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utils: { collapseAd: Wellness.GPT.collapseAd, buildGptUrl: Wellness.GPT.buildGptUrl }, displayOnScroll: false, displayOnConsent: true, adsToCollapse: ['leaderboard*','square*'], refreshConfig: { 'defaultConfig': { refresh: false, timedRefresh: 0, refreshLimit: "unlimited", userClickRefreshSelector: "", timeoutRefreshOnceOnly: false, fiftyPercentAdRefresh: true, sizeOverrides: null }, 'square-fixed': { refresh: false, timedRefresh: 30000, refreshLimit: "unlimited", userClickRefreshSelector: "", timeoutRefreshOnceOnly: false, fiftyPercentAdRefresh: true, sizeOverrides: null }, 'square-flex-2': { refresh: false, timedRefresh: 30000, refreshLimit: "unlimited", userClickRefreshSelector: "", timeoutRefreshOnceOnly: false, fiftyPercentAdRefresh: true, sizeOverrides: null }, 'square-flex-1': { refresh: false, timedRefresh: 30000, refreshLimit: "unlimited", userClickRefreshSelector: "", timeoutRefreshOnceOnly: false, fiftyPercentAdRefresh: true, sizeOverrides: null } } }; if (Mntl.AdMetrics) { Mntl.AdMetrics.init("2794986", "n8c1f94ca602347ff80d2a3e64114b44e14", initialSlots.map(slot => slot.config.id), Date.now()); } else { Mntl.AdMetrics = { pushMetrics: () => {} }; } Mntl.GPT.setMantleDependencies(mantleDependencies); Mntl.GPT.init(options); }());window.dataLayer = window.dataLayer || []; // moved from gtm.ftl so we can initialize GTM only onLoad. 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In: Swinscow TDV. <em>Statistics at Square One</em>. The BMJ." ,"Mukaka M. <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3576830/" class="pseudoStyle" data-component="link" data-source="inlineLink" data-type="externalLink" data-ordinal="1">A guide to appropriate use of correlation coefficient in medical research</a>. <em>Malawi Med J</em>. 2012;24(3):69-71.", "Heath W. <a href="https://www.cambridge.org/us/academic/subjects/psychology/psychology-research-methods-and-statistics/psychology-research-methods-connecting-research-students-lives?format&#61;PB" data-component="link" data-source="inlineLink" data-type="externalLink" data-ordinal="1"><em>Psychology Research Methods: Connecting Research to Students’ Lives</em></a>. Cambridge University Press.", "Chen DT. <a href="https://sitn.hms.harvard.edu/flash/2021/when-correlation-does-not-imply-causation-why-your-gut-microbes-may-not-yet-be-a-silver-bullet-to-all-your-problems/" data-component="link" data-source="inlineLink" data-type="externalLink" data-ordinal="1">When correlation does not imply causation: Why your gut microbes may not (yet) be a silver bullet to all your problems</a>. Harvard University.", "Association for Psychological Science. <a href="https://www.psychologicalscience.org/news/releases/research-states-that-prejudice-comes-from-a-basic-human-need-and-way-of-thinking.html" data-component="link" data-source="inlineLink" data-type="externalLink" data-ordinal="1">Research states that prejudice comes from a basic human need and way of thinking</a>." ] ,"mainEntityOfPage": { "@type": ["WebPage"] ,"@id": "https://www.verywellmind.com/what-is-correlation-2794986" ,"breadcrumb": { "@type": "BreadcrumbList", "itemListElement": [ { "@type": "ListItem", "position": 1, "item": { "@id": "https://www.verywellmind.com/psychology-4157187", "name": "Psychology" } } , { "@type": "ListItem", "position": 2, "item": { "@id": "https://www.verywellmind.com/student-resources-overview-4581768", "name": "Student Resources" } } ] },"reviewedBy": [ {"@type": "Person" ,"name": "James Lacy" ,"url": "https://www.verywellmind.com/james-lacy-4800734" } ]} , "about": [ { "@type": "FAQPage", "mainEntity": [ { "@type": "Question", "name": "How do you find the correlation coefficient?", "acceptedAnswer": { "@type": "Answer", "text": "<p>You can calculate the correlation coefficient in a few different ways, with the same result. The general formula is <em>r<sub>XY<\/sub>=COV<sub>XY<\/sub>/(S<sub>X<\/sub> S<sub>Y<\/sub>)<\/em>, which is the covariance between the two variables, divided by the product of their standard deviations:<\/p>" } } , { "@type": "Question", "name": "How do you calculate a correlation coefficient in Excel?", "acceptedAnswer": { "@type": "Answer", "text": "<p>In the cell in which you want the correlation coefficient to appear, enter <em>=CORREL(A2:A7,B2:B7),<\/em> where A2:A7 and B2:B7 are the variable lists to compare. Press <strong>Enter<\/strong>.<\/p>" } } , { "@type": "Question", "name": "How do you find a linear correlation coefficient?", "acceptedAnswer": { "@type": "Answer", "text": "<p>Finding the linear correlation coefficient requires a long, difficult calculation, so most people use a calculator or software such as Excel or a statistics program.<\/p>" } } , { "@type": "Question", "name": "How do you interpret a correlation coefficient?", "acceptedAnswer": { "@type": "Answer", "text": "<p>Correlations range from -1.00 to +1.00. The correlation coefficient (expressed as <em>r<\/em> ) shows the direction and strength of a relationship between two variables. 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</h1> <div id="article-meta_1-0" class="comp article-meta mntl-block not-news" data-tracking-container="true"><div id="article-meta__wrapper_1-0" class="comp article-meta__wrapper mntl-block"><div id="wellness-bylines_1-0" class="comp wellness-bylines mntl-bylines"><div id="mntl-bylines__group_1-0" class="comp mntl-bylines__group mntl-block mntl-bylines__group--author "><div id="mntl-bylines__item_1-0" class="comp mntl-bylines__item mntl-attribution__item mntl-attribution__item--has-date"> <span class="mntl-attribution__item-descriptor">By</span> <div data-tooltip="<p>Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."