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</button> <ul id="toc-Standard_definition-sublist" class="vector-toc-list"> <li id="toc-Establishment_methods" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Establishment_methods"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Establishment methods</span> </div> </a> <ul id="toc-Establishment_methods-sublist" class="vector-toc-list"> <li id="toc-Normal_distribution" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Normal_distribution"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1.1</span> <span>Normal distribution</span> </div> </a> <ul id="toc-Normal_distribution-sublist" class="vector-toc-list"> <li id="toc-Confidence_interval_of_limit" class="vector-toc-list-item vector-toc-level-4"> <a class="vector-toc-link" href="#Confidence_interval_of_limit"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1.1.1</span> <span>Confidence interval of limit</span> </div> </a> <ul id="toc-Confidence_interval_of_limit-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Log-normal_distribution" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Log-normal_distribution"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1.2</span> <span>Log-normal distribution</span> </div> </a> <ul id="toc-Log-normal_distribution-sublist" class="vector-toc-list"> <li id="toc-Necessity" class="vector-toc-list-item vector-toc-level-4"> <a class="vector-toc-link" href="#Necessity"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1.2.1</span> <span>Necessity</span> </div> </a> <ul id="toc-Necessity-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-From_logarithmized_sample_values" class="vector-toc-list-item vector-toc-level-4"> <a class="vector-toc-link" href="#From_logarithmized_sample_values"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1.2.2</span> <span>From logarithmized sample values</span> </div> </a> <ul id="toc-From_logarithmized_sample_values-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-From_arithmetic_mean_and_variance" class="vector-toc-list-item vector-toc-level-4"> <a class="vector-toc-link" href="#From_arithmetic_mean_and_variance"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1.2.3</span> <span>From arithmetic mean and variance</span> </div> </a> <ul id="toc-From_arithmetic_mean_and_variance-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Directly_from_percentages_of_interest" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Directly_from_percentages_of_interest"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1.3</span> <span>Directly from percentages of interest</span> </div> </a> <ul id="toc-Directly_from_percentages_of_interest-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Bimodal_distribution" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Bimodal_distribution"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1.4</span> <span>Bimodal distribution</span> </div> </a> <ul id="toc-Bimodal_distribution-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Interpretation_of_standard_ranges_in_medical_tests" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Interpretation_of_standard_ranges_in_medical_tests"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Interpretation of standard ranges in medical tests</span> </div> </a> <ul id="toc-Interpretation_of_standard_ranges_in_medical_tests-sublist" class="vector-toc-list"> <li id="toc-Probability_of_random_variability" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Probability_of_random_variability"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2.1</span> <span>Probability of random variability</span> </div> </a> <ul id="toc-Probability_of_random_variability-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Example" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Example"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2.2</span> <span>Example</span> </div> </a> <ul id="toc-Example-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </li> <li id="toc-Optimal_health_range" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Optimal_health_range"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Optimal health range</span> </div> </a> <ul id="toc-Optimal_health_range-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-One-sided_cut-off_values" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#One-sided_cut-off_values"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>One-sided cut-off values</span> </div> </a> <ul id="toc-One-sided_cut-off_values-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-General_drawbacks" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#General_drawbacks"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>General drawbacks</span> </div> </a> <ul id="toc-General_drawbacks-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Examples" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Examples"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Examples</span> </div> </a> <ul id="toc-Examples-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</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 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</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 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Further reading</span> </div> </a> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main 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href="https://bs.wikipedia.org/wiki/Referentni_raspon" title="Referentni raspon – Bosnian" lang="bs" hreflang="bs" data-title="Referentni raspon" data-language-autonym="Bosanski" data-language-local-name="Bosnian" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Referenzbereich_(Medizin)" title="Referenzbereich (Medizin) – German" lang="de" hreflang="de" data-title="Referenzbereich (Medizin)" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%B1%D9%86%D8%AC_%D9%85%D8%B1%D8%AC%D8%B9" title="رنج مرجع – Persian" lang="fa" hreflang="fa" data-title="رنج مرجع" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Valeurs_de_r%C3%A9f%C3%A9rence_pour_les_principaux_tests_biologiques" title="Valeurs de référence pour les principaux tests biologiques – French" lang="fr" hreflang="fr" data-title="Valeurs de référence pour les principaux tests biologiques" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EA%B8%B0%EC%A4%80%EC%B9%98" title="기준치 – Korean" lang="ko" hreflang="ko" data-title="기준치" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Normaalwaarde" title="Normaalwaarde – Dutch" lang="nl" hreflang="nl" data-title="Normaalwaarde" data-language-autonym="Nederlands" 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style="display:none">Measured values that are relatively normal for a particular medical test</div> <style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist dt::after{content:": "}.mw-parser-output .hlist dd::after,.mw-parser-output .hlist li::after{content:" · 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.sidebar:not(.notheme) .sidebar-list-title,html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-list-title,html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media print{body.ns-0 .mw-parser-output .sidebar{display:none!important}}</style><table class="sidebar nomobile nowraplinks" style="width:auto"><tbody><tr><th class="sidebar-title" style="font-size:115%;background:#ccccff;"><a class="mw-selflink selflink">Reference<br />ranges</a></th></tr><tr><td class="sidebar-content" style="text-align:left"> <p>In: </p> <ul><li><a href="/wiki/Reference_ranges_for_blood_tests" title="Reference ranges for blood tests">Blood</a></li> <li><a href="/wiki/Urinalysis#Target_parameters" title="Urinalysis">Urine</a></li> <li><a href="/wiki/List_of_reference_ranges_for_cerebrospinal_fluid" title="List of reference ranges for cerebrospinal fluid">CSF</a></li> <li><a href="/wiki/Human_feces#Fecal_markers" title="Human feces">Feces</a></li> <li><a href="/wiki/Vital_signs#Variations_by_age" title="Vital signs">Vital signs</a></li></ul></td> </tr><tr><td class="sidebar-navbar"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Reference_ranges" title="Template:Reference ranges"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Reference_ranges" title="Template talk:Reference ranges"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Reference_ranges" title="Special:EditPage/Template:Reference ranges"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table> <p>In <a href="/wiki/Medicine" title="Medicine">medicine</a> and <a href="/wiki/Health" title="Health">health</a>-related fields, a <b>reference range</b> or <b>reference interval</b> is the <a href="/wiki/Range_(statistics)" title="Range (statistics)">range</a> or the <a href="/wiki/Interval_(mathematics)" title="Interval (mathematics)">interval</a> of values that is deemed normal for a <a href="/wiki/Physiology" title="Physiology">physiological</a> measurement in healthy persons (for example, the amount of <a href="/wiki/Creatinine" title="Creatinine">creatinine</a> in the <a href="/wiki/Blood" title="Blood">blood</a>, or the <a href="/wiki/Blood_gas_tension" title="Blood gas tension">partial pressure of oxygen</a>). It is a basis for comparison for a <a href="/wiki/Physician" title="Physician">physician</a> or other <a href="/wiki/Health_professional" title="Health professional">health professional</a> to interpret a set of test results for a particular patient. Some important reference ranges in medicine are <a href="/wiki/Reference_ranges_for_blood_tests" title="Reference ranges for blood tests">reference ranges for blood tests</a> and <a href="/wiki/Urinalysis#Target_parameters" title="Urinalysis">reference ranges for urine tests</a>. </p><p>The standard definition of a reference range (usually referred to if not otherwise specified) originates in what is most prevalent in a <a href="/wiki/Reference_group" class="mw-redirect" title="Reference group">reference group</a> taken from the general (i.e. total) population. This is the general reference range. However, there are also <i>optimal health ranges</i> (ranges that appear to have the optimal health impact) and ranges for particular conditions or statuses (such as pregnancy reference ranges for hormone levels). </p><p>Values <b>within the reference range</b> (<b>WRR</b>) are those <b>within normal limits</b> (<b>WNL</b>). The limits are called the <i>upper reference limit</i> (URL) or <i>upper limit of normal</i> (ULN) and the <i>lower reference limit</i> (LRL) or <i>lower limit of normal</i> (LLN). In <a href="/wiki/Health_care" title="Health care">health care</a>–related publishing, <a href="/wiki/Style_guide" title="Style guide">style sheets</a> sometimes prefer the word <i>reference</i> over the word <i>normal</i> to prevent the nontechnical <a href="/wiki/Word_sense" title="Word sense">senses</a> of <i>normal</i> from being conflated with the statistical sense. Values outside a reference range are not <a href="https://en.wiktionary.org/wiki/in_and_of_itself#Adverb" class="extiw" title="wikt:in and of itself">necessarily</a> pathologic, and they are not necessarily abnormal in any sense other than statistically. Nonetheless, they are indicators of probable pathosis. Sometimes the underlying cause is obvious; in other cases, challenging <a href="/wiki/Differential_diagnosis" title="Differential diagnosis">differential diagnosis</a> is required to determine what is wrong and thus how to treat it. </p><p>A <b>cutoff</b> or <b>threshold</b> is a limit used for <a href="/wiki/Binary_classification" title="Binary classification">binary classification</a>, mainly between normal versus pathological (or probably pathological). Establishment methods for cutoffs include using an upper or a lower limit of a reference range. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Standard_definition">Standard definition</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Reference_range&action=edit&section=1" title="Edit section: Standard definition"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The standard definition of a reference range for a particular measurement is defined as the interval between which 95% of values of a reference population fall into, in such a way that 2.5% of the time a value will be less than the lower limit of this interval, and 2.5% of the time it will be larger than the upper limit of this interval, whatever the distribution of these values.<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> </p><p>Reference ranges that are given by this definition are sometimes referred as <i>standard ranges</i>. </p><p>Since a range is a defined statistical value (<a href="/wiki/Range_(statistics)" title="Range (statistics)">Range (statistics)</a>) that describes the interval between the smallest and largest values, many, including the International Federation of Clinical Chemistry prefer to use the expression reference interval rather than reference range.