{"id":307,"date":"2023-08-02T18:50:10","date_gmt":"2023-08-02T18:50:10","guid":{"rendered":"https:\/\/statorials.org\/cn\/%e6%96%b9%e5%b7%ae%e5%88%86%e6%9e%90\/"},"modified":"2023-08-02T18:50:10","modified_gmt":"2023-08-02T18:50:10","slug":"%e6%96%b9%e5%b7%ae%e5%88%86%e6%9e%90","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/%e6%96%b9%e5%b7%ae%e5%88%86%e6%9e%90\/","title":{"rendered":"\u65b9\u5dee\u5206\u6790 (anova)"},"content":{"rendered":"<p>\u672c\u6587\u89e3\u91ca\u4e86\u7edf\u8ba1\u5b66\u4e2d\u7684\u65b9\u5dee\u5206\u6790\uff08\u4e5f\u79f0\u4e3a\u65b9\u5dee\u5206\u6790\uff09\u3002\u56e0\u6b64\uff0c\u60a8\u5c06\u4e86\u89e3\u5982\u4f55\u8fdb\u884c\u65b9\u5dee\u5206\u6790\u3001\u65b9\u5dee\u5206\u6790\u8868\u662f\u4ec0\u4e48\u4ee5\u53ca\u9010\u6b65\u89e3\u51b3\u7684\u7ec3\u4e60\u3002\u6b64\u5916\uff0c\u5b83\u8fd8\u663e\u793a\u4e86\u6267\u884c\u65b9\u5dee\u5206\u6790\u65f6\u5fc5\u987b\u9075\u5b88\u7684\u5148\u9a8c\u5047\u8bbe\uff0c\u4ee5\u53ca\u65b9\u5dee\u5206\u6790\u7684\u4f18\u70b9\u548c\u7f3a\u70b9\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-el-analisis-de-la-varianza-anova\"><\/span>\u4ec0\u4e48\u662f\u65b9\u5dee\u5206\u6790 (ANOVA)\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5728\u7edf\u8ba1\u5b66\u4e2d\uff0c<strong>\u65b9\u5dee\u5206\u6790<\/strong>\uff0c\u4e5f\u79f0\u4e3a<strong>ANOVA<\/strong> \uff08\u65b9\u5dee\u5206\u6790\uff09\uff0c\u662f\u4e00\u79cd\u5141\u8bb8\u60a8\u6bd4\u8f83\u4e0d\u540c\u6837\u672c\u5747\u503c\u4e4b\u95f4\u65b9\u5dee\u7684\u6280\u672f\u3002<\/p>\n<p>\u65b9\u5dee\u5206\u6790\uff08ANOVA\uff09\u7528\u4e8e\u5206\u6790\u4e24\u4e2a\u4ee5\u4e0a\u603b\u4f53\u7684\u5747\u503c\u4e4b\u95f4\u662f\u5426\u5b58\u5728\u5dee\u5f02\u3002\u56e0\u6b64\uff0c\u65b9\u5dee\u5206\u6790\u4f7f\u6211\u4eec\u80fd\u591f\u901a\u8fc7\u5206\u6790\u6837\u672c\u5747\u503c\u4e4b\u95f4\u7684\u53d8\u5f02\u6027\u6765\u786e\u5b9a\u4e24\u4e2a\u6216\u591a\u4e2a\u7ec4\u7684\u603b\u4f53\u5747\u503c\u662f\u5426\u4e0d\u540c\u3002<\/p>\n<p>\u56e0\u6b64\uff0c\u65b9\u5dee\u5206\u6790\u7684\u96f6\u5047\u8bbe\u662f\u6240\u6709\u5206\u6790\u7ec4\u7684\u5747\u503c\u76f8\u7b49\u3002\u800c\u5907\u62e9\u5047\u8bbe\u5219\u8ba4\u4e3a\u81f3\u5c11\u6709\u4e00\u79cd\u624b\u6bb5\u662f\u4e0d\u540c\u7684\u3002<\/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-6918550a8ad2954432ea33e07c7b83d0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{cases}H_0: \\mu_1=\\mu_2=\\ldots=\\mu_k=\\mu\\\\[2ex]H_1: \\exists \\mu_i\\neq \\mu \\quad