</p>" tabindex="0" data-inline-tooltip="true"> <a href="https://www.verywellmind.com/kendra-cherry-2794702" rel="nocaes" data-trigger-link="true" class="mntl-attribution__item-name" tabindex="-1" >Kendra Cherry, MSEd</a> <div id="mntl-author-tooltip_1-0" class="comp mntl-author-tooltip mntl-tooltip mntl-group"> <div class="mntl-author-tooltip__top "> <div class="mntl-author-tooltip__image-wrapper"> <div class="img-placeholder" style="padding-bottom:134.8%;"> <img data-srcset="https://www.verywellmind.com/thmb/w7x__KIPSpoxWRRBurM9Kqk8MvQ=/40x0/filters:no_upscale():max_bytes(150000):strip_icc()/IMG_9791-89504ab694d54b66bbd72cb84ffb860e.jpg 40w, https://www.verywellmind.com/thmb/66vhMa_zlCFnP773y8eC1o3_HCY=/58x0/filters:no_upscale():max_bytes(150000):strip_icc()/IMG_9791-89504ab694d54b66bbd72cb84ffb860e.jpg 58w, https://www.verywellmind.com/thmb/5KCnnppbCs8VTdyXMfsDbo04AYU=/76x0/filters:no_upscale():max_bytes(150000):strip_icc()/IMG_9791-89504ab694d54b66bbd72cb84ffb860e.jpg 76w, https://www.verywellmind.com/thmb/UVkbjl0TZ6eJA9G--TvedkYdSfE=/94x0/filters:no_upscale():max_bytes(150000):strip_icc()/IMG_9791-89504ab694d54b66bbd72cb84ffb860e.jpg 94w, https://www.verywellmind.com/thmb/eL5wL-UPVwXxQ5uQCnpwFteUlQ8=/112x0/filters:no_upscale():max_bytes(150000):strip_icc()/IMG_9791-89504ab694d54b66bbd72cb84ffb860e.jpg 112w" data-sizes="80px" data-src="https://www.verywellmind.com/thmb/6si2AfQ0ueWEXTMhF4mbaynu6II=/200x200/filters:no_upscale():max_bytes(150000):strip_icc()/IMG_9791-89504ab694d54b66bbd72cb84ffb860e.jpg" alt="Kendra Cherry" class="lazyload mntl-author-tooltip__image" width="200" height="200" /> <noscript> <img src="https://www.verywellmind.com/thmb/6si2AfQ0ueWEXTMhF4mbaynu6II=/200x200/filters:no_upscale():max_bytes(150000):strip_icc()/IMG_9791-89504ab694d54b66bbd72cb84ffb860e.jpg" srcset="https://www.verywellmind.com/thmb/w7x__KIPSpoxWRRBurM9Kqk8MvQ=/40x0/filters:no_upscale():max_bytes(150000):strip_icc()/IMG_9791-89504ab694d54b66bbd72cb84ffb860e.jpg 40w, https://www.verywellmind.com/thmb/66vhMa_zlCFnP773y8eC1o3_HCY=/58x0/filters:no_upscale():max_bytes(150000):strip_icc()/IMG_9791-89504ab694d54b66bbd72cb84ffb860e.jpg 58w, https://www.verywellmind.com/thmb/5KCnnppbCs8VTdyXMfsDbo04AYU=/76x0/filters:no_upscale():max_bytes(150000):strip_icc()/IMG_9791-89504ab694d54b66bbd72cb84ffb860e.jpg 76w, https://www.verywellmind.com/thmb/UVkbjl0TZ6eJA9G--TvedkYdSfE=/94x0/filters:no_upscale():max_bytes(150000):strip_icc()/IMG_9791-89504ab694d54b66bbd72cb84ffb860e.jpg 94w, https://www.verywellmind.com/thmb/eL5wL-UPVwXxQ5uQCnpwFteUlQ8=/112x0/filters:no_upscale():max_bytes(150000):strip_icc()/IMG_9791-89504ab694d54b66bbd72cb84ffb860e.jpg 112w" alt="Kendra Cherry" width="200" height="200" class="img--noscript mntl-author-tooltip__image" /> </noscript> </div> </div> <div id="mntl-author-tooltip__name_1-0" class="comp mntl-author-tooltip__name mntl-attribution__item "> <a href="https://www.verywellmind.com/kendra-cherry-2794702" rel="nocaes" class="mntl-attribution__item-name" tabindex="0" >Kendra Cherry, MSEd</a> </div> <div class="mntl-author-tooltip__bio"> <p>Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."</p> </div> </div> <div class="mntl-author-tooltip__bottom"> <span class="mntl-author-tooltip__learn-more-text">Learn about our </span> <a href="/our-editorial-process-4778006" rel="nocaes" class="mntl-author-tooltip__learn-more-link" >editorial process</a> </div> </div></div> </div> <div class="mntl-attribution__item-date">Updated on November 30, 2023</div></div> <div id="mntl-bylines__group_2-0" class="comp mntl-bylines__group mntl-block mntl-bylines__group--fact_checker "><div id="mntl-bylines__item_2-0" class="comp mntl-bylines__item mntl-attribution__item "><svg class="icon reviewer-icon mntl-attribution__item-icon" > <use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#reviewer-icon" href="#reviewer-icon"></use> </svg> <span id="review-descriptor-override_2-0" class="comp review-descriptor-override "><span data-tooltip="Verywell Mind content is rigorously reviewed by a team of qualified and experienced fact checkers. 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about our </span> <a href="/our-editorial-process-4778006" rel="nocaes" class="mntl-author-tooltip__learn-more-link" >editorial process</a> </div> </div></div> </div></div> </div> <div id="social-share-container_1-0" class="comp social-share-container mntl-block"><form id="print-button_1-0" class="comp print-button" method="POST" action="/what-is-correlation-2794986?print" data-tracking-container="true" target="_blank"> <button class="btn"> Print <svg class="icon icon-print text-btn-icon" > <use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-print" href="#icon-print"></use> </svg> </button> <input type="hidden" value="true" name="print" /> <input type="hidden" value="a2d495b271d24ca51a3c1c102f6cb66c" name="CSRFToken" /> </form></div></div></div> </div><div class="loc article-post-header"><figure id="figure-article_1-0" class="comp figure-article mntl-block lock-journey" data-tracking-container="true"><div id="figure-article__media_1-0" class="comp figure-article__media mntl-block"><figure id="figure-article__image_1-0" class="comp figure-article__image mntl-universal-primary-image primary-image"> <div class="primary-image__media"> <div class="img-placeholder" style="padding-bottom:55.2%;"> <img src="https://www.verywellmind.com/thmb/X9seYgk-Q29Ozll7ByNlUcEdPTA=/1500x0/filters:no_upscale():max_bytes(150000):strip_icc()/Correlation_coefficient-56a792873df78cf77297414e.png" width="960" height="530" srcset="https://www.verywellmind.com/thmb/e1UdienouGMjGTGph75znXDoKhE=/750x0/filters:no_upscale():max_bytes(150000):strip_icc()/Correlation_coefficient-56a792873df78cf77297414e.png 750w" sizes="750px" alt="Correlations" class=" primary-image__image mntl-primary-image--blurry" onload="(function(e){e.classList.add('loaded')})(this)" style="--blurry: url('data:image/gif;charset=utf-8;base64,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')" /> <noscript> <img src="https://www.verywellmind.com/thmb/X9seYgk-Q29Ozll7ByNlUcEdPTA=/1500x0/filters:no_upscale():max_bytes(150000):strip_icc()/Correlation_coefficient-56a792873df78cf77297414e.png" width="960" height="530" class="loaded primary-img--noscript primary-image__image mntl-primary-image--blurry" srcset="https://www.verywellmind.com/thmb/e1UdienouGMjGTGph75znXDoKhE=/750x0/filters:no_upscale():max_bytes(150000):strip_icc()/Correlation_coefficient-56a792873df78cf77297414e.png 750w" sizes="750px" alt="Correlations" /> </noscript> </div> </div> <figcaption id="primary-image__figcap_1-0" class="comp primary-image__figcap mntl-figure-caption figure-article-caption"> <svg class="icon icon-camera figure-article-caption-icon" > <use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-camera" href="#icon-camera"></use> </svg> <span class="figure-article-caption-text">Correlations indicate relationships between variables.</span> <span class="figure-article-caption-owner">Kiatdd / Wikimedia Commons</span> </figcaption></figure></div></figure> </div><div class="loc article-left-rail"><div id="sticky-toc-wrapper_1-0" class="comp sticky-toc-wrapper mntl-block js-sticky-container"><div id="sticky-toc_1-0" class="comp sticky-toc mntl-sticky-toc mntl-block sticky-toc-widget" data-desktop-bp="70em"><div id="toc-wrapper_1-0" class="comp toc-wrapper mntl-toc mntl-block" data-chop-mobile="true" data-desktop-bp="70em" data-offset="60" data-tracking-container="true"><div id="mntl-toc__inner_1-0" class="comp mntl-toc__inner mntl-block"><div id="mntl-toc__heading_1-0" class="comp mntl-toc__heading mntl-block js-toc-toggle" data-click-tracked="true" data-desktop-bp="70em"><span id="mntl-toc__heading-text_1-0" class="comp mntl-toc__heading-text mntl-text-block">Table of Contents</span> <div id="mntl-toc-toggle_1-0" class="comp mntl-toc-toggle mntl-block"><div id="mntl-toc-toggle__btn_1-0" class="comp mntl-toc-toggle__btn mntl-text-block js-mntl-toc-toggle" data-click-tracked="true" data-desktop-bp="70em" data-collapsed-text="View All" data-expanded-text="View All">View All</div> <svg class="icon icon-circle-arrow icon-circle-arrow" > <use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-circle-arrow" href="#icon-circle-arrow"></use> </svg></div> <svg class="icon icon-arrow " > <use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-arrow" href="#icon-arrow"></use> </svg></div> <div id="mntl-toc__mobile-toggle_1-0" class="comp mntl-toc__mobile-toggle mntl-block js-sticky-toggle"><span id="mntl-toc__heading-text_2-0" class="comp mntl-toc__heading-text mntl-text-block">Table of Contents</span> <svg class="icon icon-arrow " > <use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-arrow" href="#icon-arrow"></use> </svg></div> <ul id="mntl-toc__list_1-0" class="comp mntl-toc__list mntl-toc__list-heading expert-content"><li id="mntl-toc__list-item_1-0" class="comp mntl-toc__list-item mntl-block"><div id="mntl-toc__list-item-heading_1-0" class="comp mntl-toc__list-item-heading mntl-block"><a href="#toc-what-is-a-correlation-coefficient" rel="nocaes" id="mntl-toc__list-item-link_1-0" class="mntl-toc__list-item-link mntl-text-link mntl-toc__list-item-link js-mntl-toc-link" data-tracking-container="true" ><span class="link__wrapper">What Is a Correlation Coefficient?</span></a></div></li> <li id="mntl-toc__list-item_2-0" class="comp mntl-toc__list-item mntl-block"><div id="mntl-toc__list-item-heading_2-0" class="comp mntl-toc__list-item-heading mntl-block"><a href="#toc-types-of-correlation" rel="nocaes" id="mntl-toc__list-item-link_2-0" class="mntl-toc__list-item-link mntl-text-link mntl-toc__list-item-link js-mntl-toc-link" data-tracking-container="true" ><span class="link__wrapper">Types</span></a></div></li> <li id="mntl-toc__list-item_3-0" class="comp mntl-toc__list-item mntl-block"><div id="mntl-toc__list-item-heading_3-0" class="comp mntl-toc__list-item-heading mntl-block"><a href="#toc-scatter-plots-and-correlation" rel="nocaes" id="mntl-toc__list-item-link_3-0" class="mntl-toc__list-item-link mntl-text-link mntl-toc__list-item-link js-mntl-toc-link" data-tracking-container="true" ><span class="link__wrapper">Scatter Plots and Correlation</span></a></div></li> <li id="mntl-toc__list-item_4-0" class="comp mntl-toc__list-item mntl-block"><div id="mntl-toc__list-item-heading_4-0" class="comp mntl-toc__list-item-heading mntl-block"><a href="#toc-strong-vs-weak-correlations" rel="nocaes" id="mntl-toc__list-item-link_4-0" class="mntl-toc__list-item-link mntl-text-link mntl-toc__list-item-link js-mntl-toc-link" data-tracking-container="true" ><span class="link__wrapper">Strong vs. Weak Correlations</span></a></div></li> <li id="mntl-toc__list-item_5-0" class="comp mntl-toc__list-item mntl-block"><div id="mntl-toc__list-item-heading_5-0" class="comp mntl-toc__list-item-heading mntl-block"><a href="#toc-correlation-does-not-equal-causation" rel="nocaes" id="mntl-toc__list-item-link_5-0" class="mntl-toc__list-item-link mntl-text-link mntl-toc__list-item-link js-mntl-toc-link" data-tracking-container="true" ><span class="link__wrapper">Correlation Does Not Equal Causation</span></a></div></li> <li id="mntl-toc__list-item_6-0" class="comp mntl-toc__list-item mntl-block"><div id="mntl-toc__list-item-heading_6-0" class="comp mntl-toc__list-item-heading mntl-block"><a href="#toc-illusory-correlations" rel="nocaes" id="mntl-toc__list-item-link_6-0" class="mntl-toc__list-item-link mntl-text-link mntl-toc__list-item-link js-mntl-toc-link" data-tracking-container="true" ><span class="link__wrapper">Illusory Correlations</span></a></div></li> <li id="mntl-toc__list-item_7-0" class="comp mntl-toc__list-item mntl-block"><div id="mntl-toc__list-item-heading_7-0" class="comp