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p><p>Regarding the target population, if not otherwise specified, a standard reference range generally denotes the one in healthy individuals, or without any known condition that directly affects the ranges being established. These are likewise established using reference groups from the healthy population, and are sometimes termed <i>normal ranges</i> or <i>normal values</i> (and sometimes "usual" ranges/values). However, using the term <i>normal</i> may not be appropriate as not everyone outside the interval is abnormal, and people who have a particular condition may still fall within this interval. </p><p>However, reference ranges may also be established by taking samples from the whole population, with or without diseases and conditions. In some cases, diseased individuals are taken as the population, establishing reference ranges among those having a disease or condition. Preferably, there should be specific reference ranges for each subgroup of the population that has any factor that affects the measurement, such as, for example, specific ranges for each <i>sex</i>, <i>age group</i>, <i>race</i> or any other <a href="/wiki/General_determinant" class="mw-redirect" title="General determinant">general determinant</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Establishment_methods">Establishment methods</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Reference_range&action=edit&section=2" title="Edit section: Establishment methods"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Methods for establishing reference ranges can be based on assuming a <a href="/wiki/Normal_distribution" title="Normal distribution">normal distribution</a> or a <a href="/wiki/Log-normal_distribution" title="Log-normal distribution">log-normal distribution</a>, or directly from percentages of interest, as detailed respectively in following sections. When establishing reference ranges from bilateral organs (e.g., vision or hearing), both results from the same individual can be used, although intra-subject correlation must be taken into account.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Normal_distribution">Normal distribution</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Reference_range&action=edit&section=3" title="Edit section: Normal distribution"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></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">Further information: <a href="/wiki/68%E2%80%9395%E2%80%9399.7_rule" title="68–95–99.7 rule">68–95–99.7 rule</a></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Standard_deviation_diagram.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8c/Standard_deviation_diagram.svg/350px-Standard_deviation_diagram.svg.png" decoding="async" width="350" height="175" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8c/Standard_deviation_diagram.svg/525px-Standard_deviation_diagram.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8c/Standard_deviation_diagram.svg/700px-Standard_deviation_diagram.svg.png 2x" data-file-width="400" data-file-height="200" /></a><figcaption>When assuming a normal distribution, the reference range is obtained by measuring the values in a reference group and taking two standard deviations either side of the mean. This encompasses ~95% of the total population.</figcaption></figure> <p>The 95% interval, is often estimated by assuming a <a href="/wiki/Normal_distribution" title="Normal distribution">normal distribution</a> of the measured parameter, in which case it can be defined as the interval limited by 1.96<sup id="cite_ref-MedicalStatistics_4-0" class="reference"><a href="#cite_note-MedicalStatistics-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> (often rounded up to 2) population <a href="/wiki/Standard_deviation" title="Standard deviation">standard deviations</a> from either side of the population mean (also called the <a href="/wiki/Expected_value" title="Expected value">expected value</a>). However, in the real world, neither the population mean nor the population standard deviation are known. They both need to be estimated from a sample, whose size can be designated <i>n</i>. The population standard deviation is estimated by the sample standard deviation and the population mean is estimated by the sample mean (also called mean or <a href="/wiki/Arithmetic_mean" title="Arithmetic mean">arithmetic mean</a>). To account for these estimations, the 95% <a href="/wiki/Prediction_interval" title="Prediction interval">prediction interval</a> (95% PI) is calculated as: </p> <dl><dd><span class="texhtml">95% PI = mean ± <i>t</i><sub>0.975,<i>n</i>−1</sub>·<span class="nowrap">√<span style="border-top:1px solid; padding:0 0.1em;">(<i>n</i>+1)/<i>n</i></span></span>·sd</span>,</dd></dl> <p>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t_{0.975,n-1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0.975</mn> <mo>,</mo> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t_{0.975,n-1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/69fc56dbc6a180ffacdf9b8e98d338aaa731c483" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:8.361ex; height:2.676ex;" alt="{\displaystyle t_{0.975,n-1}}"></span> is the 97.5% quantile of a <a href="/wiki/Student%27s_t-distribution" title="Student's t-distribution">Student's t-distribution</a> with <i>n</i>−1 <a href="/wiki/Degrees_of_freedom_(statistics)" title="Degrees of freedom (statistics)">degrees of freedom</a>. </p><p>When the sample size is large (<i>n</i>≥30) <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t_{0.975,n-1}\simeq 2.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0.975</mn> <mo>,</mo> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> </msub> <mo>≃</mo> <mn>2.</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t_{0.975,n-1}\simeq 2.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3158d729582b6f87168d22590425be2eafe8f680" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:13.269ex; height:2.843ex;" alt="{\displaystyle t_{0.975,n-1}\simeq 2.}"></span> </p><p>This method is often acceptably accurate if the standard deviation, as compared to the mean, is not very large. A more accurate method is to perform the calculations on logarithmized values, as described in separate section later. </p><p>The following example of this (<i>not</i> logarithmized) method is based on values of <a href="/wiki/Fasting_plasma_glucose" class="mw-redirect" title="Fasting plasma glucose">fasting plasma glucose</a> taken from a reference group of 12 subjects:<sup id="cite_ref-Keevil1998_5-0" class="reference"><a href="#cite_note-Keevil1998-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p> <table class="wikitable"> <tbody><tr> <th></th> <th><a href="/wiki/Fasting_plasma_glucose" class="mw-redirect" title="Fasting plasma glucose">Fasting plasma glucose</a><br /> (FPG) <br />in mmol/L</th> <th>Deviation from<br /> mean <i>m</i></th> <th>Squared deviation<br />from mean <i>m</i> </th></tr> <tr> <td>Subject 1</td> <td>5.5</td> <td>0.17</td> <td>0.029 </td></tr> <tr> <td>Subject 2</td> <td>5.2</td> <td>-0.13</td> <td>0.017 </td></tr> <tr> <td>Subject 3</td> <td>5.2</td> <td>-0.13</td> <td>0.017 </td></tr> <tr> <td>Subject 4</td> <td>5.8</td> <td>0.47</td> <td>0.221 </td></tr> <tr> <td>Subject 5</td> <td>5.6</td> <td>0.27</td> <td>0.073 </td></tr> <tr> <td>Subject 6</td> <td>4.6</td> <td>-0.73</td> <td>0.533 </td></tr> <tr> <td>Subject 7</td> <td>5.6</td> <td>0.27</td> <td>0.073 </td></tr> <tr> <td>Subject 8</td> <td>5.9</td> <td>0.57</td> <td>0.325 </td></tr> <tr> <td>Subject 9</td> <td>4.7</td> <td>-0.63</td> <td>0.397 </td></tr> <tr> <td>Subject 10</td> <td>5</td> <td>-0.33</td> <td>0.109 </td></tr> <tr> <td>Subject 11</td> <td>5.7</td> <td>0.37</td> <td>0.137 </td></tr> <tr> <td>Subject 12</td> <td>5.2</td> <td>-0.13</td> <td>0.017 </td></tr> <tr> <td></td> <td><b>Mean = 5.33</b> (<i>m</i>) <br /> <i>n</i>=12</td> <td>Mean = 0.00</td> <td>Sum/(<i>n</i>−1) = 1.95/11 =0.18 <br /> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\sqrt {0.18}}=0.42}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>0.18</mn> </msqrt> </mrow> <mo>=</mo> <mn>0.42</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\sqrt {0.18}}=0.42}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ff67414807677799cefc4aedf9b472545ebcf335" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:13.303ex; height:2.843ex;" alt="{\displaystyle {\sqrt {0.18}}=0.42}"></span><br />= <b>standard deviation (s.d.)</b> </td></tr></tbody></table> <p>As can be given from, for example, a <a href="/wiki/Student%27s_t-distribution#Table_of_selected_values" title="Student's t-distribution">table of selected values of Student's t-distribution</a>, the 97.5% percentile with (12-1) degrees of freedom corresponds to <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t_{0.975,11}=2.20}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0.975</mn> <mo>,</mo> <mn>11</mn> </mrow> </msub> <mo>=</mo> <mn>2.20</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t_{0.975,11}=2.20}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a8bbadee90329ce16b52e4d3555ee295c1968737" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:14.151ex; height:2.843ex;" alt="{\displaystyle t_{0.975,11}=2.20}"></span> </p><p>Subsequently, the lower and upper limits of the standard reference range are calculated as: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Lower~limit=m-t_{0.975,11}\times {\sqrt {\frac {n+1}{n}}}\times s.d.=5.33-2.20\times {\sqrt {\frac {13}{12}}}\times 0.42=4.4}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> <mi>o</mi> <mi>w</mi> <mi>e</mi> <mi>r</mi> <mtext> </mtext> <mi>l</mi> <mi>i</mi> <mi>m</mi> <mi>i</mi> <mi>t</mi> <mo>=</mo> <mi>m</mi> <mo>−</mo> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0.975</mn> <mo>,</mo> <mn>11</mn> </mrow> </msub> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <mrow> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>n</mi> </mfrac> </msqrt> </mrow> <mo>×</mo> <mi>s</mi> <mo>.</mo> <mi>d</mi> <mo>.</mo> <mo>=</mo> <mn>5.33</mn> <mo>−</mo> <mn>2.20</mn> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <mn>13</mn> <mn>12</mn> </mfrac> </msqrt> </mrow> <mo>×</mo> <mn>0.42</mn> <mo>=</mo> <mn>4.4</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Lower~limit=m-t_{0.975,11}\times {\sqrt {\frac {n+1}{n}}}\times s.d.=5.33-2.20\times {\sqrt {\frac {13}{12}}}\times 0.42=4.4}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a969b37e2aef928fcea553d01461528ef8e2967c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:80.708ex; height:6.176ex;" alt="{\displaystyle Lower~limit=m-t_{0.975,11}\times {\sqrt {\frac {n+1}{n}}}\times s.d.=5.33-2.20\times {\sqrt {\frac {13}{12}}}\times 0.42=4.4}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Upper~limit=m+t_{0.975,11}\times {\sqrt {\frac {n+1}{n}}}\times s.d.=5.33+2.20\times {\sqrt {\frac {13}{12}}}\times 0.42=6.3.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>U</mi> <mi>p</mi> <mi>p</mi> <mi>e</mi> <mi>r</mi> <mtext> </mtext> <mi>l</mi> <mi>i</mi> <mi>m</mi> <mi>i</mi> <mi>t</mi> <mo>=</mo> <mi>m</mi> <mo>+</mo> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0.975</mn> <mo>,</mo> <mn>11</mn> </mrow> </msub> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <mrow> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>n</mi> </mfrac> </msqrt> </mrow> <mo>×</mo> <mi>s</mi> <mo>.</mo> <mi>d</mi> <mo>.</mo> <mo>=</mo> <mn>5.33</mn> <mo>+</mo> <mn>2.20</mn> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <mn>13</mn> <mn>12</mn> </mfrac> </msqrt> </mrow> <mo>×</mo> <mn>0.42</mn> <mo>=</mo> <mn>6.3.</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Upper~limit=m+t_{0.975,11}\times {\sqrt {\frac {n+1}{n}}}\times s.d.=5.33+2.20\times {\sqrt {\frac {13}{12}}}\times 0.42=6.3.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c45c9b00c2328ebc37c203f0c5fb08366e64ed3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:81.102ex; height:6.176ex;" alt="{\displaystyle Upper~limit=m+t_{0.975,11}\times {\sqrt {\frac {n+1}{n}}}\times s.d.=5.33+2.20\times {\sqrt {\frac {13}{12}}}\times 0.42=6.3.}"></span></dd></dl> <p>Thus, the standard reference range for this example is estimated to be 4.4 to 6.3 mmol/L. </p> <div class="mw-heading mw-heading5"><h5 id="Confidence_interval_of_limit">Confidence interval of limit</h5><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Reference_range&action=edit&section=4" title="Edit section: Confidence interval of limit"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The 90% <i>confidence interval of a standard reference range limit</i> as estimated assuming a normal distribution can be calculated by:<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> </p> <dl><dd>Lower limit of the confidence interval = percentile limit - 2.81 × <style data-mw-deduplicate="TemplateStyles:r1154941027">.mw-parser-output .frac{white-space:nowrap}.mw-parser-output .frac .num,.mw-parser-output .frac .den{font-size:80%;line-height:0;vertical-align:super}.mw-parser-output .frac .den{vertical-align:sub}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}</style><span class="frac"><span class="num"><i>SD</i></span>⁄<span class="den"><span class="nowrap">√<span style="border-top:1px solid; padding:0 0.1em;"><i>n</i></span></span></span></span></dd></dl> <dl><dd>Upper limit of the confidence interval = percentile limit + 2.81 × <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac"><span class="num"><i>SD</i></span>⁄<span class="den"><span class="nowrap">√<span style="border-top:1px solid; padding:0 0.1em;"><i>n</i></span></span></span></span>,</dd></dl> <p>where SD is the standard deviation, and n is the number of samples. </p><p>Taking the example from the previous section, the number of samples is 12 and the standard deviation is 0.42 mmol/L, resulting in: </p> <dl><dd><i>Lower limit of the confidence interval</i> of the <i>lower limit of the standard reference range</i> = 4.4 - 2.81 × <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac"><span class="num">0.42</span>⁄<span class="den"><span class="nowrap">√<span style="border-top:1px solid; padding:0 0.1em;">12</span></span></span></span> ≈ 4.1</dd></dl> <dl><dd><i>Upper limit of the confidence interval</i> of the <i>lower limit of the standard reference range</i> = 4.4 + 2.81 × <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1154941027"><span class="frac"><span class="num">0.42</span>⁄<span class="den"><span class="nowrap">√<span style="border-top:1px solid; padding:0 0.1em;">12</span></span></span></span> ≈ 4.7</dd></dl> <p>Thus, the lower limit of the reference range can be written as 4.4 (90% CI 4.1–4.7) mmol/L. </p><p>Likewise, with similar calculations, the upper limit of the reference range can be written as 6.3 (90% CI 6.0–6.6) mmol/L. </p><p>These confidence intervals reflect <a href="/wiki/Random_error" class="mw-redirect" title="Random error">random error</a>, but do not compensate for <a href="/wiki/Systematic_error" class="mw-redirect" title="Systematic error">systematic error</a>, which in this case can arise from, for example, the reference group not having fasted long enough before blood sampling. </p><p>As a comparison, actual reference ranges used clinically for fasting plasma glucose are estimated to have a lower limit of approximately 3.8<sup id="cite_ref-firstaid_7-0" class="reference"><a href="#cite_note-firstaid-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> to 4.0,<sup id="cite_ref-uppsala_8-0" class="reference"><a href="#cite_note-uppsala-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> and an upper limit of approximately 6.0<sup id="cite_ref-uppsala_8-1" class="reference"><a href="#cite_note-uppsala-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> to 6.1.