{"id":73318,"date":"2016-08-05T07:16:41","date_gmt":"2016-08-04T23:16:41","guid":{"rendered":"http:\/\/highscope.ch.ntu.edu.tw\/wordpress\/?p=73318"},"modified":"2021-10-06T16:04:00","modified_gmt":"2021-10-06T08:04:00","slug":"%e9%a1%9e%e5%88%a5%e8%b3%87%e6%96%99%e5%88%86%e6%9e%90-%e5%90%8c%e8%b3%aa%e6%80%a7%e6%aa%a2%e5%ae%9a","status":"publish","type":"post","link":"http:\/\/localhost\/%e9%a1%9e%e5%88%a5%e8%b3%87%e6%96%99%e5%88%86%e6%9e%90-%e5%90%8c%e8%b3%aa%e6%80%a7%e6%aa%a2%e5%ae%9a\/","title":{"rendered":"\u985e\u5225\u8cc7\u6599\u5206\u6790\u2014\u540c\u8cea\u6027\u6aa2\u5b9a"},"content":{"rendered":"

\u985e\u5225\u8cc7\u6599\u5206\u6790\u2014\u540c\u8cea\u6027\u6aa2\u5b9a(Categorical Data Analysis \u2013 Test of Homogeneity)<\/strong><\/span>
\n\u570b\u7acb\u81fa\u7063\u5927\u5b78\u8fb2\u85dd\u6240\u751f\u7269\u7d71\u8a08\u7d44\u78a9\u58eb\u73ed \u8cf4\u8587\u4e91<\/strong><\/span><\/p>\n

\u4e00\u3001\u524d\u8a00<\/span><\/strong><\/p>\n

\u540c\u8cea\u6027\u6aa2\u5b9a\u8207\u7368\u7acb\u6027\u6aa2\u5b9a\u540c\u70ba\u61c9\u7528\u5361\u65b9\u5206\u5e03\u7684\u6aa2\u5b9a\u6cd5\uff0c\u5169\u8005\u6aa2\u5b9a\u53ef\u7528\u4f86\u6aa2\u9a57\u8a18\u6578\u578b\u7684\u8cc7\u6599\uff0c\u5176\u8cc7\u6599\u901a\u5e38\u8868\u793a\u70ba \\(r \\times c\\) \u5217\u806f\u8868\u7684\u578b\u614b\u3002\u5217\u806f\u8868\u7684\u683c\u5f0f\u8207\u63a1\u7528\u5361\u65b9\u5206\u5e03\u9032\u884c\u7368\u7acb\u6027\u6aa2\u5b9a\u7684\u65b9\u6cd5\u5c07\u53e6\u6587\u4ecb\u7d39\uff08\u53c3\u95b1\u300c\u5217\u806f\u8868\u8207\u7368\u7acb\u6027\u6aa2\u5b9a<\/a>\u300d\uff09\uff0c\u672c\u7bc7\u5c07\u4ecb\u7d39\u5361\u65b9\u5206\u5e03\u9032\u884c\u540c\u8cea\u6027\u6aa2\u5b9a\u7684\u65b9\u6cd5\u3002\u540c\u8cea\u6027\u6aa2\u5b9a\u76ee\u7684\u662f\u6bd4\u8f03\u6578\u7d44\u8a18\u6578\u578b\u8cc7\u6599\u7684\u7d50\u679c\u662f\u5426\u4e00\u81f4\uff0c\u5982\u63a1\u7528\u5169\u7a2e\u6559\u5b78\u65b9\u6cd5\u5c0d\u5b78\u751f\u9032\u884c\u6559\u5b78\uff0c\u63a2\u8a0e\u4e0d\u540c\u6559\u5b78\u6cd5\u4e0b\u5b78\u751f\u6e2c\u9a57\u6210\u7e3e\u7684\u7b49\u7b2c\u5206\u5e03\u662f\u5426\u76f8\u540c\u3002<\/p>\n

\u4e8c\u3001\u5361\u65b9\u540c\u8cea\u6027\u6aa2\u5b9a<\/span><\/strong><\/p>\n

\u5361\u65b9\u540c\u8cea\u6027\u6aa2\u5b9a\u662f\u7528\u4f86\u6aa2\u5b9a\u6578\u500b\u6bcd\u9ad4\u6a23\u672c\u5728\u540c\u4e00\u8b8a\u9805\u4e0b\u7684\u5206\u5e03\u662f\u5426\u76f8\u540c\u3002\u5047\u8a2d\u4eca\u5929\u9032\u884c\u4e86 \\(r\\) \u7a2e\u8a66\u9a57\uff0c\u6bcf\u7a2e\u8a66\u9a57\u7684\u53ef\u80fd\u7d50\u679c\u5747\u53ef\u88ab\u5206\u70ba \\(c\\) \u7d44\uff0c\u8868\u793a\u70ba \\(r \\times c\\) \u7684\u5217\u806f\u8868\u5982\u4e0b\uff08\u5217\u806f\u8868\u7684\u4ecb\u7d39\u53ef\u53c3\u8003\u524d\u6587\u300a\u985e\u5225\u8cc7\u6599\u5206\u6790\u2014\u5217\u806f\u8868\u8207\u7368\u7acb\u6027\u6aa2\u5b9a\u300b\uff09\uff1a<\/p>\n