mntl-toc__list-item-heading mntl-block"><a href="#toc-frequently-asked-questions-52be0b7d-5f9a-49e7-a1b9-00078f64c7ee" rel="nocaes" id="mntl-toc__list-item-link_7-0" class="mntl-toc__list-item-link mntl-text-link mntl-toc__list-item-link js-mntl-toc-link" data-tracking-container="true" ><span class="link__wrapper">Frequently Asked Questions</span></a></div></li></ul></div></div></div></div> </div><div class="loc article-content"><div id="article__broad-video-jw_1-0" class="comp article__broad-video-jw mntl-jwplayer-broad mntl-block is-hidden" data-pixel-depth="100"><div id="mntl-jwplayer-broad__video_1-0" class="comp mntl-jwplayer-broad__video mntl-jwplayer mm-video lazyload" data-bgset data-sizes="auto"></div> <div id="mntl-jwplayer-broad__title_1-0" class="comp mntl-jwplayer-broad__title mntl-block"><div id="mntl-jwplayer-broad__title--text_1-0" class="comp mntl-jwplayer-broad__title--text mntl-text-block type--mouse"></div> <button id="mntl-jwplayer-broad__title-icon--close_1-0" class="comp mntl-jwplayer-broad__title-icon--close mntl-block type--shrew-bold" data-click-tracked="false"><span id="mntl-text-block_1-0" class="comp mntl-text-block">Close</span> <svg class="icon close-icon " > <use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#close-icon" href="#close-icon"></use> </svg></button></div></div> <div id="wellness-sc-page_1-0" class="comp wellness-sc-page mntl-sc-page mntl-block structured-content article-content expert-content right-rail__offset lock-journey" data-sc-sticky-offset="60" data-sc-ad-label-height="24" data-sc-ad-track-spacing="100" data-sc-min-track-height="250" data-sc-max-track-height="600" data-sc-breakpoint="50em" data-sc-load-immediate="4" data-sc-content-positions="[400, 1400, 1400, 1700, 2000, 2200, 2400, 2600, 2800]" data-bind-scroll-on-start="true"><p id="mntl-sc-block_1-0" class="comp mntl-sc-block mntl-sc-block-html"> A correlation means that there is a relationship between two or more variables. This does not imply, however, that there is necessarily a cause or effect relationship between them. Instead, it simply means that there is some type of relationship, meaning they change together at a constant rate. </p> <div id="mntl-sc-block_2-0" class="comp mntl-sc-block mntl-sc-block-adslot mntl-block"></div> <p id="mntl-sc-block_3-0" class="comp mntl-sc-block mntl-sc-block-html"> A correlation coefficient is a number that expresses the strength of the relationship between the two variables.<br/> </p> <div id="mntl-sc-block_4-0" class="comp mntl-sc-block mntl-sc-block-adslot mntl-block"></div> <div id="wellness-sc-block-callout--key-takeaway_1-0" class="comp wellness-sc-block-callout--key-takeaway wellness-sc-block-callout-base mntl-sc-block-callout mntl-block theme-key-takeaway theme-key-takeaway" data-tracking-id="mntl-sc-block-callout" data-tracking-container="true"><h3 id="mntl-sc-block-callout-heading_1-0" class="comp mntl-sc-block-callout-heading mntl-text-block">At a Glance</h3> <div id="mntl-sc-block-callout-body_1-0" class="comp mntl-sc-block-callout-body mntl-text-block expert-content"><p>Correlation can help researchers understand if there is an association between two variables of interest. Such relationships can be positive, meaning they move in the same direction together, or negative, meaning that as one goes up, the other goes down. Correlations can be visualized using scatter plots to show how measurements of a variable change along an x- and y-axis.</p><p>It is important to remember that while correlations can help show a relationship, correlation does not indicate causation.</p></div></div> <span class="heading-toc" id="toc-what-is-a-correlation-coefficient"></span><h2 id="mntl-sc-block_6-0" class="comp mntl-sc-block wellness-sc-block-heading mntl-sc-block-heading"> <span class="mntl-sc-block-heading__text"> What Is a Correlation Coefficient? </span> </h2> <p id="mntl-sc-block_7-0" class="comp mntl-sc-block mntl-sc-block-html"> A correlation coefficient, often expressed as <em>r</em>, indicates a measure of the direction and strength of a relationship between two variables. When the <em>r</em> value is closer to +1 or -1, it indicates that there is a stronger linear relationship between the two variables.<span class="ql-inline-citation" data-cite="2"></span><br/> </p> <div id="mntl-sc-block_8-0" class="comp mntl-sc-block mntl-sc-block-adslot mntl-block"></div> <div id="wellness-sc-block-callout--takeaway_1-0" class="comp wellness-sc-block-callout--takeaway wellness-sc-block-callout-base mntl-sc-block-callout mntl-block theme-takeaway theme-takeaway" data-tracking-id="mntl-sc-block-callout" data-tracking-container="true"><div id="mntl-sc-block-callout-body_2-0" class="comp mntl-sc-block-callout-body mntl-text-block expert-content"><p><a href="https://www.verywellmind.com/correlational-research-2795774" data-component="link" data-source="inlineLink" data-type="internalLink" data-ordinal="1">Correlational studies</a> are quite common in psychology, particularly because some things are impossible to recreate or <a href="https://www.verywellmind.com/introduction-to-research-methods-2795793" data-component="link" data-source="inlineLink" data-type="internalLink" data-ordinal="2">research in a lab setting</a>.</p></div></div> <p id="mntl-sc-block_10-0" class="comp mntl-sc-block mntl-sc-block-html"> Instead of performing an <a href="https://www.verywellmind.com/how-to-conduct-a-psychology-experiment-2795792" data-component="link" data-source="inlineLink" data-type="internalLink" data-ordinal="1">experiment</a>, researchers may collect data to look at possible relationships between variables. From the data they collect and its analysis, researchers then make inferences and predictions about the nature of the relationships between variables.