<sup id="cite_ref-Medline-GTT_9-0" class="reference"><a href="#cite_note-Medline-GTT-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Log-normal_distribution">Log-normal distribution</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Reference_range&action=edit&section=5" title="Edit section: Log-normal distribution"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:PDF-log_normal_distributions.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/ae/PDF-log_normal_distributions.svg/220px-PDF-log_normal_distributions.svg.png" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/ae/PDF-log_normal_distributions.svg/330px-PDF-log_normal_distributions.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/ae/PDF-log_normal_distributions.svg/440px-PDF-log_normal_distributions.svg.png 2x" data-file-width="390" data-file-height="390" /></a><figcaption>Some functions of <a href="/wiki/Log-normal_distribution" title="Log-normal distribution">log-normal distribution</a> (here shown with the measurements non-logarithmized), with the same means - <i>μ</i> (as calculated after logarithmizing) but different standard deviations - <i>σ</i> (after logarithmizing)</figcaption></figure> <p>In reality, biological parameters tend to have a <a href="/wiki/Log-normal_distribution" title="Log-normal distribution">log-normal distribution</a>,<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> rather than the normal distribution or Gaussian distribution. </p><p>An explanation for this log-normal distribution for biological parameters is: The event where a sample has half the value of the mean or median tends to have almost equal probability to occur as the event where a sample has twice the value of the mean or median. Also, only a log-normal distribution can compensate for the inability of almost all biological parameters to be of <a href="/wiki/Negative_number" title="Negative number">negative numbers</a> (at least when measured on <a href="/wiki/Absolute_scale" title="Absolute scale">absolute scales</a>), with the consequence that there is no definite limit to the size of outliers (extreme values) on the high side, but, on the other hand, they can never be less than zero, resulting in a positive <a href="/wiki/Skewness" title="Skewness">skewness</a>. </p><p>As shown in diagram at right, this phenomenon has relatively small effect if the standard deviation (as compared to the mean) is relatively small, as it makes the log-normal distribution appear similar to a normal distribution. Thus, the normal distribution may be more appropriate to use with small standard deviations for convenience, and the log-normal distribution with large standard deviations. </p><p>In a log-normal distribution, the <a href="/wiki/Geometric_standard_deviation" title="Geometric standard deviation">geometric standard deviations</a> and <a href="/wiki/Geometric_mean" title="Geometric mean">geometric mean</a> more accurately estimate the 95% prediction interval than their arithmetic counterparts. </p> <div class="mw-heading mw-heading5"><h5 id="Necessity">Necessity</h5><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Reference_range&action=edit&section=6" title="Edit section: Necessity"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Reference ranges for substances that are usually within relatively narrow limits (coefficient of variation less than 0.213, as detailed below) such as <a href="/wiki/Electrolytes" class="mw-redirect" title="Electrolytes">electrolytes</a> can be estimated by assuming normal distribution, whereas reference ranges for those that vary significantly (coefficient of variation generally over 0.213) such as most <a href="/wiki/Hormones" class="mw-redirect" title="Hormones">hormones</a><sup id="cite_ref-pmid19758299_11-0" class="reference"><a href="#cite_note-pmid19758299-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> are more accurately established by log-normal distribution. </p><p>The necessity to establish a reference range by log-normal distribution rather than normal distribution can be regarded as depending on how much difference it would make to <i>not</i> do so, which can be described as the ratio: </p> <dl><dd><span class="texhtml">Difference ratio = <style data-mw-deduplicate="TemplateStyles:r1214402035">.mw-parser-output .sfrac{white-space:nowrap}.mw-parser-output .sfrac.tion,.mw-parser-output .sfrac .tion{display:inline-block;vertical-align:-0.5em;font-size:85%;text-align:center}.mw-parser-output .sfrac .num{display:block;line-height:1em;margin:0.0em 0.1em;border-bottom:1px solid}.mw-parser-output .sfrac .den{display:block;line-height:1em;margin:0.1em 0.1em}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}</style><span class="sfrac">⁠<span class="tion"><span class="num">|<span class="nowrap" style="padding-left:0.1em; padding-right:0.1em;"> Limit<sub>log-normal</sub> - Limit<sub>normal</sub> </span>|</span><span class="sr-only">/</span><span class="den"> Limit<sub>log-normal</sub> </span></span>⁠</span></span></dd></dl> <p>where: </p> <ul><li><i>Limit<sub>log-normal</sub></i> is the (lower or upper) limit as estimated by assuming log-normal distribution</li> <li><i>Limit<sub>normal</sub></i> is the (lower or upper) limit as estimated by assuming normal distribution.</li></ul> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Diagram_of_coefficient_of_variation_versus_deviation_in_reference_ranges_erroneously_not_established_by_log-normal_distribution.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/93/Diagram_of_coefficient_of_variation_versus_deviation_in_reference_ranges_erroneously_not_established_by_log-normal_distribution.png/350px-Diagram_of_coefficient_of_variation_versus_deviation_in_reference_ranges_erroneously_not_established_by_log-normal_distribution.png" decoding="async" width="350" height="191" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/93/Diagram_of_coefficient_of_variation_versus_deviation_in_reference_ranges_erroneously_not_established_by_log-normal_distribution.png/525px-Diagram_of_coefficient_of_variation_versus_deviation_in_reference_ranges_erroneously_not_established_by_log-normal_distribution.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/93/Diagram_of_coefficient_of_variation_versus_deviation_in_reference_ranges_erroneously_not_established_by_log-normal_distribution.png/700px-Diagram_of_coefficient_of_variation_versus_deviation_in_reference_ranges_erroneously_not_established_by_log-normal_distribution.png 2x" data-file-width="3219" data-file-height="1759" /></a><figcaption>Coefficient of variation versus deviation in reference ranges established by assuming normal distribution when there is actually a log-normal distribution.</figcaption></figure> <p>This difference can be put solely in relation to the <a href="/wiki/Coefficient_of_variation" title="Coefficient of variation">coefficient of variation</a>, as in the diagram at right, where: </p> <dl><dd><span class="texhtml">Coefficient of variation = <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">s.d.</span><span class="sr-only">/</span><span class="den">m</span></span>⁠</span></span></dd></dl> <p>where: </p> <ul><li><i>s.d.</i> is the standard deviation</li> <li><i>m</i> is the arithmetic mean</li></ul> <p>In practice, it can be regarded as necessary to use the establishment methods of a log-normal distribution if the difference ratio becomes more than 0.1, meaning that a (lower or upper) limit estimated from an assumed normal distribution would be more than 10% different from the corresponding limit as estimated from a (more accurate) log-normal distribution. As seen in the diagram, a difference ratio of 0.1 is reached for the lower limit at a coefficient of variation of 0.213 (or 21.3%), and for the upper limit at a coefficient of variation at 0.413 (41.3%). The lower limit is more affected by increasing coefficient of variation, and its "critical" coefficient of variation of 0.213 corresponds to a ratio of (upper limit)/(lower limit) of 2.43, so as a rule of thumb, if the upper limit is more than 2.4 times the lower limit when estimated by assuming normal distribution, then it should be considered to do the calculations again by log-normal distribution. </p><p>Taking the example from previous section, the standard deviation (s.d.) is estimated at 0.42 and the arithmetic mean (m) is estimated at 5.33. Thus the coefficient of variation is 0.079. This is less than both 0.213 and 0.413, and thus both the lower and upper limit of fasting blood glucose can most likely be estimated by assuming normal distribution. More specifically, the coefficient of variation of 0.079 corresponds to a difference ratio of 0.01 (1%) for the lower limit and 0.007 (0.7%) for the upper limit. </p> <div class="mw-heading mw-heading5"><h5 id="From_logarithmized_sample_values">From logarithmized sample values</h5><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Reference_range&action=edit&section=7" title="Edit section: From logarithmized sample values"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A method to estimate the reference range for a parameter with log-normal distribution is to logarithmize all the measurements with an arbitrary <a href="/wiki/Base_of_a_logarithm" class="mw-redirect" title="Base of a logarithm">base</a> (for example <a href="/wiki/E_(mathematical_constant)" title="E (mathematical constant)"><i>e</i></a>), derive the mean and standard deviation of these logarithms, determine the logarithms located (for a 95% prediction interval) 1.96 standard deviations below and above that mean, and subsequently <a href="/wiki/Exponentiation" title="Exponentiation">exponentiate</a> using those two logarithms as exponents and using the same base as was used in logarithmizing, with the two resultant values being the lower and upper limit of the 95% prediction interval. </p><p>The following example of this method is based on the same values of <a href="/wiki/Fasting_plasma_glucose" class="mw-redirect" title="Fasting plasma glucose">fasting plasma glucose</a> as used in the previous section, using <a href="/wiki/E_(mathematical_constant)" title="E (mathematical constant)"><i>e</i></a> as a <a href="/wiki/Base_of_a_logarithm" class="mw-redirect" title="Base of a logarithm">base</a>:<sup id="cite_ref-Keevil1998_5-1" class="reference"><a href="#cite_note-Keevil1998-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p> <table class="wikitable"> <tbody><tr> <th></th> <th><a href="/wiki/Fasting_plasma_glucose" class="mw-redirect" title="Fasting plasma glucose">Fasting plasma glucose</a><br /> (FPG) <br />in mmol/L</th> <th>log<sub><a href="/wiki/E_(mathematical_constant)" title="E (mathematical constant)"><i>e</i></a></sub>(FPG)</th> <th>log<sub>e</sub>(FPG) deviation from<br /> mean <i>μ</i><sub>log</sub></th> <th>Squared deviation<br />from mean </th></tr> <tr> <td>Subject 1</td> <td>5.5</td> <td>1.70</td> <td>0.029</td> <td>0.000841 </td></tr> <tr> <td>Subject 2</td> <td>5.2</td> <td>1.65</td> <td>0.021</td> <td>0.000441 </td></tr> <tr> <td>Subject 3</td> <td>5.2</td> <td>1.65</td> <td>0.021</td> <td>0.000441 </td></tr> <tr> <td>Subject 4</td> <td>5.8</td> <td>1.76</td> <td>0.089</td> <td>0.007921 </td></tr> <tr> <td>Subject 5</td> <td>5.6</td> <td>1.72</td> <td>0.049</td> <td>0.002401 </td></tr> <tr> <td>Subject 6</td> <td>4.6</td> <td>1.53</td> <td>0.141</td> <td>0.019881 </td></tr> <tr> <td>Subject 7</td> <td>5.6</td> <td>1.72</td> <td>0.049</td> <td>0.002401 </td></tr> <tr> <td>Subject 8</td> <td>5.9</td> <td>1.77</td> <td>0.099</td> <td>0.009801 </td></tr> <tr> <td>Subject 9</td> <td>4.7</td> <td>1.55</td> <td>0.121</td> <td>0.014641 </td></tr> <tr> <td>Subject 10</td> <td>5.0</td> <td>1.61</td> <td>0.061</td> <td>0.003721 </td></tr> <tr> <td>Subject 11</td> <td>5.7</td> <td>1.74</td> <td>0.069</td> <td>0.004761 </td></tr> <tr> <td>Subject 12</td> <td>5.2</td> <td>1.65</td> <td>0.021</td> <td>0.000441 </td></tr> <tr> <td></td> <td><b>Mean: 5.33</b> <br /> (<i>m</i>)</td> <td><b>Mean: 1.67</b><br /> (<i>μ</i><sub>log</sub>)</td> <td></td> <td>Sum/(n-1) : 0.068/11 = 0.0062 <br /> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\sqrt {0.0062}}=0.079}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>0.0062</mn> </msqrt> </mrow> <mo>=</mo> <mn>0.079</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\sqrt {0.0062}}=0.079}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c8e3c02c0329d8f6984518f541c1bb6dd0b12835" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:16.79ex; height:2.843ex;" alt="{\displaystyle {\sqrt {0.0062}}=0.079}"></span><br />= <b>standard deviation of log<sub>e</sub>(FPG)</b><br /> (<i>σ</i><sub>log</sub>) </td></tr></tbody></table> <p>Subsequently, the still logarithmized lower limit of the reference range is calculated