{"id":322,"date":"2023-08-02T13:08:08","date_gmt":"2023-08-02T13:08:08","guid":{"rendered":"https:\/\/statorials.org\/cn\/%e5%8d%a1%e6%96%b9-2-%e6%a3%80%e9%aa%8c\/"},"modified":"2023-08-02T13:08:08","modified_gmt":"2023-08-02T13:08:08","slug":"%e5%8d%a1%e6%96%b9-2-%e6%a3%80%e9%aa%8c","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/%e5%8d%a1%e6%96%b9-2-%e6%a3%80%e9%aa%8c\/","title":{"rendered":"\u5361\u65b9\u68c0\u9a8c"},"content":{"rendered":"<p>\u672c\u6587\u89e3\u91ca\u4e86\u7edf\u8ba1\u5b66\u4e2d\u7684\u5361\u65b9\u68c0\u9a8c\u662f\u4ec0\u4e48\u4ee5\u53ca\u5b83\u7684\u7528\u9014\u3002\u60a8\u8fd8\u5c06\u4e86\u89e3\u5982\u4f55\u8fdb\u884c\u5361\u65b9\u68c0\u9a8c\uff0c\u4ee5\u53ca\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-prueba-chi-cuadrado\"><\/span>\u4ec0\u4e48\u662f\u5361\u65b9\u68c0\u9a8c\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u5361\u65b9\u68c0\u9a8c<\/strong>\u662f\u4e00\u79cd\u7edf\u8ba1\u68c0\u9a8c\uff0c\u7528\u4e8e\u786e\u5b9a\u9884\u671f\u9891\u7387\u548c\u89c2\u5bdf\u5230\u7684\u9891\u7387\u4e4b\u95f4\u662f\u5426\u5b58\u5728\u7edf\u8ba1\u663e\u7740\u5dee\u5f02\u3002<\/p>\n<p>\u4ece\u903b\u8f91\u4e0a\u8bb2\uff0c\u5361\u65b9\u68c0\u9a8c\u7edf\u8ba1\u91cf\u9075\u5faa<a href=\"https:\/\/statorials.org\/cn\/\u5361\u65b9\u5206\u5e03\/\">\u5361\u65b9\u5206\u5e03<\/a>\u3002\u56e0\u6b64\uff0c\u68c0\u9a8c\u7edf\u8ba1\u91cf\u7684\u503c\u5fc5\u987b\u4e0e\u5361\u65b9\u5206\u5e03\u7684\u7279\u5b9a\u503c\u8fdb\u884c\u6bd4\u8f83\u3002\u4e0b\u9762\u6211\u4eec\u5c06\u770b\u5230\u5982\u4f55\u6267\u884c\u5361\u65b9\u68c0\u9a8c\u3002<\/p>\n<p>\u8fd9\u79cd\u7c7b\u578b\u7684\u7edf\u8ba1\u68c0\u9a8c\u4e5f\u79f0\u4e3a<strong>Pearson \u5361\u65b9\u68c0\u9a8c<\/strong>\uff0c\u6709\u65f6\u7528\u5361\u65b9\u5206\u5e03\u7684\u7b26\u53f7\u8868\u793a\uff1a <strong>\u03c72 \u68c0\u9a8c<\/strong>\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-prueba-chi-cuadrado\"><\/span>\u5361\u65b9\u68c0\u9a8c\u516c\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5361\u65b9\u68c0\u9a8c\u7edf\u8ba1\u91cf\u7b49\u4e8e\u89c2\u6d4b\u503c\u4e0e\u671f\u671b\u503c\u4e4b\u5dee\u7684\u5e73\u65b9\u548c\u9664\u4ee5\u671f\u671b\u503c\u3002<\/p>\n<p>\u56e0\u6b64\uff0c<strong>\u5361\u65b9\u68c0\u9a8c\u7684\u516c\u5f0f<\/strong>\u4e3a\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-ca52fc2f501a2bff49c05e6c321e242e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\chi^2=\\sum_{i=1}^k\\frac{(O_i-E_i)^2}{E_i}\" title=\"Rendered by QuickLaTeX.com\" height=\"52\" width=\"154\" style=\"vertical-align: -21px;\"><\/p>\n<\/p>\n<p style=\"margin-bottom:5px\">\u91d1\u5b50\uff1a<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-984dc78529fc235b078a9f3b62d0f0c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\chi^2\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"18\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u662f\u5361\u65b9\u68c0\u9a8c\u7edf\u8ba1\u91cf\uff0c\u9075\u5faa\u5361\u65b9\u5206\u5e03<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-7dfca2445cd362ac42fb9032c9cf2367_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k-