i=1,2,\\ldots, k\\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"232\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u65b9\u5dee\u5206\u6790\u5bf9\u4e8e\u6bd4\u8f83\u4e24\u4e2a\u4ee5\u4e0a\u7ec4\u7684\u5747\u503c\u7279\u522b\u6709\u7528\uff0c\u56e0\u4e3a\u901a\u8fc7\u8fd9\u79cd\u7c7b\u578b\u7684\u5206\u6790\uff0c\u60a8\u53ef\u4ee5\u540c\u65f6\u7814\u7a76\u6240\u6709\u7ec4\u7684\u5747\u503c\uff0c\u800c\u4e0d\u662f\u6210\u5bf9\u6bd4\u8f83\u5747\u503c\u3002\u4e0b\u9762\u6211\u4eec\u5c06\u4e86\u89e3\u65b9\u5dee\u5206\u6790\u7684\u4f18\u70b9\u548c\u7f3a\u70b9\u3002<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"tabla-anova\"><\/span>\u65b9\u5dee\u5206\u6790\u8868<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u65b9\u5dee\u5206\u6790\u603b\u7ed3\u5728\u4e00\u4e2a\u79f0\u4e3a<strong>\u65b9\u5dee\u5206\u6790<\/strong>\u8868\u7684\u8868\u4e2d\uff0c\u5176\u516c\u5f0f\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\u6216\u65b9\u5dee\u5206\u6790\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-un-analisis-de-la-varianza-anova\"><\/span>\u65b9\u5dee\u5206\u6790 (ANOVA) \u793a\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4e3a\u4e86\u7406\u89e3\u65b9\u5dee\u5206\u6790\u7684\u6982\u5ff5\uff0c\u8ba9\u6211\u4eec\u901a\u8fc7\u9010\u6b65\u6c42\u89e3\u793a\u4f8b\u6765\u4e86\u89e3\u5982\u4f55\u8fdb\u884c\u65b9\u5dee\u5206\u6790\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\u6267\u884c\u65b9\u5dee\u5206\u6790\u4ee5\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>\u6b64\u65b9\u5dee\u5206\u6790\u7684\u96f6\u5047\u8bbe\u662f\u4e09\u4e2a\u53d7\u8bd5\u8005\u7684\u5206\u6570\u5747\u503c\u76f8\u7b49\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u96f6\u5047\u8bbe\u662f\u5176\u4e2d\u4e00\u4e9b\u5747\u503c\u4e0d\u540c\u3002<\/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-d1587da405a54d6a2bae626989b04562_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{cases}H_0: \\mu_A=\\mu_B=\\mu_C=\\mu\\\\[2ex]H_1: \\exists \\mu_i\\neq \\mu \\quad i=A, B, C\\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"215\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u8981\u8fdb\u884c\u65b9\u5dee\u5206\u6790\uff0c\u9996\u5148\u8981\u505a\u7684\u662f\u8ba1\u7b97\u6bcf\u4e2a\u53d7\u8bd5\u8005\u7684\u5747\u503c\u548c\u6570\u636e\u7684\u603b\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\u4e86\u5747\u503c\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u4f7f\u7528\u4e0a\u9762\u770b\u5230\u7684\u65b9\u5dee\u5206\u6790 (ANOVA) \u516c\u5f0f\u6765\u8ba1\u7b97\u5e73\u65b9\u548c\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 (ANOVA) \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\u83b7\u5f97\u7684\u7ed3\u679c\u3002\u4e3a\u6b64\uff0c\u6211\u4eec\u9700\u8981\u627e\u5230\u5728\u5177\u6709\u76f8\u5e94\u81ea\u7531\u5ea6\u7684 Snedecor F \u5206\u5e03\u4e2d\u83b7\u5f97\u5927\u4e8e F \u7edf\u8ba1\u91cf\u7684\u503c\u7684\u6982\u7387\uff0c\u5373\u6211\u4eec\u9700\u8981\u786e\u5b9a\u68c0\u9a8c\u7684 p \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-b706e5d710c3919d145399dc9d8efca5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P[F>11,08]=0,004&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;18&#8243; width=&#8221;172&#8243; style=&#8221;vertical-align: -5px;&#8221;><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u5982\u679c\u6211\u4eec\u91c7\u7528\u663e\u7740\u6027\u6c34\u5e73 \u03b1=0.05\uff08\u6700\u5e38\u89c1\uff09\uff0c\u6211\u4eec\u5fc5\u987b\u62d2\u7edd\u539f\u5047\u8bbe\u5e76\u63a5\u53d7\u5907\u62e9\u5047\u8bbe\uff0c\u56e0\u4e3a\u68c0\u9a8c\u7684 p \u503c\u4f4e\u4e8e\u663e\u7740\u6027\u6c34\u5e73\u3002\u8fd9\u610f\u5473\u7740\u6240\u7814\u7a76\u7684\u7fa4\u4f53\u81f3\u5c11\u6709\u4e00\u4e9b\u624b\u6bb5\u4e0e\u5176\u4ed6\u7fa4\u4f53\u4e0d\u540c\u3002<\/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-df22e22716e8cfbb1ab37d5e3e74fc9d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"0,004 < 0,05 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black}\\ \\text{Se rechaza } H_0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"346\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p>\u5e94\u8be5\u6307\u51fa\u7684\u662f\uff0c\u76ee\u524d\u6709\u51e0\u79cd\u8ba1\u7b97\u673a\u7a0b\u5e8f\u53ef\u4ee5\u5728\u77ed\u77ed\u51e0\u79d2\u949f\u5185\u6267\u884c\u65b9\u5dee\u5206\u6790\u3002\u7136\u800c\uff0c\u4e86\u89e3\u8ba1\u7b97\u80cc\u540e\u7684\u7406\u8bba\u4e5f\u5f88\u91cd\u8981\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"supuestos-del-analisis-de-la-varianza-anova\"><\/span>\u65b9\u5dee\u5206\u6790 (ANOVA) \u7684\u5047\u8bbe<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4e3a\u4e86\u6267\u884c\u65b9\u5dee\u5206\u6790 (ANOVA)\uff0c\u5fc5\u987b\u6ee1\u8db3\u4ee5\u4e0b\u6761\u4ef6\uff1a<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:16px\"><span style=\"color:#101010;font-weight: normal;\"><strong>\u72ec\u7acb\u6027<\/strong>\uff1a\u89c2\u6d4b\u503c\u76f8\u4e92\u72ec\u7acb\u3002\u786e\u4fdd\u89c2\u5bdf\u72ec\u7acb\u6027\u7684\u4e00\u79cd\u65b9\u6cd5\u662f\u5728\u62bd\u6837\u8fc7\u7a0b\u4e2d\u589e\u52a0\u968f\u673a\u6027\u3002<\/span><\/li>\n<li style=\"margin-bottom:16px\"><span style=\"color:#101010;font-weight: normal;\"><strong>\u540c\u65b9\u5dee\u6027<\/strong>\uff1a\u65b9\u5dee\u5fc5\u987b\u5177\u6709\u540c\u8d28\u6027\uff0c\u5373\u6b8b\u5dee\u7684\u53d8\u5f02\u6027\u662f\u6052\u5b9a\u7684\u3002<\/span><\/li>\n<li style=\"margin-bottom:16px\"><span style=\"color:#101010;font-weight: