{"id":7267,"date":"2019-05-22T15:55:01","date_gmt":"2019-05-22T15:55:01","guid":{"rendered":"http:\/\/www.lancaster.ac.uk\/fas\/psych\/glossary\/analysis_of_variance_-anova\/"},"modified":"2019-05-22T15:55:01","modified_gmt":"2019-05-22T15:55:01","slug":"analysis_of_variance_-anova","status":"publish","type":"post","link":"https:\/\/www.lancaster.ac.uk\/fas\/psych\/glossary\/analysis_of_variance_-anova\/","title":{"rendered":"Analysis of variance (ANOVA)"},"content":{"rendered":"<p>The statistical analysis of mean differences that are traced back to the effects of one or more factors (or independent variables). &nbsp;The simplest ANOVA is a one-way design in which N subjects are (randomly) allocated to a number of different levels of a single factor. &nbsp;Strictly speaking, ANOVA does not analyse variance <span class=\"\" style=\"font-style: italic;\">per se<\/span>, but rather sums of squares. &nbsp;Thus, the total variation in observations is partitioned into the between-groups sum of squares (between level means), and the within-groups (or residual) sum of squares (differences between subjects in the same group). &nbsp;The desired outcome in most cases is that the between-groups sum of squares is greater than that for the within groups. &nbsp;This is the <span class=\"\" style=\"font-style: italic;\">F<\/span>-ratio named by <a href=\"http:\/\/www.amstat.org\/about\/statisticiansinhistory\/bios\/snedecorgeorge.pdf\" class=\"cc-route-enabled\" data-editable-link=\"http:\/\/www.amstat.org\/about\/statisticiansinhistory\/bios\/snedecorgeorge.pdf&amp;target=_self\" target=\"_self\" rel=\"noopener noreferrer\">George W. Snedecor<\/a> (1881-1974) after <a href=\"http:\/\/www-history.mcs.st-and.ac.uk\/Biographies\/Fisher.html\" class=\"cc-route-enabled\" data-editable-link=\"http:\/\/www-history.mcs.st-and.ac.uk\/Biographies\/Fisher.html&amp;target=_self\" target=\"_self\" rel=\"noopener noreferrer\">Ronald A. Fisher<\/a> (1890-1962) who originally developed the test.<\/p>\n<p>See <a href=\"additive_model\">Additive model<\/a>, Balanced or orthogonal) design, <a href=\"compound_symmetry\">Compound symmetry<\/a>, <a href=\"design_matrix\">Design matrix<\/a>, <a href=\"effect_size\">Effect size<\/a>, <a href=\"error_term\">Error term<\/a>, <a href=\"error_variance\">Error variance<\/a>, <a href=\"generalized_linear_model_-glm-\">Generalized linear model (GLM)<\/a>, <a href=\"greenhouse-geisser_epsilon\">Greenhouse-Geisser epsilon<\/a>, <a href=\"homoscedasticity\">Homoscedasticity<\/a>, <a href=\"mixed-effects_models\">Mixed-effects models<\/a>, <a href=\"multivariate_analysis_of_variance_-manova-\">Multivariate analysis of variance (MANOVA)<\/a>, <a href=\"orthogonality\">Orthogonality<\/a>, <a href=\"planned_comparison\">Planned comparison<\/a>, <a href=\"polynomial_analysis_of_variance\">Polynomial analysis of variance<\/a>, <a href=\"repeated_measures_analysis_of_variance\">Repeated measures analysis of variance<\/a>, Residuals, <a href=\"sphericity\">Sphericity<\/a>, Sphericity assumption<\/p>\n<p><\/body><\/html><\/p>\n","protected":false},"excerpt":{"rendered":"<p>The statistical analysis of mean differences that are traced back to the effects of one or more factors (or independent variables). &nbsp;The simplest ANOVA is a one-way design in which N subjects are (randomly) allocated to a number of different levels of a single factor. &nbsp;Strictly speaking, ANOVA does not analyse variance per se, but &hellip; <\/p>\n<p class=\"link-more\"><a href=\"https:\/\/www.lancaster.ac.uk\/fas\/psych\/glossary\/analysis_of_variance_-anova\/\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;Analysis of variance (ANOVA)&#8221;<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[2],"class_list":["post-7267","post","type-post","status-publish","format-standard","hentry","category-uncategorized","tag-glossary","entry"],"_links":{"self":[{"href":"https:\/\/www.lancaster.ac.uk\/fas\/psych\/glossary\/wp-json\/wp\/v2\/posts\/7267","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.lancaster.ac.uk\/fas\/psych\/glossary\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.lancaster.ac.uk\/fas\/psych\/glossary\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.lancaster.ac.uk\/fas\/psych\/glossary\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.lancaster.ac.uk\/fas\/psych\/glossary\/wp-json\/wp\/v2\/comments?post=7267"}],"version-history":[{"count":0,"href":"https:\/\/www.lancaster.ac.uk\/fas\/psych\/glossary\/wp-json\/wp\/v2\/posts\/7267\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.lancaster.ac.uk\/fas\/psych\/glossary\/wp-json\/wp\/v2\/media?parent=7267"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.lancaster.ac.uk\/fas\/psych\/glossary\/wp-json\/wp\/v2\/categories?post=7267"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.lancaster.ac.uk\/fas\/psych\/glossary\/wp-json\/wp\/v2\/tags?post=7267"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}