1\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"39\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u81ea\u7531\u7a0b\u5ea6\u3002<\/li>\n<li>\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\u6570\u636e\u6837\u672c\u5927\u5c0f\u3002<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-434bc05ea7818e67065a4f690de03718_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"O_i\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"19\" style=\"vertical-align: -3px;\"><\/p>\n<p>\u662f\u6570\u636e i \u7684\u89c2\u6d4b\u503c\u3002<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-a1e6cfc87bb6b00130570c8c9f348b98_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"E_i\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"18\" style=\"vertical-align: -3px;\"><\/p>\n<p>\u662f\u6570\u636e i \u7684\u671f\u671b\u503c\u3002<\/li>\n<\/ul>\n<p>\u5047\u8bbe\u68c0\u9a8c\u5361\u65b9\u68c0\u9a8c\u7684\u539f\u5047\u8bbe\u662f\u89c2\u5bdf\u503c\u4e0e\u671f\u671b\u503c\u76f8\u7b49\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u68c0\u9a8c\u7684\u5907\u62e9\u5047\u8bbe\u662f\u5176\u4e2d\u4e00\u4e2a\u89c2\u6d4b\u503c\u4e0e\u5176\u671f\u671b\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-3ef850ed6bba6d33fed54194e3e675e4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{cases}H_0:O_i=E_i \\quad \\forall i\\\\[2ex]H_1:\\exists \\ O_i\\neq E_i \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"145\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u8003\u8651\u5230\u91cd\u8981\u6027\u6c34\u5e73<\/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-5f44d9bbc8046069be4aa2989bff19aa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\alpha\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p>\uff0c\u8ba1\u7b97\u51fa\u7684\u68c0\u9a8c\u7edf\u8ba1\u91cf\u5e94\u4e0e\u4e34\u754c\u68c0\u9a8c\u503c\u8fdb\u884c\u6bd4\u8f83\uff0c\u4ee5\u786e\u5b9a\u662f\u5426\u62d2\u7edd\u539f\u5047\u8bbe\u6216\u5907\u62e9\u5047\u8bbe\uff1a<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:16px\"><span style=\"color:#101010;font-weight: normal;\">\u5982\u679c\u68c0\u9a8c\u7edf\u8ba1\u91cf\u5c0f\u4e8e\u4e34\u754c\u503c\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-63233cd2098dd4d4be73a18d4ab3df18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\chi_{1-\\alpha|k-1}^2\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"66\" style=\"vertical-align: -10px;\"><\/p>\n<p><\/span>\uff0c\u62d2\u7edd\u5907\u62e9\u5047\u8bbe\uff08\u5e76\u63a5\u53d7\u539f\u5047\u8bbe\uff09\u3002<\/li>\n<li style=\"margin-bottom:16px\"><span style=\"color:#101010;font-weight: normal;\">\u5982\u679c\u68c0\u9a8c\u7edf\u8ba1\u91cf\u5927\u4e8e\u4e34\u754c\u503c\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-63233cd2098dd4d4be73a18d4ab3df18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\chi_{1-\\alpha|k-1}^2\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"66\" style=\"vertical-align: -10px;\"><\/p>\n<p><\/span>\uff0c\u62d2\u7edd\u539f\u5047\u8bbe\uff08\u5e76\u63a5\u53d7\u5907\u62e9\u5047\u8bbe\uff09\u3002 <\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-6b48f7bb620dca865b7e652e81cc247a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{l}\\text{Si } \\chi^2<\\chi^2_{1-\\alpha|k-1}\\text{ se rechaza } H_1\\\\[3ex]\\text{Si } \\chi^2>\\chi^2_{1-\\alpha|k-1}\\text{ se rechaza } H_0\\end{array}&#8221; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;70&#8243; width=&#8221;243&#8243; style=&#8221;vertical-align: 0px;&#8221;><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-la-prueba-chi-cuadrado\"><\/span>\u5361\u65b9\u68c0\u9a8c\u793a\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4e00\u65e6\u6211\u4eec\u4e86\u89e3\u4e86\u5361\u65b9\u68c0\u9a8c\u7684\u5b9a\u4e49\u53ca\u5176\u516c\u5f0f\u662f\u4ec0\u4e48\uff0c\u4e0b\u9762\u5c06\u4ecb\u7ecd\u4e00\u4e2a\u9010\u6b65\u89e3\u51b3\u7684\u793a\u4f8b\uff0c\u4ee5\u4fbf\u60a8\u53ef\u4ee5\u4e86\u89e3\u5982\u4f55\u6267\u884c\u6b64\u7c7b\u7edf\u8ba1\u68c0\u9a8c\u3002<\/p>\n<ul>\n<li>\u5e97\u4e3b\u8bf4\uff0c\u4ed6\u7684\u9500\u552e\u989d\u7684 50% \u662f\u4ea7\u54c1 A\uff0c\u4ed6\u7684\u9500\u552e\u989d\u7684 35% \u662f\u4ea7\u54c1 B\uff0c\u4ed6\u7684\u9500\u552e\u989d\u7684 15% \u662f\u4ea7\u54c1 C\u3002\u4f46\u662f\uff0c\u6bcf\u79cd\u4ea7\u54c1\u7684\u9500\u552e\u5355\u4f4d\u662f\u5b83\u4eec\u6240\u5c55\u793a\u7684\u5355\u4f4d\u5728\u4e0b\u9762\u7684<a href=\"https:\/\/statorials.org\/cn\/\u5217\u8054\u8868\/\">\u5217\u8054\u8868<\/a>\u4e2d\u3002\u5206\u6790\u4e1a\u4e3b\u7684\u7406\u8bba\u6570\u636e\u4e0e\u5b9e\u9645\u6536\u96c6\u7684\u6570\u636e\u662f\u5426\u5b58\u5728\u7edf\u8ba1\u5dee\u5f02\u3002<\/li>\n<\/ul>\n<figure class=\"wp-block-table aligncenter is-style-stripes\">\n<table>\n<thead>\n<tr>\n<th>\u4ea7\u54c1<\/th>\n<th class=\"has-text-align-center\" data-align=\"center\">\u89c2\u5bdf\u5230\u7684\u9500\u552e\u989d (O <sub>i<\/sub> )<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\u4ea7\u54c1A<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">\u7b2c453\u7ae0<\/td>\n<\/tr>\n<tr>\n<td>\u4ea7\u54c1B<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 268<\/td>\n<\/tr>\n<tr>\n<td>\u4ea7\u54c1C<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 79<\/td>\n<\/tr>\n<tr>\n<td>\u5168\u90e8\u7684<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">800<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/figure>\n<p>\u9996\u5148\uff0c\u6211\u4eec\u9700\u8981\u8ba1\u7b97\u5e97\u4e3b\u671f\u671b\u7684\u4ef7\u503c\u3002\u4e3a\u6b64\uff0c\u6211\u4eec\u5c06\u6bcf\u79cd\u4ea7\u54c1\u7684\u9884\u671f\u9500\u552e\u989d\u767e\u5206\u6bd4\u4e58\u4ee5\u5df2\u5b9e\u73b0\u7684\u603b\u9500\u552e\u989d\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-cfd0d5e1cc7a049ddd825c5db9eb4bec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}E_A=800\\cdot 0,5=400\\\\[2ex]E_B=800\\cdot 0,35=280\\\\[2ex]E_A=800\\cdot 0,15=120\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"92\" width=\"173\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u8be5\u95ee\u9898\u7684<a href=\"https:\/\/statorials.org\/cn\/\u9891\u7387\u5206\u5e03\/\">\u9891\u6570\u5206\u5e03\u8868<\/a>\u5982\u4e0b\uff1a<\/p>\n<figure class=\"wp-block-table aligncenter