{"id":299,"date":"2023-08-02T20:15:08","date_gmt":"2023-08-02T20:15:08","guid":{"rendered":"https:\/\/statorials.org\/uk\/%d0%b0%d0%bd%d0%be%d0%b2%d0%b0-%d1%82%d0%b0%d0%b1%d0%bb%d0%b8%d1%86%d1%8f\/"},"modified":"2023-08-02T20:15:08","modified_gmt":"2023-08-02T20:15:08","slug":"%d0%b0%d0%bd%d0%be%d0%b2%d0%b0-%d1%82%d0%b0%d0%b1%d0%bb%d0%b8%d1%86%d1%8f","status":"publish","type":"post","link":"https:\/\/statorials.org\/uk\/%d0%b0%d0%bd%d0%be%d0%b2%d0%b0-%d1%82%d0%b0%d0%b1%d0%bb%d0%b8%d1%86%d1%8f\/","title":{"rendered":"\u0422\u0430\u0431\u043b\u0438\u0446\u044f anova"},"content":{"rendered":"<p>\u0423 \u0446\u0456\u0439 \u0441\u0442\u0430\u0442\u0442\u0456 \u0432\u0438 \u0437\u043d\u0430\u0439\u0434\u0435\u0442\u0435 \u043f\u043e\u044f\u0441\u043d\u0435\u043d\u043d\u044f \u0442\u0430\u0431\u043b\u0438\u0446\u0456 ANOVA. \u041e\u0442\u0436\u0435, \u043c\u0438 \u043f\u043e\u044f\u0441\u043d\u044e\u0454\u043c\u043e \u0432\u0430\u043c, \u0449\u043e \u0442\u0430\u043a\u0435 \u0442\u0430\u0431\u043b\u0438\u0446\u044f ANOVA, \u044f\u043a \u0441\u0442\u0432\u043e\u0440\u0438\u0442\u0438 \u0442\u0430\u0431\u043b\u0438\u0446\u044e ANOVA, \u044f\u043a\u0456 \u0444\u043e\u0440\u043c\u0443\u043b\u0438 \u0442\u0430\u0431\u043b\u0438\u0446\u0456 ANOVA, \u0456, \u043a\u0440\u0456\u043c \u0442\u043e\u0433\u043e, \u0432\u0438 \u0437\u043c\u043e\u0436\u0435\u0442\u0435 \u043f\u043e\u0431\u0430\u0447\u0438\u0442\u0438 \u0432\u043f\u0440\u0430\u0432\u0443, \u0440\u043e\u0437\u0432\u2019\u044f\u0437\u0430\u043d\u0443 \u043a\u0440\u043e\u043a \u0437\u0430 \u043a\u0440\u043e\u043a\u043e\u043c. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-tabla-anova\"><\/span> \u0429\u043e \u0442\u0430\u043a\u0435 \u0442\u0430\u0431\u043b\u0438\u0446\u044f ANOVA?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>\u0422\u0430\u0431\u043b\u0438\u0446\u044f ANOVA<\/strong> \u2014 \u0446\u0435 \u0442\u0430\u0431\u043b\u0438\u0446\u044f, \u044f\u043a\u0430 \u0432\u0438\u043a\u043e\u0440\u0438\u0441\u0442\u043e\u0432\u0443\u0454\u0442\u044c\u0441\u044f \u0432 \u0441\u0442\u0430\u0442\u0438\u0441\u0442\u0438\u0446\u0456 \u0434\u043b\u044f \u0434\u0438\u0441\u043f\u0435\u0440\u0441\u0456\u0439\u043d\u043e\u0433\u043e \u0430\u043d\u0430\u043b\u0456\u0437\u0443. \u0411\u0456\u043b\u044c\u0448 \u043a\u043e\u043d\u043a\u0440\u0435\u0442\u043d\u043e, \u0442\u0430\u0431\u043b\u0438\u0446\u044f ANOVA \u043c\u0456\u0441\u0442\u0438\u0442\u044c \u0432\u0441\u044e \u0456\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0456\u044e, \u043d\u0435\u043e\u0431\u0445\u0456\u0434\u043d\u0443 \u0434\u043b\u044f \u0434\u0438\u0441\u043f\u0435\u0440\u0441\u0456\u0439\u043d\u043e\u0433\u043e \u0430\u043d\u0430\u043b\u0456\u0437\u0443.