<br> </p> <div id="mntl-sc-block_11-0" class="comp mntl-sc-block mntl-sc-block-adslot mntl-block"></div> <div id="wellness-sc-block-callout--explainer_1-0" class="comp wellness-sc-block-callout--explainer wellness-sc-block-callout-base mntl-sc-block-callout mntl-block theme-explainer theme-explainer" data-tracking-id="mntl-sc-block-callout" data-tracking-container="true"><h3 id="mntl-sc-block-callout-heading_2-0" class="comp mntl-sc-block-callout-heading mntl-text-block">Helpful Hint</h3> <div id="mntl-sc-block-callout-body_3-0" class="comp mntl-sc-block-callout-body mntl-text-block expert-content"><p>A correlation<strong> </strong>is a statistical measurement of the relationship between two variables.<span class="ql-inline-citation" data-cite="1"></span> Remember this handy rule: The closer the correlation is to 0, the weaker it is. The closer it is to +/-1, the stronger it is.</p></div></div> <span class="heading-toc" id="toc-types-of-correlation"></span><h2 id="mntl-sc-block_13-0" class="comp mntl-sc-block wellness-sc-block-heading mntl-sc-block-heading"> <span class="mntl-sc-block-heading__text"> Types of Correlation </span> </h2> <p id="mntl-sc-block_14-0" class="comp mntl-sc-block mntl-sc-block-html"> Correlation strength ranges from -1 to +1. </p> <div id="mntl-sc-block_15-0" class="comp mntl-sc-block mntl-sc-block-adslot mntl-block"></div> <h3 id="mntl-sc-block_17-0" class="comp mntl-sc-block mntl-sc-block-subheading"> <span class="mntl-sc-block-subheading__text"> Positive Correlation </span> </h3> <p id="mntl-sc-block_18-0" class="comp mntl-sc-block mntl-sc-block-html"> A correlation of +1 indicates a perfect positive correlation, meaning that both variables move in the same direction together. In other words, +1 is the strong positive correlation you can find. </p> <div id="mntl-sc-block_19-0" class="comp mntl-sc-block mntl-sc-block-adslot mntl-block"></div> <h3 id="mntl-sc-block_21-0" class="comp mntl-sc-block mntl-sc-block-subheading"> <span class="mntl-sc-block-subheading__text"> Negative Correlation </span> </h3> <p id="mntl-sc-block_22-0" class="comp mntl-sc-block mntl-sc-block-html"> A correlation of –1 indicates a perfect negative correlation, meaning that as one variable goes up, the other goes down. </p> <div id="mntl-sc-block_23-0" class="comp mntl-sc-block mntl-sc-block-adslot mntl-block"></div> <h3 id="mntl-sc-block_25-0" class="comp mntl-sc-block mntl-sc-block-subheading"> <span class="mntl-sc-block-subheading__text"> Zero Correlation </span> </h3> <p id="mntl-sc-block_26-0" class="comp mntl-sc-block mntl-sc-block-html"> A zero correlation suggests that the correlation statistic does not indicate a relationship between the two variables. This does not mean that there is no relationship at all; it simply means that there is not a linear relationship. A zero correlation is often indicated using the abbreviation <em>r </em>= 0.<br/> </p> <div id="mntl-sc-block_27-0" class="comp mntl-sc-block mntl-sc-block-adslot mntl-block"></div> <div id="wellness-sc-block-featuredlink--related_1-0" class="comp wellness-sc-block-featuredlink--related wellness-sc-block-featuredlink-base mntl-sc-block-featuredlink mntl-block related-link related-link theme-related"><a href="https://www.verywellmind.com/what-is-a-variable-2795789" rel="nocaes" id="mntl-sc-block-featuredlink__link_1-0" class="mntl-sc-block-featuredlink__link mntl-text-link " data-tracking-container="true" data-tracking-id="featured-link" ><span class="link__wrapper">How Are Variables Used in Psychology Research?</span></a></div> <div id="mntl-sc-block_29-0" class="comp mntl-sc-block mntl-sc-block-adslot mntl-block"></div> <span class="heading-toc" id="toc-scatter-plots-and-correlation"></span><h2 id="mntl-sc-block_30-0" class="comp mntl-sc-block wellness-sc-block-heading mntl-sc-block-heading"> <span class="mntl-sc-block-heading__text"> Scatter Plots and Correlation </span> </h2> <p id="mntl-sc-block_31-0" class="comp mntl-sc-block mntl-sc-block-html"> Scatter plots (also called scatter charts, scattergrams, and scatter diagrams) are used to plot variables on a chart to observe the associations or relationships between them. The horizontal axis represents one variable, and the vertical axis represents the other. </p> <div id="mntl-sc-block_32-0" class="comp mntl-sc-block mntl-sc-block-adslot mntl-block"></div> <figure id="wellness-sc-block-image--none_1-0" class="comp wellness-sc-block-image--none wellness-sc-block-image-base mntl-sc-block-universal-image mntl-sc-block-image--no-theme no-theme mntl-sc-block-image mntl-sc-block theme-none figure-landscape figure-high-res"> <div class="figure-media"> <div class="img-placeholder" style="padding-bottom:50.0%;"> <img data-src="https://www.verywellmind.com/thmb/Q1Kn09TMy-mDVAw_46uM_nFI9gg=/1500x0/filters:no_upscale():max_bytes(150000):strip_icc()/Scatter_plot-5c63e7d446e0fb00017c2711.jpg" width="1280" height="640" data-srcset="https://www.verywellmind.com/thmb/CPM3mkH_AkyecjGA0_Md-bgXjpc=/750x0/filters:no_upscale():max_bytes(150000):strip_icc()/Scatter_plot-5c63e7d446e0fb00017c2711.jpg 750w" data-sizes="(max-width: 1248px) 1500px, 1500px" alt="Scatter Plot diagram" class="lazyload universal-image__image" data-expand="300" id=mntl-sc-block-image_1-0 data-tracking-container="true" data-img-lightbox="true" data-click-tracked="true" /> <noscript> <img src="https://www.verywellmind.com/thmb/Q1Kn09TMy-mDVAw_46uM_nFI9gg=/1500x0/filters:no_upscale():max_bytes(150000):strip_icc()/Scatter_plot-5c63e7d446e0fb00017c2711.jpg" width="1280" height="640" class="img--noscript universal-image__image" srcset="https://www.verywellmind.com/thmb/CPM3mkH_AkyecjGA0_Md-bgXjpc=/750x0/filters:no_upscale():max_bytes(150000):strip_icc()/Scatter_plot-5c63e7d446e0fb00017c2711.jpg 750w" sizes="(max-width: 1248px) 1500px, 1500px" alt="Scatter Plot diagram" /> </noscript> </div> </div> <figcaption id="mntl-figure-caption_1-0" class="comp mntl-figure-caption type--mouse figure-article-caption"> <span class="figure-article-caption-text">Scatter Plot diagram.