is-style-stripes\">\n<table>\n<thead>\n<tr>\n<th>\u4ea7\u54c1<\/th>\n<th class=\"has-text-align-center\" data-align=\"center\">\u89c2\u5bdf\u5230\u7684\u9500\u552e\u989d (O <sub>i<\/sub> )<\/th>\n<th class=\"has-text-align-center\" data-align=\"center\">\u9884\u671f\u9500\u552e\u989d (E <sub>i<\/sub> )<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\u4ea7\u54c1A<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">\u7b2c453\u7ae0<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">400<\/td>\n<\/tr>\n<tr>\n<td>\u4ea7\u54c1B<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 268<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 280<\/td>\n<\/tr>\n<tr>\n<td>\u4ea7\u54c1C<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 79<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 120<\/td>\n<\/tr>\n<tr>\n<td>\u5168\u90e8\u7684<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">800<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 800<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/figure>\n<p>\u73b0\u5728\u6211\u4eec\u5df2\u7ecf\u8ba1\u7b97\u4e86\u6240\u6709\u503c\uff0c\u6211\u4eec\u5e94\u7528\u5361\u65b9\u68c0\u9a8c\u516c\u5f0f\u6765\u8ba1\u7b97\u68c0\u9a8c\u7edf\u8ba1\u91cf\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-8c76621fbe8504217dfe8ac55b2d6e67_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}\\displaystyle\\chi^2=\\sum_{i=1}^k\\frac{(O_i-E_i)^2}{E_i}\\\\[6ex]\\chi^2=\\cfrac{(453-400)^2}{400}+\\cfrac{(268-280)^2}{280}+\\cfrac{(79-120)^2}{120}\\\\[6ex]\\chi^2=7,02+0,51+14,00\\\\[6ex]\\chi^2=21,53\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"252\" width=\"372\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u4e00\u65e6\u8ba1\u7b97\u51fa\u68c0\u9a8c\u7edf\u8ba1\u91cf\u7684\u503c\uff0c\u6211\u4eec\u5c31\u4f7f\u7528\u5361\u65b9\u5206\u5e03\u8868\u6765\u67e5\u627e\u68c0\u9a8c\u7684\u4e34\u754c\u503c\u3002\u5361\u65b9\u5206\u5e03\u6709<\/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-d7ae885b62b57867e96527f583044991_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k-1=3-1=2\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"135\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u81ea\u7531\u5ea6\uff0c\u6240\u4ee5\u5982\u679c\u6211\u4eec\u9009\u62e9\u4e00\u4e2a\u663e\u7740\u6027\u6c34\u5e73<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-76d20f2945704d6640a4b9986b8b7c16_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\alpha=0,05\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"69\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u68c0\u9a8c\u7684\u4e34\u754c\u503c\u5982\u4e0b\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-1850e764fc71b1e7b49b0c4d8133ab89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}\\chi^2_{1-\\alpha|k-1}=\\ \\color{orange}\\bm{?}\\color{black}\\\\[4ex]\\chi^2_{0,95|2}=5,991\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"78\" width=\"199\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u68c0\u9a8c\u7edf\u8ba1\u91cf (21.53) \u5927\u4e8e\u4e34\u754c\u68c0\u9a8c\u503c 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