<\/p>\n<p> \u0422\u0430\u043a\u0438\u043c \u0447\u0438\u043d\u043e\u043c, \u0442\u0430\u0431\u043b\u0438\u0446\u044f ANOVA \u0432\u0438\u043a\u043e\u0440\u0438\u0441\u0442\u043e\u0432\u0443\u0454\u0442\u044c\u0441\u044f \u0434\u043b\u044f \u0443\u0437\u0430\u0433\u0430\u043b\u044c\u043d\u0435\u043d\u043d\u044f \u0434\u0438\u0441\u043f\u0435\u0440\u0441\u0456\u0439\u043d\u043e\u0433\u043e \u0430\u043d\u0430\u043b\u0456\u0437\u0443. \u041f\u043e\u0431\u0443\u0434\u0443\u0432\u0430\u0432\u0448\u0438 \u0440\u043e\u0437\u0440\u0430\u0445\u0443\u043d\u043a\u0438 \u0434\u0438\u0441\u043f\u0435\u0440\u0441\u0456\u0439\u043d\u043e\u0433\u043e \u0430\u043d\u0430\u043b\u0456\u0437\u0443 \u0432 \u0442\u0430\u0431\u043b\u0438\u0446\u0456, \u0432\u0438 \u043c\u043e\u0436\u0435\u0442\u0435 \u043b\u0435\u0433\u043a\u043e \u0437\u0440\u043e\u0431\u0438\u0442\u0438 \u0432\u0438\u0441\u043d\u043e\u0432\u043a\u0438, \u0430 \u0442\u0430\u043a\u043e\u0436 \u0434\u043e\u0437\u0432\u043e\u043b\u0438\u0442\u0438 \u0432\u0430\u043c \u0448\u0432\u0438\u0434\u043a\u043e \u043e\u0431\u0447\u0438\u0441\u043b\u0438\u0442\u0438 \u0437\u043d\u0430\u0447\u0435\u043d\u043d\u044f \u0441\u0442\u0430\u0442\u0438\u0441\u0442\u0438\u043a\u0438 \u0442\u0435\u0441\u0442\u0443 ANOVA. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formulas-de-la-tabla-anova\"><\/span> \u0424\u043e\u0440\u043c\u0443\u043b\u0438 \u0442\u0430\u0431\u043b\u0438\u0446\u0456 ANOVA<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0423 \u0442\u0430\u0431\u043b\u0438\u0446\u0456 \u043e\u0434\u043d\u043e\u0441\u0442\u043e\u0440\u043e\u043d\u043d\u044c\u043e\u0433\u043e \u0434\u0438\u0441\u043f\u0435\u0440\u0441\u0456\u0439\u043d\u043e\u0433\u043e \u0430\u043d\u0430\u043b\u0456\u0437\u0443 \u0454 \u0442\u0440\u0438 \u0440\u044f\u0434\u043a\u0438: \u0444\u0430\u043a\u0442\u043e\u0440, \u043f\u043e\u043c\u0438\u043b\u043a\u0430 \u0442\u0430 \u043f\u0456\u0434\u0441\u0443\u043c\u043e\u043a. \u0422\u0430\u043a\u0438\u043c \u0447\u0438\u043d\u043e\u043c, \u0443 \u0442\u0430\u0431\u043b\u0438\u0446\u0456 ANOVA \u0440\u043e\u0437\u0440\u0430\u0445\u043e\u0432\u0443\u044e\u0442\u044c\u0441\u044f \u0441\u0443\u043c\u0438 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0456\u0432 \u043a\u043e\u0436\u043d\u043e\u0433\u043e \u0440\u044f\u0434\u043a\u0430 \u0442\u0430 \u0457\u0445 \u0441\u0442\u0443\u043f\u0435\u043d\u0456 \u0432\u0456\u043b\u044c\u043d\u043e\u0441\u0442\u0456. \u041a\u0440\u0456\u043c \u0442\u043e\u0433\u043e, \u0440\u043e\u0437\u0440\u0430\u0445\u043e\u0432\u0443\u0454\u0442\u044c\u0441\u044f \u0441\u0435\u0440\u0435\u0434\u043d\u044f \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0438\u0447\u043d\u0430 \u043f\u043e\u043c\u0438\u043b\u043a\u0430 \u0444\u0430\u043a\u0442\u043e\u0440\u0430 \u0442\u0430 \u043f\u043e\u043c\u0438\u043b\u043a\u0438 \u0456, \u043d\u0430\u0440\u0435\u0448\u0442\u0456, \u0432\u0438\u0437\u043d\u0430\u0447\u0430\u0454\u0442\u044c\u0441\u044f \u0442\u0435\u0441\u0442\u043e\u0432\u0430 \u0441\u0442\u0430\u0442\u0438\u0441\u0442\u0438\u043a\u0430 ANOVA, \u044f\u043a\u0430 \u0434\u043e\u0440\u0456\u0432\u043d\u044e\u0454 \u0432\u0456\u0434\u043d\u043e\u0448\u0435\u043d\u043d\u044e \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0438\u0447\u043d\u0438\u0445 \u043f\u043e\u043c\u0438\u043b\u043e\u043a.