</span> <span class="figure-article-caption-owner"><p>Investopedia</p></span> </figcaption></figure> <p id="mntl-sc-block_34-0" class="comp mntl-sc-block mntl-sc-block-html"> Each point on the plot is a different measurement. From those measurements, a trend line can be calculated. The correlation coefficient is the slope of that line. When the correlation is weak (<em>r</em> is close to zero), the line is hard to distinguish. When the correlation is strong (<em>r</em> is close to 1), the line will be more apparent.<br/> </p> <div id="mntl-sc-block_35-0" class="comp mntl-sc-block mntl-sc-block-adslot mntl-block"></div> <span class="heading-toc" id="toc-strong-vs-weak-correlations"></span><h2 id="mntl-sc-block_36-0" class="comp mntl-sc-block wellness-sc-block-heading mntl-sc-block-heading"> <span class="mntl-sc-block-heading__text"> Strong vs. Weak Correlations </span> </h2> <p id="mntl-sc-block_37-0" class="comp mntl-sc-block mntl-sc-block-html"> Correlations can be confusing, and many people equate positive with strong and negative with weak. A relationship between two variables can be negative, but that doesn't mean that the relationship isn't strong.<br/> </p> <div id="mntl-sc-block_38-0" class="comp mntl-sc-block mntl-sc-block-adslot mntl-block"></div> <div id="wellness-sc-block-callout--explainer_2-0" class="comp wellness-sc-block-callout--explainer wellness-sc-block-callout-base mntl-sc-block-callout mntl-block theme-explainer theme-explainer" data-tracking-id="mntl-sc-block-callout" data-tracking-container="true"><div id="mntl-sc-block-callout-body_4-0" class="comp mntl-sc-block-callout-body mntl-text-block expert-content"><ul><li><strong>A weak positive correlation</strong> indicates that, although both variables tend to go up in response to one another, the relationship is not very strong. </li><li><strong>A strong negative correlation</strong>, on the other hand, indicates a strong connection between the two variables, but that one goes up whenever the other one goes down.</li></ul></div></div> <p id="mntl-sc-block_40-0" class="comp mntl-sc-block mntl-sc-block-html"> For example, a correlation of -0.97 is a strong negative correlation, whereas a correlation of 0.10 indicates a weak positive correlation. A correlation of +0.10 is weaker than -0.74, and a correlation of -0.98 is stronger than +0.79.<br/> </p> <div id="mntl-sc-block_41-0" class="comp mntl-sc-block mntl-sc-block-adslot mntl-block"></div> <span class="heading-toc" id="toc-correlation-does-not-equal-causation"></span><h2 id="mntl-sc-block_42-0" class="comp mntl-sc-block wellness-sc-block-heading mntl-sc-block-heading"> <span class="mntl-sc-block-heading__text"> Correlation Does Not Equal Causation </span> </h2> <p id="mntl-sc-block_43-0" class="comp mntl-sc-block mntl-sc-block-html"> Correlation does not equal causation. Just because two variables have a relationship does not mean that changes in one variable <em>cause </em>changes in the other. </p> <div id="mntl-sc-block_44-0" class="comp mntl-sc-block mntl-sc-block-adslot mntl-block"></div> <div id="wellness-sc-block-callout--center-bold_1-0" class="comp wellness-sc-block-callout--center-bold wellness-sc-block-callout-base mntl-sc-block-callout mntl-block theme-center-bold theme-center-bold" data-tracking-id="mntl-sc-block-callout" data-tracking-container="true"><div id="mntl-sc-block-callout-body_5-0" class="comp mntl-sc-block-callout-body mntl-text-block expert-content"><p>Correlations tell us that there is a relationship between variables, but this does not necessarily mean that one variable causes the other to change.</p></div></div> <p id="mntl-sc-block_46-0" class="comp mntl-sc-block mntl-sc-block-html"> An oft-cited example is the correlation between ice cream consumption and homicide rates. Studies have found a correlation between increased ice cream sales and spikes in homicides. However, eating ice cream does not cause you to commit murder. Instead, there is a third variable: heat. Both variables increase <a href="https://www.verywellmind.com/how-weather-changes-can-affect-your-mental-health-5222029" data-component="link" data-source="inlineLink" data-type="internalLink" data-ordinal="1">during summertime</a>.<span class="ql-inline-citation" data-cite="3"></span><br> </p> <div id="mntl-sc-block_47-0" class="comp mntl-sc-block mntl-sc-block-adslot mntl-block"></div> <span class="heading-toc" id="toc-illusory-correlations"></span><h2 id="mntl-sc-block_48-0" class="comp mntl-sc-block wellness-sc-block-heading mntl-sc-block-heading"> <span class="mntl-sc-block-heading__text"> Illusory Correlations </span> </h2> <p id="mntl-sc-block_49-0" class="comp mntl-sc-block mntl-sc-block-html"> An illusory correlation is the perception of a relationship between two variables when only a minor relationship—or none at all—actually exists. An illusory correlation does not always mean inferring causation; it can also mean inferring a relationship between two variables when one does not exist. </p> <div id="mntl-sc-block_50-0" class="comp mntl-sc-block mntl-sc-block-adslot mntl-block"></div> <p id="mntl-sc-block_51-0" class="comp mntl-sc-block mntl-sc-block-html"> For example, people sometimes assume that, because two events occurred together at one point in the past, one event must be the cause of the other. These illusory correlations can occur both in scientific investigations and in real-world situations.