonic analysis</a></li> <li><a href="/wiki/Measure_(mathematics)" title="Measure (mathematics)">Measure theory</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Discrete_mathematics" title="Discrete mathematics">Discrete</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Combinatorics" title="Combinatorics">Combinatorics</a></li> <li><a href="/wiki/Graph_theory" title="Graph theory">Graph theory</a></li> <li><a href="/wiki/Order_theory" title="Order theory">Order theory</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Geometry" title="Geometry">Geometry</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Algebraic_geometry" title="Algebraic geometry">Algebraic</a></li> <li><a href="/wiki/Analytic_geometry" title="Analytic geometry">Analytic</a></li> <li><a href="/wiki/Arithmetic_geometry" title="Arithmetic geometry">Arithmetic</a></li> <li><a href="/wiki/Differential_geometry" title="Differential geometry">Differential</a></li> <li><a href="/wiki/Discrete_geometry" title="Discrete geometry">Discrete</a></li> <li><a href="/wiki/Euclidean_geometry" title="Euclidean geometry">Euclidean</a></li> <li><a href="/wiki/Finite_geometry" title="Finite geometry">Finite</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Number_theory" title="Number theory">Number theory</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Arithmetic" title="Arithmetic">Arithmetic</a></li> <li><a href="/wiki/Algebraic_number_theory" title="Algebraic number theory">Algebraic number theory</a></li> <li><a href="/wiki/Analytic_number_theory" title="Analytic number theory">Analytic number theory</a></li> <li><a href="/wiki/Diophantine_geometry" title="Diophantine geometry">Diophantine geometry</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Topology" title="Topology">Topology</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/General_topology" title="General topology">General</a></li> <li><a href="/wiki/Algebraic_topology" title="Algebraic topology">Algebraic</a></li> <li><a href="/wiki/Differential_topology" title="Differential topology">Differential</a></li> <li><a href="/wiki/Geometric_topology" title="Geometric topology">Geometric</a></li> <li><a href="/wiki/Homotopy_theory" title="Homotopy theory">Homotopy theory</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Applied_mathematics" title="Applied mathematics">Applied</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Engineering_mathematics" title="Engineering mathematics">Engineering mathematics</a></li> <li><a href="/wiki/Mathematical_and_theoretical_biology" title="Mathematical and theoretical biology">Mathematical biology</a></li> <li><a href="/wiki/Mathematical_chemistry" title="Mathematical chemistry">Mathematical chemistry</a></li> <li><a href="/wiki/Mathematical_economics" title="Mathematical economics">Mathematical economics</a></li> <li><a href="/wiki/Mathematical_finance" title="Mathematical finance">Mathematical finance</a></li> <li><a href="/wiki/Mathematical_physics" title="Mathematical physics">Mathematical physics</a></li> <li><a href="/wiki/Mathematical_psychology" title="Mathematical psychology">Mathematical psychology</a></li> <li><a href="/wiki/Mathematical_sociology" title="Mathematical sociology">Mathematical sociology</a></li> <li><a href="/wiki/Mathematical_statistics" title="Mathematical statistics">Mathematical statistics</a></li> <li><a href="/wiki/Probability_theory" title="Probability theory">Probability</a></li> <li><a class="mw-selflink selflink">Statistics</a></li> <li><a href="/wiki/Systems_science" title="Systems science">Systems science</a> <ul><li><a href="/wiki/Control_theory" title="Control theory">Control theory</a></li> <li><a href="/wiki/Game_theory" title="Game theory">Game theory</a></li> <li><a href="/wiki/Operations_research" title="Operations research">Operations research</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Computational_mathematics" 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title="Glossary of computer hardware terms">Computer hardware</a></li> <li><a href="/wiki/Glossary_of_computer_science" title="Glossary of computer science">Computer science</a></li> <li><a href="/wiki/Glossary_of_developmental_biology" title="Glossary of developmental biology">Developmental and reproductive biology</a></li> <li><a href="/wiki/Glossary_of_ecology" title="Glossary of ecology">Ecology</a></li> <li><a href="/wiki/Glossary_of_economics" title="Glossary of economics">Economics</a></li> <li><a href="/wiki/Glossary_of_electrical_and_electronics_engineering" title="Glossary of electrical and electronics engineering">Electrical and electronics engineering</a></li> <li>Engineering <ul><li><a href="/wiki/Glossary_of_engineering:_A%E2%80%93L" title="Glossary of engineering: A–L">A–L</a></li> <li><a href="/wiki/Glossary_of_engineering:_M%E2%80%93Z" title="Glossary of engineering: M–Z">M–Z</a></li></ul></li> <li><a href="/wiki/Glossary_of_entomology_terms" title="Glossary of entomology terms">Entomology</a></li> <li><a href="/wiki/Glossary_of_environmental_science" title="Glossary of environmental science">Environmental science</a></li> <li><a href="/wiki/Glossary_of_genetics_and_evolutionary_biology" title="Glossary of genetics and evolutionary biology">Genetics and evolutionary biology</a></li> <li>Cellular and molecular biology <ul><li><a href="/wiki/Glossary_of_cellular_and_molecular_biology_(0%E2%80%93L)" title="Glossary of cellular and molecular biology (0–L)">0–L</a></li> <li><a href="/wiki/Glossary_of_cellular_and_molecular_biology_(M%E2%80%93Z)" title="Glossary of cellular and molecular biology (M–Z)">M–Z</a></li></ul></li> <li>Geography <ul><li><a href="/wiki/Glossary_of_geography_terms_(A%E2%80%93M)" title="Glossary of geography terms (A–M)">A–M</a></li> <li><a href="/wiki/Glossary_of_geography_terms_(N%E2%80%93Z)" title="Glossary of geography terms (N–Z)">N–Z</a></li> <li><a href="/wiki/Glossary_of_Arabic_toponyms" title="Glossary of Arabic 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