<\/p>\n<p> \u041e\u0442\u0436\u0435, <strong>\u0444\u043e\u0440\u043c\u0443\u043b\u0438 \u0434\u043b\u044f \u0442\u0430\u0431\u043b\u0438\u0446\u0456 ANOVA<\/strong> \u0442\u0430\u043a\u0456: <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/tableau-anova-formules-.png\" alt=\"\u0424\u043e\u0440\u043c\u0443\u043b\u0438 \u0442\u0430\u0431\u043b\u0438\u0446\u0456 ANOVA\" class=\"wp-image-6387\" width=\"664\" height=\"397\" srcset=\"\" sizes=\"\"><\/figure>\n<p style=\"margin-bottom:5px\"> \u0437\u043e\u043b\u043e\u0442\u043e:<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-5f087375b50e0b49186779714206626b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n_i\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"16\" style=\"vertical-align: -3px;\"><\/p>\n<p> \u0446\u0435 \u0440\u043e\u0437\u043c\u0456\u0440 \u0432\u0438\u0431\u0456\u0440\u043a\u0438 i.<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-7354bae77b50b7d1faed3e8ea7a3511a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"N\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u2013 \u0437\u0430\u0433\u0430\u043b\u044c\u043d\u0430 \u043a\u0456\u043b\u044c\u043a\u0456\u0441\u0442\u044c \u0441\u043f\u043e\u0441\u0442\u0435\u0440\u0435\u0436\u0435\u043d\u044c.<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-d42bc2203d6f76ad01b27ac9acc0bee1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u2013 \u043a\u0456\u043b\u044c\u043a\u0456\u0441\u0442\u044c \u0440\u0456\u0437\u043d\u0438\u0445 \u0433\u0440\u0443\u043f \u0443 \u0434\u0438\u0441\u043f\u0435\u0440\u0441\u0456\u0439\u043d\u043e\u043c\u0443 \u0430\u043d\u0430\u043b\u0456\u0437\u0456.<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-393bb0c333649c80fe6365339bc42b38_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y_{ij}\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"20\" style=\"vertical-align: -6px;\"><\/p>\n<p> \u0454 \u0437\u043d\u0430\u0447\u0435\u043d\u043d\u044f j \u0433\u0440\u0443\u043f\u0438 i.<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-8effb66cfe7466ba329c455ccb9289f1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{y}_{i}\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"14\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u0454 \u0441\u0435\u0440\u0435\u0434\u043d\u0456\u043c \u0437\u043d\u0430\u0447\u0435\u043d\u043d\u044f\u043c \u0433\u0440\u0443\u043f\u0438 i.