{"id":304,"date":"2023-08-02T20:15:08","date_gmt":"2023-08-02T20:15:08","guid":{"rendered":"https:\/\/statorials.org\/cn\/%e6%96%b9%e5%b7%ae%e5%88%86%e6%9e%90%e8%a1%a8\/"},"modified":"2023-08-02T20:15:08","modified_gmt":"2023-08-02T20:15:08","slug":"%e6%96%b9%e5%b7%ae%e5%88%86%e6%9e%90%e8%a1%a8","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/%e6%96%b9%e5%b7%ae%e5%88%86%e6%9e%90%e8%a1%a8\/","title":{"rendered":"\u65b9\u5dee\u5206\u6790\u8868"},"content":{"rendered":"<p>\u5728\u672c\u6587\u4e2d\uff0c\u60a8\u5c06\u627e\u5230\u65b9\u5dee\u5206\u6790\u8868\u7684\u89e3\u91ca\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u5411\u60a8\u89e3\u91ca\u4ec0\u4e48\u662f\u65b9\u5dee\u5206\u6790\u8868\u3001\u5982\u4f55\u5236\u4f5c\u65b9\u5dee\u5206\u6790\u8868\u3001\u65b9\u5dee\u5206\u6790\u8868\u7684\u516c\u5f0f\u662f\u4ec0\u4e48\uff0c\u6b64\u5916\uff0c\u60a8\u5c06\u80fd\u591f\u770b\u5230\u9010\u6b65\u89e3\u51b3\u7684\u7ec3\u4e60\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-tabla-anova\"><\/span>\u4ec0\u4e48\u662f\u65b9\u5dee\u5206\u6790\u8868\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>ANOVA\u8868<\/strong>\u662f\u7edf\u8ba1\u5b66\u4e2d\u7528\u4e8e\u65b9\u5dee\u5206\u6790\u7684\u8868\u3002\u66f4\u5177\u4f53\u5730\u8bf4\uff0c\u65b9\u5dee\u5206\u6790\u8868\u5305\u542b\u65b9\u5dee\u5206\u6790\u6240\u9700\u7684\u6240\u6709\u4fe1\u606f\u3002<\/p>\n<p>\u56e0\u6b64\uff0c\u65b9\u5dee\u5206\u6790\u8868\u7528\u4e8e\u603b\u7ed3\u65b9\u5dee\u5206\u6790\u3002\u901a\u8fc7\u5728\u8868\u683c\u4e2d\u7ed8\u5236\u65b9\u5dee\u5206\u6790\u7684\u8ba1\u7b97\u7ed3\u679c\uff0c\u60a8\u53ef\u4ee5\u8f7b\u677e\u5f97\u51fa\u7ed3\u8bba\uff0c\u8fd8\u53ef\u4ee5\u5feb\u901f\u8ba1\u7b97\u65b9\u5dee\u5206\u6790\u68c0\u9a8c\u7edf\u8ba1\u91cf\u7684\u503c\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formulas-de-la-tabla-anova\"><\/span>\u65b9\u5dee\u5206\u6790\u8868\u516c\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5728\u5355\u5411\u65b9\u5dee\u5206\u6790\u8868\u4e2d\uff0c\u5171\u6709\u4e09\u884c\uff1a\u56e0\u5b50\u3001\u8bef\u5dee\u548c\u603b\u8ba1\u3002\u56e0\u6b64\uff0c\u5728 ANOVA \u8868\u4e2d\uff0c\u8ba1\u7b97\u6bcf\u884c\u7684\u5e73\u65b9\u548c\u53ca\u5176\u81ea\u7531\u5ea6\u3002\u53e6\u5916\uff0c\u8ba1\u7b97\u56e0\u5b50\u548c\u8bef\u5dee\u7684\u5747\u65b9\u8bef\u5dee\uff0c\u6700\u540e\u786e\u5b9a\u65b9\u5dee\u5206\u6790\u68c0\u9a8c\u7edf\u8ba1\u91cf\uff0c\u8be5\u7edf\u8ba1\u91cf\u7b49\u4e8e\u5747\u65b9\u8bef\u5dee\u4e4b\u6bd4\u3002<\/p>\n<p>\u56e0\u6b64\uff0c<strong>\u65b9\u5dee\u5206\u6790\u8868\u7684\u516c\u5f0f<\/strong>\u5982\u4e0b\uff1a <\/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=\"\u65b9\u5dee\u5206\u6790\u8868\u516c\u5f0f\" class=\"wp-image-6387\" width=\"664\" height=\"397\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p style=\"margin-bottom:5px\">\u91d1\u5b50\uff1a<\/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>\u662f\u6837\u672c\u5927\u5c0f i\u3002<\/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>\u662f\u89c2\u6d4b\u503c\u7684\u603b\u6570\u3002<\/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>\u662f\u65b9\u5dee\u5206\u6790\u4e2d\u4e0d\u540c\u7ec4\u7684\u6570\u91cf\u3002<\/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>\u662f\u7ec4 i \u7684\u503c j\u3002<\/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>\u662f\u7b2c