normal;\"><strong>\u6b63\u6001\u6027<\/strong>\uff1a\u6b8b\u5dee\u5e94\u8be5\u5448\u6b63\u6001\u5206\u5e03\uff0c\u6216\u8005\u6362\u53e5\u8bdd\u8bf4\uff0c\u5b83\u4eec\u5e94\u8be5\u670d\u4ece\u6b63\u6001\u5206\u5e03\u3002<\/span><\/li>\n<li style=\"margin-bottom:16px\"><span style=\"color:#101010;font-weight: normal;\"><strong>\u8fde\u7eed\u6027<\/strong>\uff1a\u56e0\u53d8\u91cf\u5fc5\u987b\u662f\u8fde\u7eed\u7684\u3002<\/span> <\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"tipos-de-analisis-de-la-varianza-anova\"><\/span>\u65b9\u5dee\u5206\u6790 (ANOVA) \u7684\u7c7b\u578b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u65b9\u5dee\u5206\u6790 (ANOVA) \u5206\u4e3a\u4e09\u79cd\u7c7b\u578b<\/strong>\uff1a<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:16px\"><span style=\"color:#101010;font-weight: normal;\"><strong>\u5355\u5411\u65b9\u5dee\u5206\u6790\uff08one-way ANOVA\uff09<\/strong> \uff1a\u65b9\u5dee\u5206\u6790\u4e2d\u53ea\u6709\u4e00\u4e2a\u56e0\u7d20\uff0c\u5373\u53ea\u6709\u4e00\u4e2a\u81ea\u53d8\u91cf\u3002<\/span><\/li>\n<li style=\"margin-bottom:16px\"><span style=\"color:#101010;font-weight: normal;\"><strong>\u53cc\u5411\u65b9\u5dee\u5206\u6790\uff08two-way ANOVA\uff09<\/strong> \uff1a\u65b9\u5dee\u5206\u6790\u6709\u4e24\u4e2a\u56e0\u7d20\uff0c\u56e0\u6b64\u5206\u6790\u4e24\u4e2a\u81ea\u53d8\u91cf\u4ee5\u53ca\u5b83\u4eec\u4e4b\u95f4\u7684\u4ea4\u4e92\u4f5c\u7528\u3002<\/span><\/li>\n<li style=\"margin-bottom:16px\"><span style=\"color:#101010;font-weight: normal;\"><strong>\u591a\u5143\u65b9\u5dee\u5206\u6790\uff08MANOVA\uff09<\/strong> \uff1a\u5728\u65b9\u5dee\u5206\u6790\u4e2d\uff0c\u5b58\u5728\u591a\u4e2a\u56e0\u53d8\u91cf\u3002\u76ee\u6807\u662f\u786e\u5b9a\u5f53\u56e0\u53d8\u91cf\u53d8\u5316\u65f6\u81ea\u53d8\u91cf\u7684\u503c\u662f\u5426\u6539\u53d8\u3002<\/span> <\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ventajas-y-desventajas-del-analisis-de-la-varianza-anova\"><\/span>\u65b9\u5dee\u5206\u6790 (ANOVA) \u7684\u4f18\u70b9\u548c\u7f3a\u70b9<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6700\u540e\uff0c\u6211\u4eec\u5c06\u4e86\u89e3\u4f55\u65f6\u9002\u5408\u4f7f\u7528\u65b9\u5dee\u5206\u6790\uff0c\u4ee5\u53ca\u6b64\u7c7b\u7edf\u8ba1\u5206\u6790\u7684\u5c40\u9650\u6027\u3002<\/p>\n<p>\u65b9\u5dee\u5206\u6790 (ANOVA) \u7684\u4e3b\u8981\u4f18\u70b9\u662f\u5b83\u5141\u8bb8\u540c\u65f6\u6bd4\u8f83\u4e24\u4e2a\u4ee5\u4e0a\u7684\u7ec4\u3002\u4e0e\u53ea\u80fd\u5206\u6790\u4e00\u4e24\u4e2a\u6837\u672c\u7684\u5747\u503c\u7684<a href=\"https:\/\/statorials.org\/cn\/\u5b66\u751ft\u68c0\u9a8c\/\">t \u68c0\u9a8c<\/a>\u4e0d\u540c\uff0c\u65b9\u5dee\u5206\u6790\u7528\u4e8e\u786e\u5b9a\u591a\u4e2a\u603b\u4f53\u662f\u5426\u5177\u6709\u76f8\u540c\u7684\u5747\u503c\u3002<\/p>\n<p>\u7136\u800c\uff0c\u65b9\u5dee\u5206\u6790\u5e76\u4e0d\u80fd\u544a\u8bc9\u6211\u4eec\u54ea\u4e2a\u7814\u7a76\u7ec4\u5177\u6709\u4e0d\u540c\u7684\u5747\u503c\uff0c\u5b83\u53ea\u80fd\u8ba9\u6211\u4eec\u77e5\u9053\u662f\u5426\u5b58\u5728\u663e\u7740\u5dee\u5f02\u7684\u5747\u503c\u6216\u6240\u6709\u5747\u503c\u662f\u5426\u76f8\u4f3c\u3002<\/p>\n<p>\u540c\u6837\uff0c\u65b9\u5dee\u5206\u6790\u7684\u53e6\u4e00\u4e2a\u7f3a\u70b9\u662f\u5fc5\u987b\u6ee1\u8db3\u524d\u9762\u7684\u56db\u4e2a\u5047\u8bbe\uff08\u89c1\u4e0a\u6587\uff09\u624d\u80fd\u8fdb\u884c\u65b9\u5dee\u5206\u6790\uff0c\u5426\u5219\u5f97\u51fa\u7684\u7ed3\u8bba\u53ef\u80fd\u662f\u9519\u8bef\u7684\u3002\u56e0\u6b64\uff0c\u5e94\u59cb\u7ec8\u9a8c\u8bc1\u7edf\u8ba1\u6570\u636e\u96c6\u662f\u5426\u6ee1\u8db3\u8fd9\u56db\u4e2a\u8981\u6c42\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u672c\u6587\u89e3\u91ca\u4e86\u7edf\u8ba1\u5b66\u4e2d\u7684\u65b9\u5dee\u5206\u6790\uff08\u4e5f\u79f0\u4e3a\u65b9\u5dee\u5206\u6790\uff09\u3002\u56e0\u6b64\uff0c\u60a8\u5c06\u4e86\u89e3\u5982\u4f55\u8fdb\u884c\u65b9\u5dee\u5206\u6790\u3001\u65b9\u5dee\u5206\u6790\u8868\u662f\u4ec0\u4e48\u4ee5\u53ca\u9010\u6b65\u89e3\u51b3\u7684 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[14],"tags":[],"class_list":["post-307","post","type-post","status-publish","format-standard","hentry","category-14"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u25b7 \u65b9\u5dee\u5206\u6790 (ANOVA)<\/title>\n<meta name=\"description\" content=\"\u5728\u8fd9\u91cc\u60a8\u5c06\u4e86\u89e3\u4ec0\u4e48\u662f\u65b9\u5dee\u5206\u6790 (ANOVA)\u3001\u5b83\u662f\u5982\u4f55\u8fdb\u884c\u7684\u3001\u5177\u4f53\u793a\u4f8b\u4ee5\u53ca ANOVA \u5206\u6790\u7684\u4f18\u70b9\u548c\u7f3a\u70b9\u3002\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/statorials.org\/cn\/\u65b9\u5dee\u5206\u6790\/\" 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content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u4f5c\u8005\" \/>\n\t<meta name=\"twitter:data1\" content=\"\u672c\u6770\u660e\u00b7\u5b89\u5fb7\u68ee\u535a\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/cn\/%e6%96%b9%e5%b7%ae%e5%88%86%e6%9e%90\/\",\"url\":\"https:\/\/statorials.org\/cn\/%e6%96%b9%e5%b7%ae%e5%88%86%e6%9e%90\/\",\"name\":\"\u25b7 \u65b9\u5dee\u5206\u6790 (ANOVA)\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/cn\/#website\"},\"datePublished\":\"2023-08-02T18:50:10+00:00\",\"dateModified\":\"2023-08-02T18:50:10+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/cn\/#\/schema\/person\/124e4e5b7c9f8dc0f1f95cc8c1db3261\"},\"description\":\"\u5728\u8fd9\u91cc\u60a8\u5c06\u4e86\u89e3\u4ec0\u4e48\u662f\u65b9\u5dee\u5206\u6790 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