as: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}\ln({\text{lower limit}})&=\mu _{\log }-t_{0.975,n-1}\times {\sqrt {\frac {n+1}{n}}}\times \sigma _{\log }\\&=1.67-2.20\times {\sqrt {\frac {13}{12}}}\times 0.079=1.49,\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mi>ln</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>lower limit</mtext> </mrow> <mo stretchy="false">)</mo> </mtd> <mtd> <mi></mi> <mo>=</mo> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>log</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0.975</mn> <mo>,</mo> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> </msub> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <mrow> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>n</mi> </mfrac> </msqrt> </mrow> <mo>×</mo> <msub> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>log</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <mn>1.67</mn> <mo>−</mo> <mn>2.20</mn> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <mn>13</mn> <mn>12</mn> </mfrac> </msqrt> </mrow> <mo>×</mo> <mn>0.079</mn> <mo>=</mo> <mn>1.49</mn> <mo>,</mo> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}\ln({\text{lower limit}})&=\mu _{\log }-t_{0.975,n-1}\times {\sqrt {\frac {n+1}{n}}}\times \sigma _{\log }\\&=1.67-2.20\times {\sqrt {\frac {13}{12}}}\times 0.079=1.49,\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e0a3d726850193b5fce3e49c1254d8e735a50fd2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -5.671ex; width:53.842ex; height:12.509ex;" alt="{\displaystyle {\begin{aligned}\ln({\text{lower limit}})&=\mu _{\log }-t_{0.975,n-1}\times {\sqrt {\frac {n+1}{n}}}\times \sigma _{\log }\\&=1.67-2.20\times {\sqrt {\frac {13}{12}}}\times 0.079=1.49,\end{aligned}}}"></span></dd></dl> <p>and the upper limit of the reference range as: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}\ln({\text{upper limit}})&=\mu _{\log }+t_{0.975,n-1}\times {\sqrt {\frac {n+1}{n}}}\times \sigma _{\log }\\&=1.67+2.20\times {\sqrt {\frac {13}{12}}}\times 0.079=1.85\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mi>ln</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>upper limit</mtext> </mrow> <mo stretchy="false">)</mo> </mtd> <mtd> <mi></mi> <mo>=</mo> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>log</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0.975</mn> <mo>,</mo> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> </msub> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <mrow> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>n</mi> </mfrac> </msqrt> </mrow> <mo>×</mo> <msub> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>log</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <mn>1.67</mn> <mo>+</mo> <mn>2.20</mn> <mo>×</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <mn>13</mn> <mn>12</mn> </mfrac> </msqrt> </mrow> <mo>×</mo> <mn>0.079</mn> <mo>=</mo> <mn>1.85</mn> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}\ln({\text{upper limit}})&=\mu _{\log }+t_{0.975,n-1}\times {\sqrt {\frac {n+1}{n}}}\times \sigma _{\log }\\&=1.67+2.20\times {\sqrt {\frac {13}{12}}}\times 0.079=1.85\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ee4f7da902df296a078747959460e25fd177817a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -5.671ex; width:53.586ex; height:12.509ex;" alt="{\displaystyle {\begin{aligned}\ln({\text{upper limit}})&=\mu _{\log }+t_{0.975,n-1}\times {\sqrt {\frac {n+1}{n}}}\times \sigma _{\log }\\&=1.67+2.20\times {\sqrt {\frac {13}{12}}}\times 0.079=1.85\end{aligned}}}"></span></dd></dl> <p>Conversion back to non-logarithmized values are subsequently performed as: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\text{Lower limit}}=e^{\ln({\text{lower limit}})}=e^{1.49}=4.4}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>Lower limit</mtext> </mrow> <mo>=</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>ln</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>lower limit</mtext> </mrow> <mo stretchy="false">)</mo> </mrow> </msup> <mo>=</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1.49</mn> </mrow> </msup> <mo>=</mo> <mn>4.4</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{Lower limit}}=e^{\ln({\text{lower limit}})}=e^{1.49}=4.4}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/98a0b8ada6b7019e9bd8f664db179ef38f2987c7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:39.874ex; height:2.843ex;" alt="{\displaystyle {\text{Lower limit}}=e^{\ln({\text{lower limit}})}=e^{1.49}=4.4}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\text{Upper limit}}=e^{\ln({\text{upper limit}})}=e^{1.85}=6.4}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>Upper limit</mtext> </mrow> <mo>=</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>ln</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>upper limit</mtext> </mrow> <mo stretchy="false">)</mo> </mrow> </msup> <mo>=</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1.85</mn> </mrow> </msup> <mo>=</mo> <mn>6.4</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{Upper limit}}=e^{\ln({\text{upper limit}})}=e^{1.85}=6.4}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0cb303e206893db6c9731343afeb892dd15b2425" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:40.184ex; height:3.176ex;" alt="{\displaystyle {\text{Upper limit}}=e^{\ln({\text{upper limit}})}=e^{1.85}=6.4}"></span></dd></dl> <p>Thus, the standard reference range for this example is estimated to be 4.4 to 6.4. </p> <div class="mw-heading mw-heading5"><h5 id="From_arithmetic_mean_and_variance">From arithmetic mean and variance</h5><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Reference_range&action=edit&section=8" title="Edit section: From arithmetic mean and variance"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>An alternative method of establishing a reference range with the assumption of log-normal distribution is to use the arithmetic mean and standard deviation. This is somewhat more tedious to perform, but may be useful in cases where a study presents only the arithmetic mean and standard deviation, while leaving out the source data. If the original assumption of normal distribution is less appropriate than the log-normal one, then, using the arithmetic mean and standard deviation may be the only available parameters to determine the reference range. </p><p>By assuming that the <a href="/wiki/Expected_value" title="Expected value">expected value</a> can represent the arithmetic mean in this case, the parameters <i>μ<sub>log</sub></i> and <i>σ<sub>log</sub></i> can be estimated from the arithmetic mean (<i>m</i>) and standard deviation (<i>s.d.</i>) as: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mu _{\log }=\ln(m)-{\frac {1}{2}}\ln \!\left(1+\!\left({\frac {\text{s.d.}}{m}}\right)^{2}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>log</mi> </mrow> </msub> <mo>=</mo> <mi>ln</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>m</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mi>ln</mi> <mspace width="negativethinmathspace" /> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>+</mo> <mspace width="negativethinmathspace" /> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mtext>s.d.</mtext> <mi>m</mi> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mu _{\log }=\ln(m)-{\frac {1}{2}}\ln \!\left(1+\!\left({\frac {\text{s.d.}}{m}}\right)^{2}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e2607c48d6c48e30c540a0e8616f8d727fc52c7c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:35.899ex; height:7.509ex;" alt="{\displaystyle \mu _{\log }=\ln(m)-{\frac {1}{2}}\ln \!\left(1+\!\left({\frac {\text{s.d.}}{m}}\right)^{2}\right)}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sigma _{\log }={\sqrt {\ln \!\left(1+\!\left({\frac {\text{s.d.}}{m}}\right)^{2}\right)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>log</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mi>ln</mi> <mspace width="negativethinmathspace" /> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>+</mo> <mspace width="negativethinmathspace" /> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mtext>s.d.</mtext> <mi>m</mi> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mo>)</mo> </mrow> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sigma _{\log }={\sqrt {\ln \!\left(1+\!\left({\frac {\text{s.d.}}{m}}\right)^{2}\right)}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0e909447cb38f78c61db4b294a31d5090c1bdbb7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:27.264ex; height:8.176ex;" alt="{\displaystyle \sigma _{\log }={\sqrt {\ln \!\left(1+\!\left({\frac {\text{s.d.}}{m}}\right)^{2}\right)}}}"></span></dd></dl> <p>Following the exampled reference group from the previous section: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mu _{\log }=\ln(5.33)-{\frac {1}{2}}\ln \!\left(1+\!\left({\frac {0.42}{5.33}}\right)^{2}\right)=1.67}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>log</mi> </mrow> </msub> <mo>=</mo> <mi>ln</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mn>5.33</mn> <mo stretchy="false">)</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mi>ln</mi> <mspace width="negativethinmathspace" /> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>+</mo> <mspace width="negativethinmathspace" /> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>0.42</mn> <mn>5.33</mn> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mn>1.67</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mu _{\log }=\ln(5.33)-{\frac {1}{2}}\ln \!\left(1+\!\left({\frac {0.42}{5.33}}\right)^{2}\right)=1.67}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/78bf896f009f09101548a3e72bde9291247890d7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:45.858ex; height:7.509ex;" alt="{\displaystyle \mu _{\log }=\ln(5.33)-{\frac {1}{2}}\ln \!\left(1+\!\left({\frac {0.42}{5.33}}\right)^{2}\right)=1.67}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sigma _{\log }={\sqrt {\ln \!\left(1+\!\left({\frac {0.42}{5.33}}\right)^{2}\right)}}=0.079}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>log</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mi>ln</mi> <mspace width="negativethinmathspace" /> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>+</mo> <mspace width="negativethinmathspace" /> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>0.42</mn> <mn>5.33</mn> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mo>)</mo> </mrow> </msqrt> </mrow> <mo>=</mo> <mn>0.079</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sigma _{\log }={\sqrt {\ln \!\left(1+\!\left({\frac {0.42}{5.33}}\right)^{2}\right)}}=0.079}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dd825864287a4d4823b20a3e9c59db3cfbcc0bd9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:36.291ex; height:8.176ex;" alt="{\displaystyle \sigma _{\log }={\sqrt {\ln \!\left(1+\!\left({\frac {0.42}{5.33}}\right)^{2}\right)}}=0.079}"></span></dd></dl> <p>Subsequently, the logarithmized, and later non-logarithmized, lower and upper limit are calculated just as by logarithmized sample values. </p> <div class="mw-heading mw-heading4"><h4 id="Directly_from_percentages_of_interest">Directly from percentages of interest</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Reference_range&action=edit&section=9" title="Edit section: Directly from percentages of interest"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Reference ranges can also be established directly from the 2.5th and 97.5th percentile of the measurements in the reference group. For example, if the reference group consists of 200 people, and counting from the measurement with lowest value to highest, the lower limit of the reference range would correspond to the 5th measurement and the upper limit would correspond to the 195th measurement. </p><p>This method can be used even when measurement values do not appear to conform conveniently to any form of normal distribution or other function. </p><p>However, the reference range limits as estimated in this way have higher variance, and therefore less reliability, than those estimated by an arithmetic or log-normal distribution (when such is applicable), because the latter ones acquire <a href="/wiki/Statistical_power" class="mw-redirect" title="Statistical power">statistical power</a> from the measurements of the whole reference group rather than just the measurements at the 2.5th and 97.5th percentiles. Still, this variance decreases with increasing size of the reference group, and therefore, this method may be optimal where a large reference group easily can be gathered, and the distribution mode of the measurements is uncertain. </p> <div class="mw-heading mw-heading4"><h4 id="Bimodal_distribution">Bimodal distribution</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Reference_range&action=edit&section=10" title="Edit section: Bimodal distribution"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Bimodal.