{"id":3851,"date":"2024-01-21T09:57:40","date_gmt":"2024-01-21T08:57:40","guid":{"rendered":"https:\/\/www.psyctc.org\/psyctc\/?post_type=docs&#038;p=3851"},"modified":"2026-02-02T20:03:01","modified_gmt":"2026-02-02T19:03:01","password":"","slug":"cohens-d","status":"publish","type":"docs","link":"https:\/\/www.psyctc.org\/psyctc\/glossary2\/cohens-d\/","title":{"rendered":"Cohen&#8217;s d"},"content":{"rendered":"\n<p>Probably the most used effect size measure at least in the psychology, MH and therapy realms.  A &#8220;standardised effect size&#8221; describing the effect size of a difference in means between two independent groups: it&#8217;s that mean divided by the SD.   <\/p>\n\n\n\n<div class=\"wp-block-math\"><math display=\"block\"><semantics><mrow><mi>d<\/mi><mo>=<\/mo><mfrac><mtext>mean<\/mtext><mtext>SD<\/mtext><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">d = \\frac{\\text{mean}}{\\text{SD}}<\/annotation><\/semantics><\/math><\/div>\n\n\n\n<p>That looks nice and simple but the devil is in the choice of standard deviation.  Cohen also had a formula for d for change or, more generally, for the mean difference in within subject, repeated, paired data but that needs another entry. <\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Details<\/h4>\n\n\n\n<p>I think (I would) that  there&#8217;s a good introductory summary in my <a href=\"https:\/\/www.psyctc.org\/Rblog\/\">Rblog<\/a> post: <a href=\"https:\/\/www.psyctc.org\/Rblog\/posts\/2024-01-19-hedgess-g\/\" title=\"\">Hedges\u2019s g and Cohen\u2019s d<\/a>.  Beyond that the main issues are about the choice of standard deviation for the denominator of the simple equation above.  The usual choice, I would say the only choice for  the between groups value is the &#8220;common&#8221; (sometimes called, a bit misleadingly, the &#8220;pooled&#8221; SD: it&#8217;s not the SD you get pooling the observations in both groups).  See that blog post for more on that SD.  Things are a bit more complicated for the repeated measures situation and I&#8217;ll give that its own Rblog post when I can.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Try also<\/h4>\n\n\n\n<p><a href=\"https:\/\/www.psyctc.org\/psyctc\/glossary2\/effect-size\/\" title=\"\">Effect size<\/a><br><a href=\"https:\/\/www.psyctc.org\/psyctc\/glossary2\/hedgess-g\/\" title=\"\">Hedges&#8217;s g<\/a><br>Repeated measures<br>&#8220;Standardising&#8221;<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Chapters<\/h4>\n\n\n\n<p>We didn\u2019t put it in the book but Chapter 8 and service comparisons would probably be where you might encounter effect sizes.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Online resources<\/h4>\n\n\n\n<p>My <a href=\"https:\/\/www.psyctc.org\/Rblog\/\">Rblog<\/a> post about <a href=\"https:\/\/www.psyctc.org\/Rblog\/posts\/2024-01-19-hedgess-g\/\" title=\"\">Hedges\u2019s g and Cohen\u2019s d<\/a><\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Dates<\/h4>\n\n\n\n<p>First created 21.i.24.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Probably the most used effect size measure at least in the psychology, MH and therapy realms. A &#8220;standardised effect size&#8221; describing the effect size of a difference in means between two independent groups: it&#8217;s that mean divided by the SD. That looks nice and simple but the devil is in the choice of standard deviation. &hellip; <a href=\"https:\/\/www.psyctc.org\/psyctc\/glossary2\/cohens-d\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">Cohen&#8217;s d<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","template":"","meta":{"footnotes":""},"doc_category":[18],"glossaries":[],"doc_tag":[],"knowledge_base":[],"class_list":["post-3851","docs","type-docs","status-publish","hentry","doc_category-om-book"],"year_month":"2026-04","word_count":246,"total_views":"953","reactions":{"happy":"0","normal":"0","sad":"0"},"author_info":{"name":"chris","author_nicename":"chris","author_url":"https:\/\/www.psyctc.org\/psyctc\/author\/chris\/"},"doc_category_info":[{"term_name":"All OM book glossary entries","term_url":"https:\/\/www.psyctc.org\/psyctc\/glossary\/non-knowledgebase\/om-book\/"}],"doc_tag_info":[],"knowledge_base_info":[],"knowledge_base_slug":[],"_links":{"self":[{"href":"https:\/\/www.psyctc.org\/psyctc\/wp-json\/wp\/v2\/docs\/3851","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.psyctc.org\/psyctc\/wp-json\/wp\/v2\/docs"}],"about":[{"href":"https:\/\/www.psyctc.org\/psyctc\/wp-json\/wp\/v2\/types\/docs"}],"author":[{"embeddable":true,"href":"https:\/\/www.psyctc.org\/psyctc\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.psyctc.org\/psyctc\/wp-json\/wp\/v2\/comments?post=3851"}],"version-history":[{"count":8,"href":"https:\/\/www.psyctc.org\/psyctc\/wp-json\/wp\/v2\/docs\/3851\/revisions"}],"predecessor-version":[{"id":5188,"href":"https:\/\/www.psyctc.org\/psyctc\/wp-json\/wp\/v2\/docs\/3851\/revisions\/5188"}],"wp:attachment":[{"href":"https:\/\/www.psyctc.org\/psyctc\/wp-json\/wp\/v2\/media?parent=3851"}],"wp:term":[{"taxonomy":"doc_category","embeddable":true,"href":"https:\/\/www.psyctc.org\/psyctc\/wp-json\/wp\/v2\/doc_category?post=3851"},{"taxonomy":"glossaries","embeddable":true,"href":"https:\/\/www.psyctc.org\/psyctc\/wp-json\/wp\/v2\/glossaries?post=3851"},{"taxonomy":"doc_tag","embeddable":true,"href":"https:\/\/www.psyctc.org\/psyctc\/wp-json\/wp\/v2\/doc_tag?post=3851"},{"taxonomy":"knowledge_base","embeddable":true,"href":"https:\/\/www.psyctc.org\/psyctc\/wp-json\/wp\/v2\/knowledge_base?post=3851"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}