<br/> </p> <div id="mntl-sc-block_52-0" class="comp mntl-sc-block mntl-sc-block-adslot mntl-block"></div> <div id="wellness-sc-block-callout--takeaway_2-0" class="comp wellness-sc-block-callout--takeaway wellness-sc-block-callout-base mntl-sc-block-callout mntl-block theme-takeaway theme-takeaway" data-tracking-id="mntl-sc-block-callout" data-tracking-container="true"><div id="mntl-sc-block-callout-body_6-0" class="comp mntl-sc-block-callout-body mntl-text-block expert-content"><p><a href="https://www.verywellmind.com/what-is-prejudice-2795476" data-component="link" data-source="inlineLink" data-type="internalLink" data-ordinal="1">Stereotypes</a> are a good example of illusory correlations. Research has shown that people tend to assume that certain groups and traits occur together and frequently overestimate the strength of the association between the two variables.<span class="ql-inline-citation" data-cite="4"></span></p></div></div> <p id="mntl-sc-block_54-0" class="comp mntl-sc-block mntl-sc-block-html"> For example, suppose someone holds the mistaken belief that all people from small towns are extremely kind. When they meet a very kind person, their immediate assumption might be that the person is from a small town, despite the fact that kindness is not related to city population.<br/> </p> <div id="mntl-sc-block_55-0" class="comp mntl-sc-block mntl-sc-block-adslot mntl-block"></div> <div id="wellness-sc-block-callout--exclamation_1-0" class="comp wellness-sc-block-callout--exclamation wellness-sc-block-callout-base mntl-sc-block-callout mntl-block theme-exclamation theme-exclamation" data-tracking-id="mntl-sc-block-callout" data-tracking-container="true"><h3 id="mntl-sc-block-callout-heading_3-0" class="comp mntl-sc-block-callout-heading mntl-text-block">What This Means For You</h3> <div id="mntl-sc-block-callout-body_7-0" class="comp mntl-sc-block-callout-body mntl-text-block expert-content"><p>Psychology research frequently uses correlations, but it's essential to understand that correlation is not the same as causation. Confusing correlation with causation assumes a cause-effect relationship that might not exist. While correlation can help you see that there is a relationship (and tell you how strong that relationship is), only experimental research can reveal a causal connection.</p></div> <svg class="icon icon-exclamation " > <use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-exclamation" href="#icon-exclamation"></use> </svg></div> <div id="wellness-sc-block-featuredlink--related_2-0" class="comp wellness-sc-block-featuredlink--related wellness-sc-block-featuredlink-base mntl-sc-block-featuredlink mntl-block related-link related-link theme-related"><a href="https://www.verywellmind.com/what-is-a-confirmation-bias-2795024" rel="nocaes" id="mntl-sc-block-featuredlink__link_2-0" class="mntl-sc-block-featuredlink__link mntl-text-link " data-tracking-container="true" data-tracking-id="featured-link" ><span class="link__wrapper">How Confirmation Bias Works</span></a></div> <div id="mntl-sc-block_58-0" class="comp mntl-sc-block mntl-sc-block-adslot mntl-block"></div> <div id="wellness-sc-block-faq--expanded_1-0" class="comp wellness-sc-block-faq--expanded wellness-sc-block-faq-base mntl-sc-block-faq mntl-block theme-expanded theme-expanded"><span class="heading-toc" id="toc-frequently-asked-questions-52be0b7d-5f9a-49e7-a1b9-00078f64c7ee"></span> <h3 id="mntl-sc-block-faq__title_1-0" class="comp mntl-sc-block-faq__title mntl-text-block">Frequently Asked Questions</h3> <ul id="mntl-sc-block-faq__content_1-0" class="comp mntl-sc-block-faq__content mntl-accordion " data-tracking-container="true"> <li class="accordion__item js-accordion-item is-active" data-ordinal="1"> <div tabindex="-1" class="accordion__header js-accordion-trigger" id="mntl-accordion__item_1-0-section-0"> <span class="accordion__title">How do you find the correlation coefficient?</span> </div> <div class="accordion__body"> <div id="mntl-accordion__content_1-0" class="comp mntl-accordion__content"> <div class="faq-accordion__item-answer"> <p>You can calculate the correlation coefficient in a few different ways, with the same result. The general formula is <em>r<sub>XY</sub>=COV<sub>XY</sub>/(S<sub>X</sub> S<sub>Y</sub>)</em>, which is the covariance between the two variables, divided by the product of their standard deviations:</p> </div> </div> </div> </li> <li class="accordion__item js-accordion-item is-active" data-ordinal="2"> <div tabindex="-1" class="accordion__header js-accordion-trigger" id="mntl-accordion__item_2-0-section-1"> <span class="accordion__title">How do you calculate a correlation coefficient in Excel?</span> </div> <div class="accordion__body"> <div id="mntl-accordion__content_2-0" class="comp mntl-accordion__content"> <div class="faq-accordion__item-answer"> <p>In the cell in which you want the correlation coefficient to appear, enter <em>=CORREL(A2:A7,B2:B7),</em> where A2:A7 and B2:B7 are the variable lists to compare. Press <strong>Enter</strong>.</p> </div> </div> </div> </li> <li class="accordion__item js-accordion-item is-active" data-ordinal="3"> <div tabindex="-1" class="accordion__header js-accordion-trigger" id="mntl-accordion__item_3-0-section-2"> <span class="accordion__title">How do you find a linear correlation coefficient?</span> </div> <div class="accordion__body"> <div id="mntl-accordion__content_3-0" class="comp mntl-accordion__content"> <div class="faq-accordion__item-answer"> <p>Finding the linear correlation coefficient requires a long, difficult calculation, so most people use a calculator or software such as Excel or a statistics program.</p> </div> </div> </div> </li> <li class="accordion__item js-accordion-item is-active" data-ordinal="4"> <div tabindex="-1" class="accordion__header js-accordion-trigger" id="mntl-accordion__item_4-0-section-3"> <span class="accordion__title">How do you interpret a correlation coefficient?