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e2/Bimodal.png/300px-Bimodal.png" decoding="async" width="300" height="158" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/e/e2/Bimodal.png 1.5x" data-file-width="350" data-file-height="184" /></a><figcaption><a href="/wiki/Bimodal_distribution" class="mw-redirect" title="Bimodal distribution">Bimodal distribution</a></figcaption></figure> <p>In case of a <a href="/wiki/Bimodal_distribution" class="mw-redirect" title="Bimodal distribution">bimodal distribution</a> (seen at right), it is useful to find out why this is the case. Two reference ranges can be established for the two different groups of people, making it possible to assume a normal distribution for each group. This bimodal pattern is commonly seen in tests that differ between men and women, such as <a href="/wiki/Prostate_specific_antigen" class="mw-redirect" title="Prostate specific antigen">prostate specific antigen</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Interpretation_of_standard_ranges_in_medical_tests">Interpretation of standard ranges in medical tests</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Reference_range&action=edit&section=11" title="Edit section: Interpretation of standard ranges in medical tests"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In case of <a href="/wiki/Medical_test" title="Medical test">medical tests</a> whose results are of continuous values, reference ranges can be used in the interpretation of an individual test result. This is primarily used for <a href="/wiki/Diagnostic_test" class="mw-redirect" title="Diagnostic test">diagnostic tests</a> and <a href="/wiki/Screening_(medicine)" title="Screening (medicine)">screening</a> tests, while <a href="/wiki/Monitoring_(medicine)" title="Monitoring (medicine)">monitoring tests</a> may optimally be interpreted from previous tests of the same individual instead. </p> <div class="mw-heading mw-heading4"><h4 id="Probability_of_random_variability">Probability of random variability</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Reference_range&action=edit&section=12" title="Edit section: Probability of random variability"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Reference ranges aid in the evaluation of whether a test result's deviation from the mean is a result of random variability or a result of an underlying disease or condition. If the reference group used to establish the reference range can be assumed to be representative of the individual person in a healthy state, then a test result from that individual that turns out to be lower or higher than the reference range can be interpreted as that there is less than 2.5% probability that this would have occurred by random variability in the absence of disease or other condition, which, in turn, is strongly indicative for considering an underlying disease or condition as a cause. </p><p>Such further consideration can be performed, for example, by an <a href="/wiki/Differential_diagnosis#Specific_methods" title="Differential diagnosis">epidemiology-based differential diagnostic procedure</a>, where potential candidate conditions are listed that may explain the finding, followed by calculations of how probable they are to have occurred in the first place, in turn followed by a comparison with the probability that the result would have occurred by random variability. </p><p>If the establishment of the reference range could have been made assuming a normal distribution, then the probability that the result would be an effect of random variability can be further specified as follows: </p><p>The <a href="/wiki/Standard_deviation" title="Standard deviation">standard deviation</a>, if not given already, can be inversely calculated by the fact that the <a href="/wiki/Absolute_value" title="Absolute value">absolute value</a> of the difference between the mean and either the upper or lower limit of the reference range is approximately 2 standard deviations (more accurately 1.96), and thus: </p> <dl><dd><span class="texhtml">Standard deviation (s.d.) ≈ <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">|<span class="nowrap" style="padding-left:0.1em; padding-right:0.1em;"> (Mean) - (Upper limit) </span>|</span><span class="sr-only">/</span><span class="den">2</span></span>⁠</span></span>.</dd></dl> <p>The <a href="/wiki/Standard_score" title="Standard score">standard score</a> for the individual's test can subsequently be calculated as: </p> <dl><dd><span class="texhtml">Standard score (<i>z</i>) = <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">|<span class="nowrap" style="padding-left:0.1em; padding-right:0.1em;"> (Mean) - (individual measurement) </span>|</span><span class="sr-only">/</span><span class="den">s.d.</span></span>⁠</span></span>.</dd></dl> <p>The probability that a value is of a certain distance from the mean can subsequently be calculated from the <a href="/wiki/Standard_score#prediction_intervals" title="Standard score">relation between standard score and prediction intervals</a>. For example, a standard score of 2.58 corresponds to a prediction interval of 99%,<sup id="cite_ref-Kirkup2002_12-0" class="reference"><a href="#cite_note-Kirkup2002-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> corresponding to a probability of 0.5% that a result is at least such far from the mean in the absence of disease. </p> <div class="mw-heading mw-heading4"><h4 id="Example">Example</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Reference_range&action=edit&section=13" title="Edit section: Example"><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">The method is described in further detail at <a href="/wiki/Differential_diagnosis" title="Differential diagnosis">differential diagnosis</a>.</div> <p>Let's say, for example, that an individual takes a test that measures the <a href="/wiki/Ionized_calcium" class="mw-redirect" title="Ionized calcium">ionized calcium</a> in the blood, resulting in a value of 1.30 mmol/L, and a reference group that appropriately represents the individual has established a reference range of 1.05 to 1.25 mmol/L. The individual's value is higher than the upper limit of the reference range, and therefore has less than 2.5% probability of being a result of random variability, constituting a strong indication to make a <a href="/wiki/Differential_diagnosis" title="Differential diagnosis">differential diagnosis</a> of possible causative conditions. </p><p>In this case, an <a href="/wiki/Differential_diagnosis#Specific_methods" title="Differential diagnosis">epidemiology-based differential diagnostic procedure</a> is used, and its first step is to find candidate conditions that can explain the finding. </p><p><a href="/wiki/Hypercalcemia" class="mw-redirect" title="Hypercalcemia">Hypercalcemia</a> (usually defined as a calcium level above the reference range) is mostly caused by either <a href="/wiki/Primary_hyperparathyroidism" title="Primary hyperparathyroidism">primary hyperparathyroidism</a> or malignancy,<sup id="cite_ref-Kumar_13-0" class="reference"><a href="#cite_note-Kumar-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> and therefore, it is reasonable to include these in the differential diagnosis. </p><p>Using for example epidemiology and the individual's risk factors, let's say that the probability that the hypercalcemia would have been caused by primary hyperparathyroidism in the first place is estimated to be 0.00125 (or 0.125%), the equivalent probability for cancer is 0.0002, and 0.0005 for other conditions. With a probability given as less than 0.025 of no disease, this corresponds to a probability that the hypercalcemia would have occurred in the first place of up to 0.02695. However, the hypercalcemia <i>has occurred</i> with a probability of 100%, resulting adjusted probabilities of at least 4.6% that primary hyperparathyroidism has caused the hypercalcemia, at least 0.7% for cancer, at least 1.9% for other conditions and up to 92.8% for that there is no disease and the hypercalcemia is caused by random variability. </p><p>In this case, further processing benefits from specification of the probability of random variability: </p><p>The value is assumed to conform acceptably to a normal distribution, so the mean can be assumed to be 1.15 in the reference group. The <a href="/wiki/Standard_deviation" title="Standard deviation">standard deviation</a>, if not given already, can be inversely calculated by knowing that the <a href="/wiki/Absolute_value" title="Absolute value">absolute value</a> of the difference between the mean and, for example, the upper limit of the reference range, is approximately 2 standard deviations (more accurately 1.96), and thus: </p> <dl><dd><span class="texhtml">Standard deviation (s.d.) ≈ <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">|<span class="nowrap" style="padding-left:0.1em; padding-right:0.1em;"> (Mean) - (Upper limit) </span>|</span><span class="sr-only">/</span><span class="den">2</span></span>⁠</span> = <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">|<span class="nowrap" style="padding-left:0.1em; padding-right:0.1em;"> 1.15 - 1.25 </span>|</span><span class="sr-only">/</span><span class="den">2</span></span>⁠</span> = <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">0.1</span><span class="sr-only">/</span><span class="den">2</span></span>⁠</span> = 0.05</span>.</dd></dl> <p>The <a href="/wiki/Standard_score" title="Standard score">standard score</a> for the individual's test is subsequently calculated as: </p> <dl><dd><span class="texhtml">Standard score (<i>z</i>) = <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">|<span class="nowrap" style="padding-left:0.1em; padding-right:0.1em;"> (Mean) - (individual measurement) </span>|</span><span class="sr-only">/</span><span class="den">s.d.</span></span>⁠</span> = <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">|<span class="nowrap" style="padding-left:0.1em; padding-right:0.1em;"> 1.15 - 1.30 </span>|</span><span class="sr-only">/</span><span class="den">0.05</span></span>⁠</span> = <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">0.15</span><span class="sr-only">/</span><span class="den">0.05</span></span>⁠</span> = 3</span>.</dd></dl> <p>The probability that a value is of so much larger value than the mean as having a standard score of 3 corresponds to a probability of approximately 0.14% (given by <span class="texhtml">(100% − 99.7%)/2</span>, with 99.7% here being given from the <a href="/wiki/68%E2%80%9395%E2%80%9399.7_rule" title="68–95–99.7 rule">68–95–99.7 rule</a>). </p><p>Using the same probabilities that the hypercalcemia would have occurred in the first place by the other candidate conditions, the probability that hypercalcemia would have occurred in the first place is 0.00335, and given the fact that hypercalcemia <i>has occurred</i> gives adjusted probabilities of 37.3%, 6.0%, 14.9% and 41.8%, respectively, for primary hyperparathyroidism, cancer, other conditions and no disease. </p> <div class="mw-heading mw-heading2"><h2 id="Optimal_health_range">Optimal health range</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Reference_range&action=edit&section=14" title="Edit section: Optimal health range"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><i>Optimal (health) range</i> or <i>therapeutic target</i> (not to be confused with <a href="/wiki/Biological_target" title="Biological target">biological target</a>) is a reference range or limit that is based on concentrations or levels that are associated with optimal health or minimal risk of related complications and diseases, rather than the standard range based on normal distribution in the population. </p><p>It may be more appropriate to use for e.g. <a href="/wiki/Folate" title="Folate">folate</a>, since approximately 90 percent of North Americans may actually suffer more or less from <a href="/wiki/Folate_deficiency" title="Folate deficiency">folate deficiency</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> but only the 2.5 percent that have the lowest levels will fall below the standard reference range. In this case, the actual folate ranges for optimal health are substantially higher than the standard reference ranges. <a href="/wiki/Vitamin_D" title="Vitamin D">Vitamin D</a> has a similar tendency. In contrast, for e.g. <a href="/wiki/Uric_acid" title="Uric acid">uric acid</a>, having a level not exceeding the standard reference range still does not exclude the risk of getting gout or kidney stones. Furthermore, for most <a href="/wiki/Toxin" title="Toxin">toxins</a>, the standard reference range is generally lower than the level of toxic effect. </p><p>A problem with optimal health range is a lack of a standard method of estimating the ranges. The limits may be defined as those where the health risks exceed a certain threshold, but with various risk profiles between different measurements (such as folate and vitamin D), and even different risk aspects for one and the same measurement (such as both <a href="/wiki/Vitamin_A_deficiency" title="Vitamin A deficiency">deficiency</a> and <a href="/wiki/Hypervitaminosis_A" title="Hypervitaminosis A">toxicity of vitamin A</a>) it is difficult to standardize. Subsequently, optimal health ranges, when given by various sources, have an additional <a href="/wiki/Statistical_variability" class="mw-redirect" title="Statistical variability">variability</a> caused by various definitions of the parameter. Also, as with standard reference ranges, there should be specific ranges for different determinants that affects the values, such as sex, age etc. Ideally, there should rather be an estimation of what is the optimal value for every individual, when taking all significant factors of that individual into account - a task that may be hard to achieve by studies, but long clinical experience by a physician may make this method preferable to using reference ranges. <span class="anchor" id="cutoff"></span> </p> <div class="mw-heading mw-heading2"><h2 id="One-sided_cut-off_values">One-sided cut-off values</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Reference_range&action=edit&section=15" title="Edit section: One-sided cut-off values"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In many cases, only one side of the range is usually of interest, such as with markers of pathology including <a href="/wiki/CA19-9" title="CA19-9">cancer antigen 19-9</a>, where it is generally without any clinical significance to have a value below what is usual in the population. Therefore, such targets are often given with only one limit of the reference range given, and, strictly, such values are rather <i>cut-off values</i> or <i>threshold values</i>. </p><p>They may represent both standard ranges and optimal health ranges. Also, they may represent an appropriate value to distinguish healthy person from a specific disease, although this gives additional variability by different diseases being distinguished. For example, for <a href="/wiki/NT-proBNP" class="mw-redirect" title="NT-proBNP">NT-proBNP</a>, a lower cut-off value is used in distinguishing healthy babies from those with <a href="/wiki/Acyanotic_heart_disease" class="mw-redirect" title="Acyanotic heart disease">acyanotic heart disease</a>, compared to the cut-off value used in distinguishing healthy babies from those with <a href="/wiki/Congenital_nonspherocytic_anemia" class="mw-redirect" title="Congenital nonspherocytic anemia">congenital nonspherocytic anemia</a>.