<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-ed5becac4ccb36fec040f449ba9fa52d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{y}\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"10\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u0426\u0435 \u0441\u0435\u0440\u0435\u0434\u043d\u0454 \u0437\u043d\u0430\u0447\u0435\u043d\u043d\u044f \u0432\u0441\u0456\u0445 \u043f\u0440\u043e\u0430\u043d\u0430\u043b\u0456\u0437\u043e\u0432\u0430\u043d\u0438\u0445 \u0434\u0430\u043d\u0438\u0445. <\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-la-tabla-anova\"><\/span> \u041f\u0440\u0438\u043a\u043b\u0430\u0434 \u0442\u0430\u0431\u043b\u0438\u0446\u0456 ANOVA<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0429\u043e\u0431 \u0434\u043e\u0431\u0440\u0435 \u0437\u0440\u043e\u0437\u0443\u043c\u0456\u0442\u0438 \u043a\u043e\u043d\u0446\u0435\u043f\u0446\u0456\u044e, \u0434\u0430\u0432\u0430\u0439\u0442\u0435 \u043f\u043e\u0434\u0438\u0432\u0438\u043c\u043e\u0441\u044f, \u044f\u043a \u0441\u0442\u0432\u043e\u0440\u0438\u0442\u0438 \u0442\u0430\u0431\u043b\u0438\u0446\u044e ANOVA, \u0440\u043e\u0437\u0432\u2019\u044f\u0437\u0443\u044e\u0447\u0438 \u043f\u0440\u0438\u043a\u043b\u0430\u0434 \u043a\u0440\u043e\u043a \u0437\u0430 \u043a\u0440\u043e\u043a\u043e\u043c.<\/p>\n<ul>\n<li> \u041f\u0440\u043e\u0432\u043e\u0434\u0438\u0442\u044c\u0441\u044f \u0441\u0442\u0430\u0442\u0438\u0441\u0442\u0438\u0447\u043d\u0435 \u0434\u043e\u0441\u043b\u0456\u0434\u0436\u0435\u043d\u043d\u044f \u0434\u043b\u044f \u043f\u043e\u0440\u0456\u0432\u043d\u044f\u043d\u043d\u044f \u0431\u0430\u043b\u0456\u0432, \u043e\u0442\u0440\u0438\u043c\u0430\u043d\u0438\u0445 \u0447\u043e\u0442\u0438\u0440\u043c\u0430 \u0443\u0447\u043d\u044f\u043c\u0438 \u0437 \u0442\u0440\u044c\u043e\u0445 \u0440\u0456\u0437\u043d\u0438\u0445 \u043f\u0440\u0435\u0434\u043c\u0435\u0442\u0456\u0432 (A, B \u0456 C). \u0423 \u043d\u0430\u0432\u0435\u0434\u0435\u043d\u0456\u0439 \u043d\u0438\u0436\u0447\u0435 \u0442\u0430\u0431\u043b\u0438\u0446\u0456 \u0434\u0435\u0442\u0430\u043b\u044c\u043d\u043e \u043e\u043f\u0438\u0441\u0430\u043d\u043e \u0431\u0430\u043b\u0438, \u043e\u0442\u0440\u0438\u043c\u0430\u043d\u0456 \u043a\u043e\u0436\u043d\u0438\u043c \u0443\u0447\u043d\u0435\u043c \u043f\u0456\u0434 \u0447\u0430\u0441 \u0442\u0435\u0441\u0442\u0443, \u043c\u0430\u043a\u0441\u0438\u043c\u0430\u043b\u044c\u043d\u0438\u0439 \u0431\u0430\u043b \u044f\u043a\u043e\u0433\u043e \u0441\u0442\u0430\u043d\u043e\u0432\u0438\u0442\u044c 20. \u041f\u043e\u0431\u0443\u0434\u0443\u0439\u0442\u0435 \u0442\u0430\u0431\u043b\u0438\u0446\u044e ANOVA, \u0449\u043e\u0431 \u043f\u043e\u0440\u0456\u0432\u043d\u044f\u0442\u0438 \u0431\u0430\u043b\u0438, \u043e\u0442\u0440\u0438\u043c\u0430\u043d\u0456 \u043a\u043e\u0436\u043d\u0438\u043c \u0443\u0447\u043d\u0435\u043c \u0437 \u043a\u043e\u0436\u043d\u043e\u0433\u043e \u043f\u0440\u0435\u0434\u043c\u0435\u0442\u0430. <\/li>\n<\/ul>\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/table-anova-donnees.png\" alt=\"\" class=\"wp-image-6389\" width=\"471\" height=\"205\" srcset=\"\" sizes=\"\"><\/figure>\n<p> \u041f\u0435\u0440\u0448\u0435, \u0449\u043e \u043d\u0430\u043c \u043f\u043e\u0442\u0440\u0456\u0431\u043d\u043e \u0437\u0440\u043e\u0431\u0438\u0442\u0438, \u0446\u0435 \u043e\u0431\u0447\u0438\u0441\u043b\u0438\u0442\u0438 \u0441\u0435\u0440\u0435\u0434\u043d\u0454 \u0437\u043d\u0430\u0447\u0435\u043d\u043d\u044f \u043a\u043e\u0436\u043d\u043e\u0433\u043e \u0441\u0443\u0431\u2019\u0454\u043a\u0442\u0430 \u0442\u0430 \u0437\u0430\u0433\u0430\u043b\u044c\u043d\u0435 \u0441\u0435\u0440\u0435\u0434\u043d\u0454 \u0437\u043d\u0430\u0447\u0435\u043d\u043d\u044f \u0434\u0430\u043d\u0438\u0445: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-792e2e662519db421d0c9c4d7f831282_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{y}_A=\\cfrac{14+12+14+10}{4}=12,5\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"239\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-ace3ea8d1e0ce91dafdf4b5458e9760a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{y}_B=\\cfrac{13+14+10+14}{4}=12,75\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"249\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-d2781ad166914d48b6d458fe8e326f7d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{y}_C=\\cfrac{19+17+16+19}{4}=17,75\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"249\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-26caf7f83546e9112594e6886e8dccae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{y}=\\cfrac{14+12+14+10+13+14+10+14+19+17+16+19}{12}=14,33\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"553\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> \u041a\u043e\u043b\u0438 \u043c\u0438 \u0437\u043d\u0430\u0454\u043c\u043e \u0437\u043d\u0430\u0447\u0435\u043d\u043d\u044f \u0441\u0435\u0440\u0435\u0434\u043d\u0456\u0445, \u043c\u0438 \u043e\u0431\u0447\u0438\u0441\u043b\u044e\u0454\u043c\u043e \u0441\u0443\u043c\u0438 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0456\u0432 \u0437\u0430 \u0434\u043e\u043f\u043e\u043c\u043e\u0433\u043e\u044e \u0444\u043e\u0440\u043c\u0443\u043b \u0443 \u0442\u0430\u0431\u043b\u0438\u0446\u0456 ANOVA (\u0434\u0438\u0432. \u0432\u0438\u0449\u0435): <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-77b3fecdc3b577841da684cd80297288_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\displaystyle SS_F&amp;=\\sum_{i=1}^k n_i(\\overline{y}_i-\\overline{y})^2\\\\[2ex] SS_F&amp;= 4\\cdot (12,5-14,33)^2+4\\cdot (12,75-14,33)^2+4\\cdot (17,75-14,33)^2\\\\[2ex] SS_F&amp;=70,17\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"138\" width=\"546\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-aa02f1b826df45c26ead3537ecc4c7e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\displaystyle SS_E=&amp;\\sum_{i=1}^k\\sum_{j=1}^{n_i} (y_{ij}-\\overline{y}_i)^2\\\\[2ex] \\displaystyle SS_E=\\ &amp;(14-12,5)^2+(12-12,5)^2+(14-12,5)^2+(10-12,5)^2+\\\\&amp;+(13-12,75)^2+(14-12,75)^2+(10-12,75)^2+(14-12,75)^2+\\\\&amp;+(19-17,75)^2+(17-17,75)^2+(16-17,75)^2+(19-17,75)^2\\\\[2ex] SS_E=\\ &amp;28,50\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"198\" width=\"575\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-2eb66d1d37653749f38916c905108a3b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\displaystyle