\u8868\u4e00\u3001\u540c\u8cea\u6027\u6aa2\u5b9a\u7684 \\(r\\times c\\)\u00a0\u5217\u806f\u8868 \u3002\uff08\u672c\u6587\u4f5c\u8005\u88fd\uff09<\/p>\n\n\n\n\n\n\n\n\n\n
<\/td>\n\u53ef\u80fd\u7d50\u679c<\/td>\n<\/tr>\n
A1<\/sub><\/td>\nA2<\/sub><\/td>\nA3<\/sub><\/td>\n\u2026<\/td>\nAc<\/sub><\/td>\n\u7e3d\u548c<\/td>\n<\/tr>\n
\u8a66\u9a57\u5225<\/td>\n\u8a66\u9a57 1<\/td>\nn11<\/sub><\/td>\nn12<\/sub><\/td>\nn13<\/sub><\/td>\n\u2026<\/td>\nn1c<\/sub><\/td>\nn1.<\/sub><\/td>\n<\/tr>\n
\u8a66\u9a57 2<\/td>\nn21<\/sub><\/td>\nn22<\/sub><\/td>\nn23<\/sub><\/td>\n\u2026<\/td>\nn2c<\/sub><\/td>\nn2.<\/sub><\/td>\n<\/tr>\n
\u2026<\/td>\n\u2026<\/td>\n\u2026<\/td>\n\u2026<\/td>\n\u2026<\/td>\n\u2026<\/td>\n\u2026<\/td>\n<\/tr>\n
\u8a66\u9a57 r<\/td>\nnr1<\/sub><\/td>\nnr2<\/sub><\/td>\nnr3<\/sub><\/td>\n\u2026<\/td>\nnrc<\/sub><\/td>\nnr.<\/sub><\/td>\n<\/tr>\n
\u7e3d\u548c<\/td>\nn.1<\/sub><\/td>\nn.2<\/sub><\/td>\nn.3<\/sub><\/td>\n\u2026<\/td>\nn.c<\/sub><\/td>\n\n

n<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\\(n_{ij}\\) \u70ba\u7b2c \\(i\\) \u8a66\u9a57\u4e0b \\(A_j\\)\u00a0\u767c\u751f\u6b21\u6578\uff0c\\(n_{i.}\\)\u00a0<\/span>\u4ee3\u8868\u7b2c \\(i\\) \u8a66\u9a57\u7684\u7e3d\u767c\u751f\u6b21\u6578\uff0c\\(n_{.j}\\)\u00a0\u4ee3\u8868\u7d50\u679c \\(A_j\\)\u00a0\u7e3d\u767c\u751f\u6b21\u6578\u3002\u5047\u8a2d\u7b2c \\(i\\) \u7a2e\u8a66\u9a57\u4e0b \\(A_j\\)\u00a0\u767c\u751f\u7684\u6a5f\u7387\u53ef\u88ab\u8868\u793a\u70ba \\(\\pi_{ij}\\)\uff0c\u5361\u65b9\u540c\u8cea\u6027\u6aa2\u5b9a\u5c31\u662f\u60f3\u6aa2\u5b9a\uff1a<\/p>\n

\\(H_0\\)\uff1a\\(r\\) \u7a2e\u8a66\u9a57\u7d50\u679c\u662f\u540c\u8cea\u7684
\n\\(H_a\\)\uff1a\\(r\\) \u7a2e\u8a66\u9a57\u7d50\u679c\u70ba\u4e0d\u540c\u8cea<\/p>\n

\u4ee5\u6a5f\u7387\u7684\u5f62\u5f0f\u8868\u793a\uff0c\u5373\u70ba\u6aa2\u5b9a\uff1a<\/p>\n

\\(H_0:\\pi_{1j}=\\pi_{2j}=…=\\pi_{rj},~~~j=1,2,…,c\\)
\n\\(H_a:H_0\\)\u4e0d\u6210\u7acb<\/p>\n