<sup id="cite_ref-Moses2011_15-0" class="reference"><a href="#cite_note-Moses2011-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="General_drawbacks">General drawbacks</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Reference_range&action=edit&section=16" title="Edit section: General drawbacks"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>For standard as well as optimal health ranges, and cut-offs, sources of <a href="/wiki/Accuracy_and_precision" title="Accuracy and precision">inaccuracy and imprecision</a> include: </p> <ul><li>Instruments and lab techniques used, or how the measurements are interpreted by observers. These may apply both to the instruments etc. used to establish the reference ranges and the instruments, etc. used to acquire the value for the individual to whom these ranges is applied. To compensate, individual laboratories should have their own lab ranges to account for the instruments used in the laboratory.</li> <li><a href="/wiki/Risk_factor_(epidemiology)" class="mw-redirect" title="Risk factor (epidemiology)">Determinants</a> such as age, diet, etc. that are not compensated for. Optimally, there should be reference ranges from a reference group that is as similar as possible to each individual they are applied to, but it is practically impossible to compensate for every single determinant, often not even when the reference ranges are established from multiple measurements of the same individual they are applied to, because of <a href="/wiki/Test-retest_reliability" class="mw-redirect" title="Test-retest reliability">test-retest</a> variability.</li></ul> <p>Also, reference ranges tend to give the impression of definite thresholds that clearly separate "good" or "bad" values, while in reality there are generally continuously increasing risks with increased distance from usual or optimal values. </p><p>With this and uncompensated factors in mind, the ideal interpretation method of a test result would rather consist of a comparison of what would be expected or optimal in the individual when taking all factors and conditions of that individual into account, rather than strictly classifying the values as "good" or "bad" by using reference ranges from other people. </p><p>In a recent paper, Rappoport et al.<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> described a novel way to redefine reference range from an <a href="/wiki/Electronic_health_record" title="Electronic health record">electronic health record</a> system. In such a system, a higher population resolution can be achieved (e.g., age, sex, race and ethnicity-specific). </p> <div class="mw-heading mw-heading2"><h2 id="Examples">Examples</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Reference_range&action=edit&section=17" title="Edit section: Examples"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Reference_ranges_for_blood_tests" title="Reference ranges for blood tests">Reference ranges for blood tests</a></li> <li><a href="/wiki/Reference_ranges_for_urine_tests" title="Reference ranges for urine tests">Reference ranges for urine tests</a></li></ul> <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=Reference_range&action=edit&section=18" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Clinical_pathology" title="Clinical pathology">Clinical pathology</a></li> <li><a href="/wiki/Joint_Committee_for_Traceability_in_Laboratory_Medicine" title="Joint Committee for Traceability in Laboratory Medicine">Joint Committee for Traceability in Laboratory Medicine</a></li> <li><a href="/wiki/Medical_technologist" class="mw-redirect" title="Medical technologist">Medical technologist</a></li> <li><a href="/wiki/Reference_ranges_for_blood_tests" title="Reference ranges for blood tests">Reference ranges for blood tests</a></li></ul> <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=Reference_range&action=edit&section=19" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><span typeof="mw:File"><a href="/wiki/File:Open_Access_logo_PLoS_transparent.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/7/77/Open_Access_logo_PLoS_transparent.svg/9px-Open_Access_logo_PLoS_transparent.svg.png" decoding="async" width="9" height="14" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/77/Open_Access_logo_PLoS_transparent.svg/14px-Open_Access_logo_PLoS_transparent.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/77/Open_Access_logo_PLoS_transparent.svg/18px-Open_Access_logo_PLoS_transparent.svg.png 2x" data-file-width="640" data-file-height="1000" /></a></span> <span class="plainlinks">This article was adapted from the following source under a <span class="plainlinks"><a rel="nofollow" class="external text" href="https://creativecommons.org/publicdomain/zero/1.0/">CC0</a></span> license (<a class="external text" href="https://en.wikipedia.org/w/index.php?title=Reference_range&action=history&date-range-to=2012-02-28">2012</a>) (<a class="external text" href="https://en.wikiversity.org/wiki/Talk:WikiJournal_of_Medicine/Reference_ranges_for_estradiol,_progesterone,_luteinizing_hormone_and_follicle-stimulating_hormone_during_the_menstrual_cycle">reviewer reports</a>): <style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .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 class="citation journal cs1">Mikael Häggström (2014). <a class="external text" href="https://upload.wikimedia.org/wikiversity/en/0/05/Reference_ranges_for_estradiol%2C_progesterone%2C_luteinizing_hormone_and_follicle-stimulating_hormone_during_the_menstrual_cycle.pdf">"Reference ranges for estradiol, progesterone, luteinizing hormone and follicle-stimulating hormone during the menstrual cycle"</a> <span class="cs1-format">(PDF)</span>. <i>WikiJournal of Medicine</i>. <b>1</b> (1). <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/10.15347%2FWJM%2F2014.001">10.15347/WJM/2014.001</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/2002-4436">2002-4436</a>. <a href="/wiki/WDQ_(identifier)" class="mw-redirect" title="WDQ (identifier)">Wikidata</a> <a href="https://www.wikidata.org/wiki/Q44275619" class="extiw" title="d:Q44275619">Q44275619</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=WikiJournal+of+Medicine&rft.atitle=Reference+ranges+for+estradiol%2C+progesterone%2C+luteinizing+hormone+and+follicle-stimulating+hormone+during+the+menstrual+cycle&rft.volume=1&rft.issue=1&rft.date=2014&rft_id=info%3Adoi%2F10.15347%2FWJM%2F2014.001&rft.issn=2002-4436&rft.au=Mikael+H%C3%A4ggstr%C3%B6m&rft_id=https%3A%2F%2Fupload.wikimedia.org%2Fwikiversity%2Fen%2F0%2F05%2FReference_ranges_for_estradiol%252C_progesterone%252C_luteinizing_hormone_and_follicle-stimulating_hormone_during_the_menstrual_cycle.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AReference+range" class="Z3988"></span></span> </p> <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 reflist-columns references-column-width" style="column-width: 30em;"> <ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://books.google.com/books?id=Je_pJfb2r0cC&pg=PA19">Page 19</a> in: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFStephen_K._Bangert_MA_MB_BChir_MSc_MBA_FRCPath;_William_J._Marshall_MA_MSc_MBBS_FRCP_FRCPath_FRCPEdin_FIBiol;_Marshall,_William_Leonard2008" class="citation book cs1">Stephen K. Bangert MA MB BChir MSc MBA FRCPath; William J. Marshall MA MSc MBBS FRCP FRCPath FRCPEdin FIBiol; Marshall, William Leonard (2008). <i>Clinical biochemistry: metabolic and clinical aspects</i>. Philadelphia: Churchill Livingstone/Elsevier. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-443-10186-1" title="Special:BookSources/978-0-443-10186-1"><bdi>978-0-443-10186-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Clinical+biochemistry%3A+metabolic+and+clinical+aspects&rft.place=Philadelphia&rft.pub=Churchill+Livingstone%2FElsevier&rft.date=2008&rft.isbn=978-0-443-10186-1&rft.au=Stephen+K.+Bangert+MA+MB+BChir+MSc+MBA+FRCPath%3B+William+J.+Marshall+MA+MSc+MBBS+FRCP+FRCPath+FRCPEdin+FIBiol%3B+Marshall%2C+William+Leonard&rfr_id=info%3Asid%2Fen.wikipedia.org%3AReference+range" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Template:Cite_book" title="Template:Cite book">cite book</a>}}</code>: CS1 maint: multiple names: authors list (<a href="/wiki/Category:CS1_maint:_multiple_names:_authors_list" title="Category:CS1 maint: multiple names: authors list">link</a>)</span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDybkaer1982" class="citation journal cs1">Dybkaer, R (November 1982). "International federation of clinical chemistry (IFCC)1),2) the theory of reference values. Part 6. Presentation of observed values related to reference values". <i>Journal of Clinical Chemistry and Clinical Biochemistry</i>. <b>20</b> (11): 841–5. <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/7153721">7153721</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+Clinical+Chemistry+and+Clinical+Biochemistry&rft.atitle=International+federation+of+clinical+chemistry+%28IFCC%291%29%2C2%29+the+theory+of+reference+values.+Part+6.+Presentation+of+observed+values+related+to+reference+values.&rft.volume=20&rft.issue=11&rft.pages=841-5&rft.date=1982-11&rft_id=info%3Apmid%2F7153721&rft.aulast=Dybkaer&rft.aufirst=R&rfr_id=info%3Asid%2Fen.wikipedia.org%3AReference+range" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDavisHamilton2021" class="citation journal cs1">Davis, C.Q.; Hamilton, R. (2021). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8494724">"Reference ranges for clinical electrophysiology of vision"</a>. <i>Doc Ophthalmol</i>. <b>143</b> (2): 155–170. <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/10.1007%2Fs10633-021-09831-1">10.1007/s10633-021-09831-1</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/PMC8494724">8494724</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/33880667">33880667</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Doc+Ophthalmol&rft.atitle=Reference+ranges+for+clinical+electrophysiology+of+vision&rft.volume=143&rft.issue=2&rft.pages=155-170&rft.date=2021&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC8494724%23id-name%3DPMC&rft_id=info%3Apmid%2F33880667&rft_id=info%3Adoi%2F10.1007%2Fs10633-021-09831-1&rft.aulast=Davis&rft.aufirst=C.Q.&rft.au=Hamilton%2C+R.&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC8494724&rfr_id=info%3Asid%2Fen.wikipedia.org%3AReference+range" class="Z3988"></span></span> </li> <li id="cite_note-MedicalStatistics-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-MedicalStatistics_4-0">^</a></b></span> <span class="reference-text">Page 48 in: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSterne,_JonathanKirkwood,_Betty_R.2003" class="citation book cs1">Sterne, Jonathan; Kirkwood, Betty R. (2003). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/essentialmedical00kirk"><i>Essential medical statistics</i></a></span>. Oxford: Blackwell Science. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-86542-871-3" title="Special:BookSources/978-0-86542-871-3"><bdi>978-0-86542-871-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Essential+medical+statistics&rft.place=Oxford&rft.pub=Blackwell+Science&rft.date=2003&rft.isbn=978-0-86542-871-3&rft.au=Sterne%2C+Jonathan&rft.au=Kirkwood%2C+Betty+R.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fessentialmedical00kirk&rfr_id=info%3Asid%2Fen.wikipedia.org%3AReference+range" class="Z3988"></span></span> </li> <li id="cite_note-Keevil1998-5"><span class="mw-cite-backlink">^ <a href="#cite_ref-Keevil1998_5-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Keevil1998_5-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.clinchem.org/cgi/content-nw/full/44/7/1535/T1">Table 1. Subject characteristics</a> in: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKeevilKilpatrickNicholsMaylor1998" class="citation journal cs1">Keevil, B. G.; Kilpatrick, E. S.; Nichols, S. P.; Maylor, P. W. (1998). <a rel="nofollow" class="external text" href="https://doi.org/10.1093%2Fclinchem%2F44.7.1535">"Biological variation of cystatin C: Implications for the assessment of glomerular filtration rate"</a>. <i>Clinical Chemistry</i>. <b>44</b> (7): 1535–1539. <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/10.1093%2Fclinchem%2F44.7.1535">10.1093/clinchem/44.7.1535</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/9665434">9665434</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Clinical+Chemistry&rft.atitle=Biological+variation+of+cystatin+C%3A+Implications+for+the+assessment+of+glomerular+filtration+rate&rft.volume=44&rft.issue=7&rft.pages=1535-1539&rft.date=1998&rft_id=info%3Adoi%2F10.1093%2Fclinchem%2F44.7.1535&rft_id=info%3Apmid%2F9665434&rft.aulast=Keevil&rft.aufirst=B.+G.&rft.au=Kilpatrick%2C+E.+S.&rft.au=Nichols%2C+S.+P.&rft.au=Maylor%2C+P.+W.&rft_id=https%3A%2F%2Fdoi.org%2F10.1093%252Fclinchem%252F44.7.1535&rfr_id=info%3Asid%2Fen.wikipedia.org%3AReference+range" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://books.google.com/books?id=p7XwAwAAQBAJ&pg=PA65">Page 65</a> in: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCarl_A._Burtis,_David_E._Bruns2014" class="citation book cs1">Carl A. Burtis, David E. Bruns (2014). <i>Tietz Fundamentals of Clinical Chemistry and Molecular Diagnostics</i> (7 ed.). Elsevier Health Sciences. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780323292061" title="Special:BookSources/9780323292061"><bdi>9780323292061</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Tietz+Fundamentals+of+Clinical+Chemistry+and+Molecular+Diagnostics&rft.edition=7&rft.pub=Elsevier+Health+Sciences&rft.date=2014&rft.isbn=9780323292061&rft.au=Carl+A.+Burtis%2C+David+E.+Bruns&rfr_id=info%3Asid%2Fen.wikipedia.org%3AReference+range" class="Z3988"></span></span> </li> <li id="cite_note-firstaid-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-firstaid_7-0">^</a></b></span> <span class="reference-text">Last page of <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDeepak_A._RaoLe,_TaoBhushan,_Vikas2007" class="citation book cs1">Deepak A. Rao; Le, Tao; Bhushan, Vikas (2007). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/firstaidforusmle00taol"><i>First Aid for the USMLE Step 1 2008 (First Aid for the Usmle Step 1)</i></a></span>. McGraw-Hill Medical. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-07-149868-5" title="Special:BookSources/978-0-07-149868-5"><bdi>978-0-07-149868-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=First+Aid+for+the+USMLE+Step+1+2008+%28First+Aid+for+the+Usmle+Step+1%29&rft.pub=McGraw-Hill+Medical&rft.date=2007&rft.isbn=978-0-07-149868-5&rft.au=Deepak+A.+Rao&rft.au=Le%2C+Tao&rft.au=Bhushan%2C+Vikas&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Ffirstaidforusmle00taol&rfr_id=info%3Asid%2Fen.wikipedia.org%3AReference+range" class="Z3988"></span></span> </li> <li id="cite_note-uppsala-8"><span class="mw-cite-backlink">^ <a href="#cite_ref-uppsala_8-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-uppsala_8-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">Reference range list from Uppsala University Hospital ("Laborationslista"). Artnr 40284 Sj74a. Issued on April 22, 2008</span> </li> <li id="cite_note-Medline-GTT-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-Medline-GTT_9-0">^</a></b></span> <span class="reference-text"><i><a href="/wiki/MedlinePlus" title="MedlinePlus">MedlinePlus Encyclopedia</a></i>: <a rel="nofollow" class="external text" href="https://medlineplus.gov/ency/article/003466.htm">Glucose tolerance test</a></span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHuxley1932" class="citation book cs1">Huxley, Julian S. (1932). <i>Problems of relative growth</i>. London. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-486-61114-3" title="Special:BookSources/978-0-486-61114-3"><bdi>978-0-486-61114-3</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/476909537">476909537</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Problems+of+relative+growth&rft.pub=London&rft.date=1932&rft_id=info%3Aoclcnum%2F476909537&rft.isbn=978-0-486-61114-3&rft.aulast=Huxley&rft.aufirst=Julian+S.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AReference+range" class="Z3988"></span></span> </li> <li id="cite_note-pmid19758299-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-pmid19758299_11-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLevitt_H,_Smith_KG,_Rosner_MH2009" class="citation journal cs1">Levitt H, Smith KG, Rosner MH (2009). <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/19758299">"Variability in calcium, phosphorus, and parathyroid hormone in patients on hemodialysis"</a>. <i>Hemodial Int</i>. <b>13</b> (4): 518–25. <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%2Fj.1542-4758.2009.00393.x">10.1111/j.1542-4758.2009.00393.x</a>. <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/19758299">19758299</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:24963421">24963421</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Hemodial+Int&rft.atitle=Variability+in+calcium%2C+phosphorus%2C+and+parathyroid+hormone+in+patients+on+hemodialysis.&rft.volume=13&rft.issue=4&rft.pages=518-25&rft.date=2009&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A24963421%23id-name%3DS2CID&rft_id=info%3Apmid%2F19758299&rft_id=info%3Adoi%2F10.1111%2Fj.1542-4758.2009.00393.x&rft.au=Levitt+H%2C+Smith+KG%2C+Rosner+MH&rft_id=https%3A%2F%2Fpubmed.ncbi.nlm.nih.gov%2F19758299&rfr_id=info%3Asid%2Fen.wikipedia.org%3AReference+range" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Template:Cite_journal" title="Template:Cite journal">cite journal</a>}}</code>: CS1 maint: multiple names: authors list (<a href="/wiki/Category:CS1_maint:_multiple_names:_authors_list" title="Category:CS1 maint: multiple names: authors list">link</a>)</span></span> </li> <li id="cite_note-Kirkup2002-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-Kirkup2002_12-0">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://books.google.com/books?id=rDsec-JnCAwC&pg=PA111">Page 111</a> in: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKirkup,_Les2002" class="citation book cs1">Kirkup, Les (2002). <i>Data analysis with Excel: an introduction for physical scientists</i>. Cambridge, UK: Cambridge University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-79737-5" title="Special:BookSources/978-0-521-79737-5"><bdi>978-0-521-79737-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Data+analysis+with+Excel%3A+an+introduction+for+physical+scientists&rft.place=Cambridge%2C+UK&rft.pub=Cambridge+University+Press&rft.date=2002&rft.isbn=978-0-521-79737-5&rft.au=Kirkup%2C+Les&rfr_id=info%3Asid%2Fen.wikipedia.org%3AReference+range" class="Z3988"></span></span> </li> <li id="cite_note-Kumar-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-Kumar_13-0">^</a></b></span> <span class="reference-text">Table 20-4 in: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMitchell,_Richard_SheppardKumar,_VinayAbbas,_Abul_K.Fausto,_Nelson2007" class="citation book cs1">Mitchell, Richard Sheppard; Kumar, Vinay; Abbas, Abul K.; Fausto, Nelson (2007). <i>Robbins Basic Pathology</i>. Philadelphia: Saunders. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4160-2973-1" title="Special:BookSources/978-1-4160-2973-1"><bdi>978-1-4160-2973-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Robbins+Basic+Pathology&rft.place=Philadelphia&rft.pub=Saunders&rft.date=2007&rft.isbn=978-1-4160-2973-1&rft.au=Mitchell%2C+Richard+Sheppard&rft.au=Kumar%2C+Vinay&rft.au=Abbas%2C+Abul+K.&rft.au=Fausto%2C+Nelson&rfr_id=info%3Asid%2Fen.wikipedia.org%3AReference+range" class="Z3988"></span> 8th edition.</span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.yourhealthbase.com/folic_acid.htm">Folic Acid: Don't Be Without It!</a> by Hans R. Larsen, MSc ChE, retrieved on July 7, 2009. In turn citing: <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBoushey_Carol_J.1995" class="citation journal cs1">Boushey Carol J.; et al. (1995). "A quantitative assessment of plasma homocysteine as a risk factor for vascular disease". <i>Journal of the American Medical Association</i>. <b>274</b> (13): 1049–57. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1001%2Fjama.274.13.1049">10.1001/jama.274.13.1049</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+Medical+Association&rft.atitle=A+quantitative+assessment+of+plasma+homocysteine+as+a+risk+factor+for+vascular+disease&rft.volume=274&rft.issue=13&rft.pages=1049-57&rft.date=1995&rft_id=info%3Adoi%2F10.1001%2Fjama.274.13.1049&rft.au=Boushey+Carol+J.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AReference+range" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMorrison_Howard_I.1996" class="citation journal cs1">Morrison Howard I.; et al. (1996). "Serum folate and risk of fatal coronary heart disease". <i>Journal of the American Medical Association</i>. <b>275</b> (24): 1893–96. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1001%2Fjama.1996.03530480035037">10.1001/jama.1996.03530480035037</a>. <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/8648869">8648869</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+Medical+Association&rft.atitle=Serum+folate+and+risk+of+fatal+coronary+heart+disease&rft.volume=275&rft.issue=24&rft.pages=1893-96&rft.date=1996&rft_id=info%3Adoi%2F10.1001%2Fjama.1996.03530480035037&rft_id=info%3Apmid%2F8648869&rft.au=Morrison+Howard+I.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AReference+range" class="Z3988"></span></li></ul> </span></li> <li id="cite_note-Moses2011-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-Moses2011_15-0">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.medscape.com/viewarticle/735842_3">Screening for Congenital Heart Disease with NT-proBNP: Results</a> By Emmanuel Jairaj Moses, Sharifah A.I. Mokhtar, Amir Hamzah, Basir Selvam Abdullah, and Narazah Mohd Yusoff. Laboratory Medicine. 2011;42(2):75–80. American Society for Clinical Pathology</span> </li> <li id="cite_note-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-16">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRappoportPaikOskotskyTor2017" class="citation biorxiv cs1">Rappoport, Nadav; Paik, Hyojung; Oskotsky, Boris; Tor, Ruth; Ziv, Elad; Zaitlen, Noah; Butte, Atul J. (2017-11-04). "Creating ethnicity-specific reference intervals for lab tests from EHR data". <a href="/wiki/BioRxiv_(identifier)" class="mw-redirect" title="BioRxiv (identifier)">bioRxiv</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1101%2F213892">10.1101/213892</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=preprint&rft.jtitle=bioRxiv&rft.atitle=Creating+ethnicity-specific+reference+intervals+for+lab+tests+from+EHR+data&rft.date=2017-11-04&rft_id=https%3A%2F%2Fdoi.org%2F10.1101%2F213892%23id-name%3DbioRxiv&rft.aulast=Rappoport&rft.aufirst=Nadav&rft.au=Paik%2C+Hyojung&rft.au=Oskotsky%2C+Boris&rft.au=Tor%2C+Ruth&rft.au=Ziv%2C+Elad&rft.au=Zaitlen%2C+Noah&rft.au=Butte%2C+Atul+J.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AReference+range" class="Z3988"></span></span> </li> </ol></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=Reference_range&action=edit&section=20" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>The procedures and vocabulary referring to reference intervals: CLSI (Committee for Laboratory Standards Institute) and IFCC (International Federation of Clinical Chemistry) <i>CLSI - Defining, Establishing, and Verifying Reference Intervals in the Laboratory; Approved guideline</i> - Third Edition. Document C28-A3 (<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/1-56238-682-4" title="Special:BookSources/1-56238-682-4">1-56238-682-4</a>)Wayne, PA, USA, 2008</li> <li><a rel="nofollow" class="external text" href="https://www.biostat.envt.fr/reference-value-advisor/">Reference Value Advisor</a> : A free set of Excel macros allowing the determination of reference intervals in accordance with the CLSI procedures. Based on: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGeffréConcordetBraunTrumel2011" class="citation journal cs1">Geffré, A.; Concordet, D.; Braun, J. P.; Trumel, C. (2011). <a rel="nofollow" class="external text" href="https://hal.inrae.fr/hal-02649142/file/VCP%20-%20GEFFRE%20A%20-%20reference%20value%20-%20.2011_1.pdf">"Reference Value Advisor: A new freeware set of macroinstructions to calculate reference intervals with Microsoft Excel"</a> <span class="cs1-format">(PDF)</span>. <i>Veterinary Clinical Pathology</i>. <b>40</b> (1): 107–112. <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%2Fj.1939-165X.2011.00287.x">10.1111/j.1939-165X.2011.00287.x</a>. <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/21366659">21366659</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Veterinary+Clinical+Pathology&rft.atitle=Reference+Value+Advisor%3A+A+new+freeware+set+of+macroinstructions+to+calculate+reference+intervals+with+Microsoft+Excel&rft.volume=40&rft.issue=1&rft.pages=107-112&rft.date=2011&rft_id=info%3Adoi%2F10.1111%2Fj.1939-165X.2011.00287.x&rft_id=info%3Apmid%2F21366659&rft.aulast=Geffr%C3%A9&rft.aufirst=A.&rft.au=Concordet%2C+D.&rft.au=Braun%2C+J.+P.&rft.au=Trumel%2C+C.&rft_id=https%3A%2F%2Fhal.inrae.fr%2Fhal-02649142%2Ffile%2FVCP%2520-%2520GEFFRE%2520A%2520-%2520reference%2520value%2520-%2520.2011_1.