SS_T=&amp;\\sum_{i=1}^k\\sum_{j=1}^{n_i} (y_{ij}-\\overline{y})^2\\\\[2ex] \\displaystyle SS_T= \\ &amp;(14-14,33)^2+(12-14,33)^2+(14-14,33)^2+(10-14,33)^2+\\\\&amp;+(13-14,33)^2+(14-14,33)^2+(10-14,33)^2+(14-14,33)^2+\\\\&amp;+(19-14,33)^2+(17-14,33)^2+(16-14,33)^2+(19-14,33)^2\\\\[2ex] SS_T= \\ &amp;98,67\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"198\" width=\"575\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> \u041f\u043e\u0442\u0456\u043c \u0432\u0438\u0437\u043d\u0430\u0447\u0430\u0454\u043c\u043e \u0441\u0442\u0443\u043f\u0435\u043d\u0456 \u0441\u0432\u043e\u0431\u043e\u0434\u0438 \u0444\u0430\u043a\u0442\u043e\u0440\u0430, \u043f\u043e\u0445\u0438\u0431\u043a\u0438 \u0442\u0430 \u0441\u0443\u043c\u0438: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-481e16a2bd9b99bcd934aa0b6e3bdce7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"GL_F=k-1=3-1=2\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"196\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-6c71951c1e79cb2368b941b79387fe82_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"GL_E=N-k=12-3=9\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"213\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-c62813e7a06bfd423af43109bfb508d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"GL_F=N-1=12-1=11\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"220\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p> \u0422\u0435\u043f\u0435\u0440 \u043c\u0438 \u043e\u0431\u0447\u0438\u0441\u043b\u044e\u0454\u043c\u043e \u0441\u0435\u0440\u0435\u0434\u043d\u0456 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0438 \u043f\u043e\u043c\u0438\u043b\u043e\u043a, \u0440\u043e\u0437\u0434\u0456\u043b\u0438\u0432\u0448\u0438 \u0441\u0443\u043c\u0438 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0456\u0432 \u0444\u0430\u043a\u0442\u043e\u0440\u0430 \u0442\u0430 \u043f\u043e\u043c\u0438\u043b\u043a\u0438 \u043d\u0430 \u0457\u0445\u043d\u0456 \u0432\u0456\u0434\u043f\u043e\u0432\u0456\u0434\u043d\u0456 \u0441\u0442\u0443\u043f\u0435\u043d\u0456 \u0441\u0432\u043e\u0431\u043e\u0434\u0438:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-477d73197865e6166394e3d20732b237_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"MSE_F=\\cfrac{SS_F}{GL_F}=\\cfrac{70,17}{2}=35,08\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"255\" style=\"vertical-align: -15px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-a5b4e07b9ec4135498762b5dbc0f173e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"MSE_R=\\cfrac{SS_R}{GL_R}=\\cfrac{28,50}{9}=3,17\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"245\" style=\"vertical-align: -15px;\"><\/p>\n<\/p>\n<p> \u0406, \u043d\u0430\u0440\u0435\u0448\u0442\u0456, \u043c\u0438 \u043e\u0431\u0447\u0438\u0441\u043b\u044e\u0454\u043c\u043e \u0437\u043d\u0430\u0447\u0435\u043d\u043d\u044f