i \u7ec4\u7684\u5e73\u5747\u503c\u3002<\/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>\u8fd9\u662f\u6240\u6709\u5206\u6790\u6570\u636e\u7684\u5e73\u5747\u503c\u3002 <\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-la-tabla-anova\"><\/span>\u65b9\u5dee\u5206\u6790\u8868\u793a\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4e3a\u4e86\u66f4\u597d\u5730\u7406\u89e3\u8fd9\u4e2a\u6982\u5ff5\uff0c\u8ba9\u6211\u4eec\u901a\u8fc7\u9010\u6b65\u6c42\u89e3\u793a\u4f8b\u6765\u4e86\u89e3\u5982\u4f55\u521b\u5efa\u65b9\u5dee\u5206\u6790\u8868\u3002<\/p>\n<ul>\n<li>\u8fdb\u884c\u7edf\u8ba1\u7814\u7a76\u4ee5\u6bd4\u8f83\u56db\u540d\u5b66\u751f\u5728\u4e09\u4e2a\u4e0d\u540c\u79d1\u76ee\uff08A\u3001B \u548c C\uff09\u4e2d\u83b7\u5f97\u7684\u5206\u6570\u3002\u4e0b\u8868\u8be6\u7ec6\u5217\u51fa\u4e86\u6bcf\u4e2a\u5b66\u751f\u5728\u6700\u9ad8\u5206\u4e3a 20 \u5206\u7684\u6d4b\u8bd5\u4e2d\u83b7\u5f97\u7684\u5206\u6570\u3002\u6784\u5efa\u65b9\u5dee\u5206\u6790\u8868\u6765\u6bd4\u8f83\u6bcf\u4e2a\u5b66\u751f\u5728\u6bcf\u4e2a\u79d1\u76ee\u4e2d\u83b7\u5f97\u7684\u5206\u6570\u3002 <\/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=\"auto, \"><\/figure>\n<p>\u6211\u4eec\u9700\u8981\u505a\u7684\u7b2c\u4e00\u4ef6\u4e8b\u662f\u8ba1\u7b97\u6bcf\u4e2a\u53d7\u8bd5\u8005\u7684\u5e73\u5747\u503c\u548c\u6570\u636e\u7684\u603b\u5e73\u5747\u503c\uff1a <\/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>\u4e00\u65e6\u6211\u4eec\u77e5\u9053\u5e73\u5747\u503c\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u4f7f\u7528\u65b9\u5dee\u5206\u6790\u8868\u4e2d\u7684\u516c\u5f0f\u8ba1\u7b97\u5e73\u65b9\u548c\uff08\u89c1\u4e0a\u6587\uff09\uff1a <\/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>\u7136\u540e\u6211\u4eec\u786e\u5b9a\u56e0\u5b50\u3001\u8bef\u5dee\u548c\u603b\u7684\u81ea\u7531\u5ea6\uff1a <\/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>\u73b0\u5728\uff0c\u6211\u4eec\u901a\u8fc7\u5c06\u56e0\u5b50\u548c\u8bef\u5dee\u7684\u5e73\u65b9\u548c\u9664\u4ee5\u5b83\u4eec\u5404\u81ea\u7684\u81ea\u7531\u5ea6\u6765\u8ba1\u7b97\u5747\u65b9\u8bef\u5dee\uff1a<\/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>\u6700\u540e\uff0c\u6211\u4eec\u901a\u8fc7\u5c06\u4e0a\u4e00\u6b65\u8ba1\u7b97\u51fa\u7684\u4e24\u4e2a\u8bef\u5dee\u76f8\u9664\u6765\u8ba1\u7b97 F \u7edf\u8ba1\u91cf\u7684\u503c\uff1a<\/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\">\u7b80\u800c\u8a00\u4e4b\uff0c\u793a\u4f8b\u6570\u636e\u7684\u65b9\u5dee\u5206\u6790\u8868\u5982\u4e0b\u6240\u793a\uff1a <\/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=\"\u65b9\u5dee\u5206\u6790\u8868\u793a\u4f8b\" class=\"wp-image-6408\" width=\"726\" height=\"279\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p>\u4e00\u65e6\u8ba1\u7b97\u5b8c\u65b9\u5dee\u5206\u6790\u8868\u4e2d\u7684\u6240\u6709\u503c\uff0c\u5269\u4e0b\u7684\u5c31\u662f\u89e3\u91ca\u5b83\u3002\u4e3a\u6b64\uff0c\u6211\u4eec\u5fc5\u987b\u6bd4\u8f83\u4e0e F \u7edf\u8ba1\u91cf\u503c\u5bf9\u5e94\u7684\u6982\u7387\uff0c\u79f0\u4e3a p \u503c\u3002\u60a8\u53ef\u4ee5\u901a\u8fc7\u5355\u51fb\u4ee5\u4e0b\u94fe\u63a5\u67e5\u770b\u8fd9\u662f\u5982\u4f55\u5b8c\u6210\u7684\uff1a <\/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>\u8bf7\u53c2\u9605\uff1a<\/strong> <a href=\"https:\/\/statorials.org\/cn\/p\u503c\/\">p 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