{"id":4233,"date":"2024-05-03T09:40:04","date_gmt":"2024-05-03T07:40:04","guid":{"rendered":"https:\/\/www.psyctc.org\/psyctc\/?post_type=docs&#038;p=4233"},"modified":"2024-05-03T09:40:05","modified_gmt":"2024-05-03T07:40:05","password":"","slug":"spearman-brown-formula","status":"publish","type":"docs","link":"https:\/\/www.psyctc.org\/psyctc\/glossary2\/spearman-brown-formula\/","title":{"rendered":"Spearman-Brown formula"},"content":{"rendered":"\n<p>Also known as the Spearman-Brown &#8220;prediction&#8221; or even &#8220;correction&#8221; formula and apparently there&#8217;s an argument that it should be Brown-Spearman, but I&#8217;ve never seen it that way round.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Details<\/h4>\n\n\n\n<p>The formula tells you that, if you have the internal reliability of a multi-item measure, what internal reliability, all things being equal, the measure would have had it more or fewer items.  Like this:<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"630\" src=\"https:\/\/www.psyctc.org\/psyctc\/wp-content\/uploads\/2024\/05\/graphic1-1-1024x630.png\" alt=\"\" class=\"wp-image-4234\" srcset=\"https:\/\/www.psyctc.org\/psyctc\/wp-content\/uploads\/2024\/05\/graphic1-1-1024x630.png 1024w, https:\/\/www.psyctc.org\/psyctc\/wp-content\/uploads\/2024\/05\/graphic1-1-300x185.png 300w, https:\/\/www.psyctc.org\/psyctc\/wp-content\/uploads\/2024\/05\/graphic1-1-768x473.png 768w, https:\/\/www.psyctc.org\/psyctc\/wp-content\/uploads\/2024\/05\/graphic1-1-360x222.png 360w, https:\/\/www.psyctc.org\/psyctc\/wp-content\/uploads\/2024\/05\/graphic1-1.png 1248w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p>The formula does make the assumption that the different length instrument would behave the same way which is almost certainly not the case, however, the predictions are probably a sensible guide and the best we can have in the absence of actual empirical data for the other lengths. See my Rblog for a bit more information and shiny app if you want to play with the predictions the formula makes.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Try also<\/h4>\n\n\n\n<p>Cronbach&#8217;s coefficient alpha<br>Internal reliability<br>Reliability<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Chapters<\/h4>\n\n\n\n<p>The issue of lengths of measures is touched on in Chapter 4 but the formula is not discussed: too geeky!<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Online resources<\/h4>\n\n\n\n<p>More detail in my <a href=\"https:\/\/www.psyctc.org\/Rblog\/index.html\" target=\"_blank\" rel=\"noopener\" title=\"\">Rblog<\/a>: entry <a href=\"https:\/\/www.psyctc.org\/Rblog\/posts\/2021-04-09-spearman-brown-formula\/\" target=\"_blank\" rel=\"noopener\" title=\"\">here<\/a>.<br>App in <a href=\"https:\/\/shiny.psyctc.org\/\" target=\"_blank\" rel=\"noopener\" title=\"\">my shiny apps<\/a> which computes the predictions for you <a href=\"https:\/\/shiny.psyctc.org\/apps\/Spearman-Brown\/\" target=\"_blank\" rel=\"noopener\" title=\"\">here<\/a>.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Dates<\/h4>\n\n\n\n<p>First created 3.v.24.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Also known as the Spearman-Brown &#8220;prediction&#8221; or even &#8220;correction&#8221; formula and apparently there&#8217;s an argument that it should be Brown-Spearman, but I&#8217;ve never seen it that way round. Details The formula tells you that, if you have the internal reliability of a multi-item measure, what internal reliability, all things being equal, the measure would have &hellip; <a href=\"https:\/\/www.psyctc.org\/psyctc\/glossary2\/spearman-brown-formula\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">Spearman-Brown formula<\/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-4233","docs","type-docs","status-publish","hentry","doc_category-om-book"],"year_month":"2026-04","word_count":184,"total_views":"1264","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\/4233","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=4233"}],"version-history":[{"count":1,"href":"https:\/\/www.psyctc.org\/psyctc\/wp-json\/wp\/v2\/docs\/4233\/revisions"}],"predecessor-version":[{"id":4235,"href":"https:\/\/www.psyctc.org\/psyctc\/wp-json\/wp\/v2\/docs\/4233\/revisions\/4235"}],"wp:attachment":[{"href":"https:\/\/www.psyctc.org\/psyctc\/wp-json\/wp\/v2\/media?parent=4233"}],"wp:term":[{"taxonomy":"doc_category","embeddable":true,"href":"https:\/\/www.psyctc.org\/psyctc\/wp-json\/wp\/v2\/doc_category?post=4233"},{"taxonomy":"glossaries","embeddable":true,"href":"https:\/\/www.psyctc.org\/psyctc\/wp-json\/wp\/v2\/glossaries?post=4233"},{"taxonomy":"doc_tag","embeddable":true,"href":"https:\/\/www.psyctc.org\/psyctc\/wp-json\/wp\/v2\/doc_tag?post=4233"},{"taxonomy":"knowledge_base","embeddable":true,"href":"https:\/\/www.psyctc.org\/psyctc\/wp-json\/wp\/v2\/knowledge_base?post=4233"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}