</span> </div> <div class="accordion__body"> <div id="mntl-accordion__content_4-0" class="comp mntl-accordion__content"> <div class="faq-accordion__item-answer"> <p>Correlations range from -1.00 to +1.00. The correlation coefficient (expressed as <em>r</em> ) shows the direction and strength of a relationship between two variables. The closer the <em>r</em> value is to +1 or -1, the stronger the linear relationship between the two variables is.<br/></p> </div> </div> </div> </li> <li class="accordion__item js-accordion-item is-active" data-ordinal="5"> <div tabindex="-1" class="accordion__header js-accordion-trigger" id="mntl-accordion__item_5-0-section-4"> <span class="accordion__title">What is the difference between correlation and causation?</span> </div> <div class="accordion__body"> <div id="mntl-accordion__content_5-0" class="comp mntl-accordion__content"> <div class="faq-accordion__item-answer"> <p>Correlations indicate a relationship between two variables, but one doesn't necessarily cause the other to change.</p> </div> </div> </div> </li> </ul></div></div> <div id="post-article_1-0" class="comp post-article mntl-block"><div id="sources_1-0" class="comp sources mntl-block"><div id="mntl-article-sources_1-0" class="comp mntl-article-sources mntl-expandable-block" data-scroll-offset="70"><div class="loc toggle-content"><div id="mntl-article-sources__wrapper_1-0" class="comp mntl-article-sources__wrapper mntl-block" data-click-tracked="true" tabindex="0"><span id="mntl-article-sources__heading_1-0" class="comp mntl-article-sources__heading mntl-text-block">4 Sources</span> <svg class="icon show-icon " > <use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#show-icon" href="#show-icon"></use> </svg> <svg class="icon hide-icon " > <use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#hide-icon" href="#hide-icon"></use> </svg></div> </div><div class="loc expandable-content"><div id="source-guidelines_1-0" class="comp source-guidelines mntl-text-block">Verywell Mind uses only high-quality sources, including peer-reviewed studies, to support the facts within our articles. Read our <a href=/our-editorial-process-4778006>editorial process</a> to learn more about how we fact-check and keep our content accurate, reliable, and trustworthy.</div> <div id="mntl-article-sources__citation-sources_1-0" class="comp mntl-article-sources__citation-sources mntl-citation-sources mntl-sources" data-tracking-container="true"> <ol class="mntl-sources__content"> <li class="mntl-sources__source" id="citation-2"><p>Mukaka M. <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3576830/" class="pseudoStyle" data-component="link" data-source="inlineLink" data-type="externalLink" data-ordinal="1">A guide to appropriate use of correlation coefficient in medical research</a>. <em>Malawi Med J</em>. 2012;24(3):69-71.</p></li> <li class="mntl-sources__source" id="citation-1"><p>Heath W. <a href="https://www.cambridge.org/us/academic/subjects/psychology/psychology-research-methods-and-statistics/psychology-research-methods-connecting-research-students-lives?format=PB" data-component="link" data-source="inlineLink" data-type="externalLink" data-ordinal="1"><em>Psychology Research Methods: Connecting Research to Students’ Lives</em></a>. Cambridge University Press.</p></li> <li class="mntl-sources__source" id="citation-3"><p>Chen DT. <a href="https://sitn.hms.harvard.edu/flash/2021/when-correlation-does-not-imply-causation-why-your-gut-microbes-may-not-yet-be-a-silver-bullet-to-all-your-problems/" data-component="link" data-source="inlineLink" data-type="externalLink" data-ordinal="1">When correlation does not imply causation: Why your gut microbes may not (yet) be a silver bullet to all your problems</a>. Harvard University.</p></li> <li class="mntl-sources__source" id="citation-4"><p>Association for Psychological Science. <a href="https://www.psychologicalscience.org/news/releases/research-states-that-prejudice-comes-from-a-basic-human-need-and-way-of-thinking.html" data-component="link" data-source="inlineLink" data-type="externalLink" data-ordinal="1">Research states that prejudice comes from a basic human need and way of thinking</a>.</p></li> </ol> </div> <span id="mntl-article-sources__subheading_1-0" class="comp mntl-article-sources__subheading mntl-text-block">Additional Reading</span> <div id="mntl-article-sources__additional-reading_1-0" class="comp mntl-article-sources__additional-reading mntl-additional-reading mntl-sources" data-tracking-container="true"> <ul class="mntl-sources__content"> <li class="mntl-sources__source"><p><a href="https://www.bmj.com/about-bmj/resources-readers/publications/statistics-square-one/11-correlation-and-regression" class="pseudoStyle" data-component="link" data-source="inlineLink" data-type="externalLink" data-ordinal="1">Correlation and regression</a>. In: Swinscow TDV. <em>Statistics at Square One</em>. The BMJ.</p></li> </ul> </div> </div></div></div> <div id="author-bio_1-0" class="comp author-bio "> <div class="loc author-bio__image"><img data-src="https://www.verywellmind.com/thmb/GUVGDZFGV45_4-qXYoJo4WDevhY=/144x144/filters:no_upscale():max_bytes(150000):strip_icc()/IMG_9791-89504ab694d54b66bbd72cb84ffb860e.jpg" width="144" height="144" alt="Kendra Cherry" class="lazyload universal-image__image" data-expand="300" /> <noscript> <img src="https://www.verywellmind.com/thmb/GUVGDZFGV45_4-qXYoJo4WDevhY=/144x144/filters:no_upscale():max_bytes(150000):strip_icc()/IMG_9791-89504ab694d54b66bbd72cb84ffb860e.jpg" width="144" height="144" class="img--noscript universal-image__image" alt="Kendra Cherry" /> </noscript> </div> <p class="author-bio__bio-text" > <span class="author-bio__bio-title">By <a href="https://www.verywellmind.com/kendra-cherry-2794702">Kendra Cherry, MSEd</a></span> <br> Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the 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