F-\u0441\u0442\u0430\u0442\u0438\u0441\u0442\u0438\u043a\u0438, \u0440\u043e\u0437\u0434\u0456\u043b\u0438\u0432\u0448\u0438 \u0434\u0432\u0456 \u043f\u043e\u043c\u0438\u043b\u043a\u0438, \u043e\u0431\u0447\u0438\u0441\u043b\u0435\u043d\u0456 \u043d\u0430 \u043f\u043e\u043f\u0435\u0440\u0435\u0434\u043d\u044c\u043e\u043c\u0443 \u043a\u0440\u043e\u0446\u0456:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-4a30a3a61861deb9f53bd1cfcdb0b664_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"F=\\cfrac{MSE_F}{MSE_R}=\\cfrac{35,09}{3,17}=11,08\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"231\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u041a\u043e\u0440\u043e\u0442\u043a\u043e \u043a\u0430\u0436\u0443\u0447\u0438, \u0442\u0430\u0431\u043b\u0438\u0446\u044f \u0434\u0438\u0441\u043f\u0435\u0440\u0441\u0456\u0439\u043d\u043e\u0433\u043e \u0430\u043d\u0430\u043b\u0456\u0437\u0443 \u0434\u043b\u044f \u043f\u0440\u0438\u043a\u043b\u0430\u0434\u0443 \u0434\u0430\u043d\u0438\u0445 \u0432\u0438\u0433\u043b\u044f\u0434\u0430\u0442\u0438\u043c\u0435 \u0442\u0430\u043a: <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/table-anova-exemple.png\" alt=\"\u041f\u0440\u0438\u043a\u043b\u0430\u0434 \u0442\u0430\u0431\u043b\u0438\u0446\u0456 ANOVA\" class=\"wp-image-6408\" width=\"726\" height=\"279\" srcset=\"\" sizes=\"\"><\/figure>\n<p> \u041f\u0456\u0441\u043b\u044f \u0442\u043e\u0433\u043e, \u044f\u043a \u0443\u0441\u0456 \u0437\u043d\u0430\u0447\u0435\u043d\u043d\u044f \u0432 \u0442\u0430\u0431\u043b\u0438\u0446\u0456 ANOVA \u0431\u0443\u043b\u0438 \u043e\u0431\u0447\u0438\u0441\u043b\u0435\u043d\u0456, \u0432\u0441\u0435, \u0449\u043e \u0437\u0430\u043b\u0438\u0448\u0430\u0454\u0442\u044c\u0441\u044f, \u0446\u0435 \u0456\u043d\u0442\u0435\u0440\u043f\u0440\u0435\u0442\u0443\u0432\u0430\u0442\u0438 \u0457\u0457. \u0414\u043b\u044f \u0446\u044c\u043e\u0433\u043e \u043c\u0438 \u043f\u043e\u0432\u0438\u043d\u043d\u0456 \u043f\u043e\u0440\u0456\u0432\u043d\u044f\u0442\u0438 \u0439\u043c\u043e\u0432\u0456\u0440\u043d\u0456\u0441\u0442\u044c, \u0449\u043e \u0432\u0456\u0434\u043f\u043e\u0432\u0456\u0434\u0430\u0454 \u0437\u043d\u0430\u0447\u0435\u043d\u043d\u044e F-\u0441\u0442\u0430\u0442\u0438\u0441\u0442\u0438\u043a\u0438, \u044f\u043a\u0430 \u043d\u0430\u0437\u0438\u0432\u0430\u0454\u0442\u044c\u0441\u044f p-\u0437\u043d\u0430\u0447\u0435\u043d\u043d\u044f\u043c. \u0412\u0438 \u043c\u043e\u0436\u0435\u0442\u0435 \u043f\u043e\u0431\u0430\u0447\u0438\u0442\u0438, \u044f\u043a \u0446\u0435 \u0440\u043e\u0431\u0438\u0442\u044c\u0441\u044f, \u043d\u0430\u0442\u0438\u0441\u043d\u0443\u0432\u0448\u0438 \u043d\u0430 \u0442\u0430\u043a\u0435 \u043f\u043e\u0441\u0438\u043b\u0430\u043d\u043d\u044f: <\/p>\n<div style=\"background-color:#FFFDE7; padding-top: 10px; padding-bottom: 10px; padding-right: 20px; padding-left: 30px; border: 2.5px dashed #FFB74D; border-radius:20px;\"> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>\u0414\u0438\u0432.:<\/strong> <a href=\"https:\/\/statorials.org\/uk\/\u0437\u043d\u0430\u0447\u0435\u043d\u043d\u044f-p\/\">\u0406\u043d\u0442\u0435\u0440\u043f\u0440\u0435\u0442\u0430\u0446\u0456\u044f p-\u0437\u043d\u0430\u0447\u0435\u043d\u043d\u044f<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u0423 \u0446\u0456\u0439 \u0441\u0442\u0430\u0442\u0442\u0456 \u0432\u0438 \u0437\u043d\u0430\u0439\u0434\u0435\u0442\u0435 \u043f\u043e\u044f\u0441\u043d\u0435\u043d\u043d\u044f \u0442\u0430\u0431\u043b\u0438\u0446\u0456 ANOVA. \u041e\u0442\u0436\u0435, \u043c\u0438 \u043f\u043e\u044f\u0441\u043d\u044e\u0454\u043c\u043e \u0432\u0430\u043c, \u0449\u043e \u0442\u0430\u043a\u0435 \u0442\u0430\u0431\u043b\u0438\u0446\u044f ANOVA, \u044f\u043a \u0441\u0442\u0432\u043e\u0440\u0438\u0442\u0438 \u0442\u0430\u0431\u043b\u0438\u0446\u044e ANOVA, \u044f\u043a\u0456 \u0444\u043e\u0440\u043c\u0443\u043b\u0438 \u0442\u0430\u0431\u043b\u0438\u0446\u0456 ANOVA, \u0456, \u043a\u0440\u0456\u043c \u0442\u043e\u0433\u043e, \u0432\u0438 \u0437\u043c\u043e\u0436\u0435\u0442\u0435 \u043f\u043e\u0431\u0430\u0447\u0438\u0442\u0438 \u0432\u043f\u0440\u0430\u0432\u0443, \u0440\u043e\u0437\u0432\u2019\u044f\u0437\u0430\u043d\u0443 \u043a\u0440\u043e\u043a \u0437\u0430 \u043a\u0440\u043e\u043a\u043e\u043c. \u0429\u043e \u0442\u0430\u043a\u0435 \u0442\u0430\u0431\u043b\u0438\u0446\u044f ANOVA? \u0422\u0430\u0431\u043b\u0438\u0446\u044f ANOVA \u2014 \u0446\u0435 \u0442\u0430\u0431\u043b\u0438\u0446\u044f, \u044f\u043a\u0430 \u0432\u0438\u043a\u043e\u0440\u0438\u0441\u0442\u043e\u0432\u0443\u0454\u0442\u044c\u0441\u044f \u0432 \u0441\u0442\u0430\u0442\u0438\u0441\u0442\u0438\u0446\u0456 \u0434\u043b\u044f \u0434\u0438\u0441\u043f\u0435\u0440\u0441\u0456\u0439\u043d\u043e\u0433\u043e \u0430\u043d\u0430\u043b\u0456\u0437\u0443. \u0411\u0456\u043b\u044c\u0448 \u043a\u043e\u043d\u043a\u0440\u0435\u0442\u043d\u043e, \u0442\u0430\u0431\u043b\u0438\u0446\u044f ANOVA [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u25b7 \u0422\u0430\u0431\u043b\u0438\u0446\u044f ANOVA<\/title>\n<meta name=\"description\" content=\"\u0422\u0443\u0442 \u0432\u0438 \u0437\u043d\u0430\u0439\u0434\u0435\u0442\u0435, \u0449\u043e \u0442\u0430\u043a\u0435 \u0442\u0430\u0431\u043b\u0438\u0446\u044f ANOVA, \u044f\u043a \u0432\u043e\u043d\u0430 \u0441\u043a\u043b\u0430\u0434\u0430\u0454\u0442\u044c\u0441\u044f (\u0444\u043e\u0440\u043c\u0443\u043b\u0438), \u044f\u043a \u0457\u0457 \u0456\u043d\u0442\u0435\u0440\u043f\u0440\u0435\u0442\u0443\u0432\u0430\u0442\u0438, \u0430 \u0442\u0430\u043a\u043e\u0436 \u043a\u043e\u043d\u043a\u0440\u0435\u0442\u043d\u0438\u0439 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\u0441\u0442\u0443\u0434\u0435\u043d\u0442\u0456\u0432 \u0447\u0435\u0440\u0435\u0437 Statorials. \u0414\u0456\u0437\u043d\u0430\u0439\u0442\u0435\u0441\u044f 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