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AReference+range" class="Z3988"></span></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 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href="/wiki/Special:EditPage/Template:Clinical_biochemistry_blood_tests" title="Special:EditPage/Template:Clinical biochemistry blood tests"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Clinical_biochemistry_blood_tests" style="font-size:114%;margin:0 4em">Clinical biochemistry <a href="/wiki/Blood_test" title="Blood test">blood tests</a></div></th></tr><tr><th scope="row" class="navbox-group" style="text-align: center;;width:1%"><a href="/wiki/Electrolyte" title="Electrolyte">Electrolytes</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Serum_sodium" class="mw-redirect" title="Serum sodium">Sodium</a></li> <li><a href="/wiki/Potassium_in_biology" title="Potassium in biology">Potassium</a></li> <li><a href="/wiki/Serum_chloride" title="Serum chloride">Chloride</a></li> <li><a href="/wiki/Calcium_in_biology" title="Calcium in biology">Calcium</a></li> <li><a href="/wiki/Renal_function" class="mw-redirect" title="Renal function">Renal function</a> <ul><li><a href="/wiki/Creatinine" title="Creatinine">Creatinine</a></li> <li><a href="/wiki/Blood_urea_nitrogen" title="Blood urea nitrogen">Urea</a></li> <li><a href="/wiki/BUN-to-creatinine_ratio" class="mw-redirect" title="BUN-to-creatinine ratio">BUN-to-creatinine ratio</a></li></ul></li> <li><a href="/wiki/Plasma_osmolality" title="Plasma osmolality">Plasma osmolality</a></li> <li><a href="/wiki/Serum_osmolal_gap" class="mw-redirect" title="Serum osmolal gap">Serum osmolal gap</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align: center;;width:1%"><a href="/wiki/Acid%E2%80%93base_homeostasis" title="Acid–base homeostasis">Acid-base</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Anion_gap" title="Anion gap">Anion gap</a></li> <li><a href="/wiki/Arterial_blood_gas_test" title="Arterial blood gas test">Arterial blood gas</a></li> <li><a href="/wiki/Base_excess" title="Base excess">Base excess</a></li> <li><a href="/wiki/Bicarbonate" title="Bicarbonate">Bicarbonate</a></li> <li><a href="/wiki/CO2_content" title="CO2 content">CO<sub>2</sub> content</a></li> <li><a href="/wiki/Lactic_acid#Blood_testing" title="Lactic acid">Lactate</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align: center;;width:1%"><a href="/wiki/Iron_tests" title="Iron tests">Iron tests</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Ferritin" title="Ferritin">Ferritin</a></li> <li><a href="/wiki/Serum_iron" title="Serum iron">Serum iron</a></li> <li><a href="/wiki/Transferrin_saturation" title="Transferrin saturation">Transferrin saturation</a></li> <li><a href="/wiki/Total_iron-binding_capacity" title="Total iron-binding capacity">Total iron-binding capacity</a></li> <li><a href="/wiki/Transferrin" title="Transferrin">Transferrin</a></li> <li><a href="/wiki/Transferrin_receptor" title="Transferrin receptor">Transferrin receptor</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align: center;;width:1%"><a href="/wiki/Endocrine_system" title="Endocrine system">Hormones</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/ACTH_stimulation_test" title="ACTH stimulation test">ACTH stimulation test</a></li> <li><a href="/wiki/Thyroid_function_tests" title="Thyroid function tests">Thyroid function tests</a> <ul><li><a href="/wiki/Thyroid-stimulating_hormone" title="Thyroid-stimulating hormone">Thyroid-stimulating hormone</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align: center;;width:1%"><a href="/wiki/Metabolism" title="Metabolism">Metabolism</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Blood_glucose" class="mw-redirect" title="Blood glucose">Blood glucose</a> <ul><li><a href="/wiki/Glycated_hemoglobin" title="Glycated hemoglobin">Hemoglobin A1c</a></li></ul></li> <li><a href="/wiki/Lipid_panel" class="mw-redirect" title="Lipid panel">Lipid panel</a> <ul><li><a href="/wiki/Low-density_lipoprotein" title="Low-density lipoprotein">LDL</a></li> <li><a href="/wiki/High-density_lipoprotein" title="High-density lipoprotein">HDL</a></li> <li><a href="/wiki/Triglyceride#Role_in_disease" title="Triglyceride">Triglycerides</a></li> <li><a href="/wiki/Cholesterol#Clinical_significance" title="Cholesterol">Total cholesterol</a></li></ul></li> <li><a href="/wiki/Basic_metabolic_panel" title="Basic metabolic panel">Basic metabolic panel</a></li> <li><a href="/wiki/Comprehensive_metabolic_panel" title="Comprehensive metabolic panel">Comprehensive metabolic panel</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align: center;;width:1%"><a href="/wiki/Cardiovascular_system" class="mw-redirect" title="Cardiovascular system">Cardiovascular</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Cardiac_marker" title="Cardiac marker">Cardiac marker</a></li> <li><a href="/wiki/Troponin_test" class="mw-redirect" title="Troponin test">Troponin test</a></li> <li><a href="/wiki/CPK-MB_test" title="CPK-MB test">CPK-MB test</a></li> <li><a href="/wiki/Lactate_dehydrogenase" title="Lactate dehydrogenase">Lactate dehydrogenase</a></li> <li><a href="/wiki/Myoglobin" title="Myoglobin">Myoglobin</a></li> <li><a href="/wiki/Glycogen_phosphorylase_isoenzyme_BB" title="Glycogen phosphorylase isoenzyme BB">Glycogen phosphorylase isoenzyme BB</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align: center;;width:1%"><a href="/wiki/Liver_function_tests" title="Liver function tests">Liver function tests</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li>Proteins <ul><li><a href="/wiki/Human_serum_albumin" title="Human serum albumin">Human serum albumin</a></li> <li><a href="/wiki/Serum_total_protein" title="Serum total protein">Serum total protein</a></li></ul></li> <li><a href="/wiki/Alkaline_phosphatase" title="Alkaline phosphatase">ALP</a></li> <li><i><a href="/wiki/Transaminase" title="Transaminase">transaminases</a></i> <ul><li><a href="/wiki/Alanine_transaminase" title="Alanine transaminase">ALT</a></li> <li><a href="/wiki/Aspartate_transaminase" title="Aspartate transaminase">AST</a></li> <li><a href="/wiki/AST/ALT_ratio" title="AST/ALT ratio">AST/ALT ratio</a></li></ul></li> <li><a href="/wiki/Gamma-glutamyltransferase#Medical_applications" title="Gamma-glutamyltransferase">GGT</a></li> <li><a href="/wiki/Bilirubin" title="Bilirubin">Bilirubin</a> <ul><li><a href="/wiki/Bilirubin#Unconjugated" title="Bilirubin">Unconjugated</a></li> <li><a href="/wiki/Bilirubin#Conjugated" title="Bilirubin">Conjugated</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align: center;;width:1%"><a href="/wiki/Pancreas" title="Pancreas">Pancreas</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Amylase" title="Amylase">Amylase</a></li> <li><a href="/wiki/Lipase" title="Lipase">Lipase</a> <ul><li><a href="/wiki/Pancreatic_lipase" class="mw-redirect" title="Pancreatic lipase">Pancreatic lipase</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="text-align: center;;width:1%"><a href="/wiki/Small_molecule" title="Small molecule">Small molecules</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" 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:1%"><a href="/wiki/Blood_sugar_level" title="Blood sugar level">Blood sugar level</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/Hypoglycemia" title="Hypoglycemia">Hypoglycemia</a></li> <li><a href="/wiki/Hyperglycemia" title="Hyperglycemia">Hyperglycemia</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Nitrogenous</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/Azotemia" title="Azotemia">Azotemia</a></li> <li><a href="/wiki/Hyperuricemia" title="Hyperuricemia">Hyperuricemia</a></li> <li><a href="/wiki/Hypouricemia" title="Hypouricemia">Hypouricemia</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="text-align: center;;width:1%">Proteins</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" 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:1%"><a href="/wiki/Liver_function_tests" title="Liver function tests">LFT</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/Elevated_transaminases" title="Elevated transaminases">Elevated transaminases</a></li> <li><a href="/wiki/Elevated_alkaline_phosphatase" title="Elevated alkaline phosphatase">Elevated ALP</a></li> <li><a href="/wiki/Hypoproteinemia" title="Hypoproteinemia">Hypoproteinemia</a> <ul><li><a href="/wiki/Hypoalbuminemia" title="Hypoalbuminemia">Hypoalbuminemia</a></li></ul></li> <li><a href="/wiki/Hyperproteinemia" title="Hyperproteinemia">Hyperproteinemia</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other</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/Elevated_alpha-fetoprotein" title="Elevated alpha-fetoprotein">Elevated alpha-fetoprotein</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Components_and_results_of_urine_tests" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse 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:Urine_tests" title="Template:Urine tests"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Urine_tests" title="Template talk:Urine tests"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Urine_tests" title="Special:EditPage/Template:Urine tests"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Components_and_results_of_urine_tests" style="font-size:114%;margin:0 4em">Components and results of <a href="/wiki/Urine_test" title="Urine test">urine tests</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Components</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Human_serum_albumin#Testing_for_albumin_loss_via_the_kidneys" title="Human serum albumin">Albumin</a></li> <li><a href="/wiki/Myoglobin" title="Myoglobin">Myoglobin</a></li> <li><a href="/wiki/Human_chorionic_gonadotropin" title="Human chorionic gonadotropin">hCG</a></li> <li><a href="/wiki/Leukocyte_esterase" title="Leukocyte esterase">Leukocyte esterase</a></li> <li><a href="/wiki/Pregnancy_test" title="Pregnancy test">Urine pregnancy test</a></li> <li><a href="/wiki/Ketone_bodies" title="Ketone bodies">Ketone bodies</a></li> <li><a href="/wiki/Glucose" title="Glucose">Glucose</a></li> <li><a href="/wiki/Urobilinogen" title="Urobilinogen">Urobilinogen</a></li> <li><a href="/wiki/Bilirubin#Urine_tests" title="Bilirubin">Bilirubin</a></li> <li><a href="/wiki/Creatinine#Urine_creatinine_.28UCr.29" title="Creatinine">Creatinine</a></li> <li><a href="/wiki/Red_blood_cell" title="Red blood cell">RBC</a></li> <li><a href="/wiki/White_blood_cell" title="White blood cell">WBC</a></li> <li><a href="/wiki/Urinary_cast" title="Urinary cast">Urinary casts</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Chemical properties</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Urinalysis" title="Urinalysis">Urinalysis</a></li> <li><a href="/wiki/Urine_specific_gravity" title="Urine specific gravity">Urine specific gravity</a> <ul><li><a href="/wiki/Isosthenuria" title="Isosthenuria">Isosthenuria</a></li></ul></li> <li><a href="/wiki/Urine_osmolality" title="Urine osmolality">Urine osmolality</a> <ul><li><a href="/wiki/Hypersthenuria" title="Hypersthenuria">Hypersthenuria</a></li></ul></li> <li><a href="/wiki/Urine#pH" title="Urine">Urine pH</a></li> <li><a href="/wiki/Urine_anion_gap" title="Urine anion gap">Urine anion gap</a></li> <li><a href="/wiki/Urine_electrolyte_levels" title="Urine electrolyte levels">Urine electrolyte levels</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Abnormal findings</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" 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:1%"><a href="/wiki/Red_blood_cell" title="Red blood cell">Red blood cells</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/Hematuria" title="Hematuria">Hematuria</a> (<a href="/wiki/Microscopic_hematuria" class="mw-redirect" title="Microscopic hematuria">Microscopic hematuria</a>)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/White_blood_cell" title="White blood cell">White blood cells</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/Eosinophiluria" title="Eosinophiluria">Eosinophiluria</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Proteinuria" title="Proteinuria">Proteinuria</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/Albuminuria" title="Albuminuria">Albuminuria</a>/<a href="/wiki/Microalbuminuria" title="Microalbuminuria">Microalbuminuria</a> <ul><li><a href="/wiki/Albumin/creatinine_ratio" class="mw-redirect" title="Albumin/creatinine ratio">Albumin/creatinine ratio</a></li> <li><a href="/wiki/Urine_protein/creatinine_ratio" title="Urine protein/creatinine ratio">Urine protein/creatinine ratio</a></li></ul></li> <li><a href="/wiki/Myoglobinuria" title="Myoglobinuria">Myoglobinuria</a></li> <li><a href="/wiki/Hemoglobinuria" title="Hemoglobinuria">Hemoglobinuria</a></li> <li><a href="/wiki/Bence_Jones_protein" title="Bence Jones protein">Bence Jones protein</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Small_molecule" title="Small molecule">Small molecules</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/Glycosuria" title="Glycosuria">Glycosuria</a></li> <li><a href="/wiki/Ketonuria" title="Ketonuria">Ketonuria</a></li> <li><a href="/wiki/Bilirubinuria" title="Bilirubinuria">Bilirubinuria</a></li> <li><a href="/wiki/Hyperuricosuria" title="Hyperuricosuria">Hyperuricosuria</a></li> <li><a href="/wiki/Aminoaciduria" title="Aminoaciduria">Aminoaciduria</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other</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/Bacteriuria" title="Bacteriuria">Bacteriuria</a></li> <li><a href="/wiki/Chyluria" title="Chyluria">Chyluria</a></li> <li><a href="/wiki/Crystalluria" title="Crystalluria">Crystalluria</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Medical_tests_on_Cerebrospinal_fluid_(CPT_82000-84999)" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse 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:CSF_tests" title="Template:CSF tests"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:CSF_tests" title="Template talk:CSF tests"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:CSF_tests" title="Special:EditPage/Template:CSF tests"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Medical_tests_on_Cerebrospinal_fluid_(CPT_82000-84999)" style="font-size:114%;margin:0 4em">Medical tests on <a href="/wiki/Cerebrospinal_fluid" title="Cerebrospinal fluid">Cerebrospinal fluid</a> (<a href="/wiki/Current_Procedural_Terminology" title="Current Procedural Terminology">CPT</a> 82000-84999)</div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Albumin" title="Albumin">Albumin</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/CSF_albumin" title="CSF albumin">CSF albumin</a></li> <li><a href="/wiki/CSF/serum_albumin_ratio" title="CSF/serum albumin ratio">CSF/serum albumin ratio</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Glucose" title="Glucose">Glucose</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/CSF_glucose" title="CSF glucose">CSF glucose</a></li> <li><a href="/wiki/CSF/serum_glucose_ratio" title="CSF/serum glucose ratio">CSF/serum glucose ratio</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Baricity" title="Baricity">Baricity</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox authority-control" aria-label="Navbox" style="padding:3px"><table class="nowraplinks hlist navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Help:Authority_control" title="Help:Authority control">Authority control databases</a>: 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