\u5047\u8a2d\u4eca\u5929\u7b2c \\(i\\) \u7a2e\u8a66\u9a57\u7e3d\u5171\u505a\u4e86 \\(n_{i.}\\)\u00a0\u6b21\uff0c\u5728 \\(H_0\\)\u00a0\u6210\u7acb\u7684\u60c5\u6cc1\u4e0b\uff0c\u5404\u7a2e\u8a66\u9a57\u4e0b \\(A_j\\)\u00a0\u767c\u751f\u7684\u6a5f\u7387\u5747\u70ba\u76f8\u540c\uff0c\u90fd\u53ef\u8868\u793a\u70ba \\(P(A_j)\\)\uff0c\\(P(A_j)\\) \u70ba\u672a\u77e5\uff0c\u53ef\u7528 \\(\\hat{P}(A_j)=\\frac{n_{.j}}{n}\\) \u4f86\u8868\u793a\u3002\u90a3\u9ebc\u7b2c \\(i\\) \u7a2e\u8a66\u9a57\u4e0b \\(A_j\\) \u767c\u751f\u7684\u671f\u671b\u6b21\u6578\u70ba<\/p>\n

\\(\\displaystyle E_{ij}=n_{i.}\\times P(A_j)=\\frac{n_{i.}n_{.j}}{n}\\)<\/p>\n

\u63a5\u4e0b\u4f86\uff0c\u6211\u5011\u53ef\u6839\u64da\u5728\u5361\u65b9\u9069\u5408\u5ea6\u6aa2\u5b9a\u4e2d\u6240\u63d0\u5230\u7684\u6aa2\u5b9a\u7d71\u8a08\u91cf\uff0c\u4f86\u6aa2\u5b9a\u6bcf\u500b\u7d30\u683c\u7684\u671f\u671b\u6b21\u6578\u8207\u89c0\u6e2c\u6b21\u6578\u662f\u5426\u76f8\u540c\uff0c\u5728 \\(H_0\\)\u00a0\u6210\u7acb\u4e4b\u4e0b\uff1a<\/p>\n

\\(\\displaystyle\\chi^2_0=\\sum\\limits^c_{j=1}\\sum\\limits^r_{i=1}\\frac{(O_{ij}-E_{ij})^2}{E_{ij}}\\)<\/p>\n

\u5176\u6703\u8fd1\u4f3c\u4e00\u81ea\u7531\u5ea6\u70ba \\((r-1)(c-1)\\)\u00a0\u7684\u5361\u65b9\u5206\u5e03\u3002\u5728 \\(\\alpha=0.05\\) \u4e0b\uff0c\u82e5\u6aa2\u5b9a\u7d71\u8a08\u91cf\u503c\u5927\u65bc\u81ea\u7531\u5ea6\u70ba \\((r-1)(c-1)\\) \u7684\u5361\u65b9\u5206\u5e03\u7684 \\(95\\%\\) \u767e\u5206\u4f4d\u6578\u6642\uff0c\u61c9\u62d2\u7d55\u865b\u7121\u5047\u8aaa\uff0c\u4ea6\u5373\u8a8d\u5b9a \\(r\\) \u7a2e\u8a66\u9a57\u7d50\u679c\u4e0d\u540c\u8cea\uff08\u5716\u4e00\u85cd\u8272\u5340\u57df\uff09\u3002<\/p>\n

\"73318_p1\"<\/a>

\u5716\u4e00\u3001\u6aa2\u5b9a\u7d71\u8a08\u91cf\u68c4\u537b\u5340\u793a\u610f\u5716\u3002\uff08\u672c\u6587\u4f5c\u8005\u8cf4\u8587\u4e91\u7e6a\uff09<\/p><\/div>\n

\u4f8b\u984c\uff1a<\/p>\n

\u67d0\u9593\u9910\u5ef3\u60f3\u8981\u4e86\u89e3\u4e0d\u540c\u70f9\u716e\u65b9\u5f0f\u5c0d\u65bc\u9867\u5ba2\u7684\u6eff\u610f\u5ea6\u662f\u5426\u76f8\u540c\uff0c\u4ed6\u7e3d\u5171\u5c0d \\(100\\)\u00a0\u500b\u9867\u5ba2\u9032\u884c\u8abf\u67e5\uff0c\u5176\u4e2d \\(53\\) \u4f4d\u98df\u7528 A \u70f9\u716e\u65b9\u5f0f\u7684\u98df\u7269\uff0c\\(47\\) \u4f4d\u98df\u7528 B \u70f9\u716e\u65b9\u5f0f\u7684\u98df\u7269\uff0c\u4e26\u4ee5\u597d\u5403\u3001\u666e\u901a\u3001\u96e3\u5403\u4f5c\u70ba\u8a55\u50f9\u3002\u5c07\u8cc7\u6599\u6574\u7406\u6210\u5217\u806f\u8868\u5f8c\u5982\u4e0b\u8868\uff1a<\/p>\n

\u8868\u4e8c\u3001\\(100\\)\u00a0\u4f4d\u9867\u5ba2\u5c0d A\u3001B \u5169\u6599\u7406\u65b9\u6cd5\u7684\u8a55\u50f9\u3002\uff08\u672c\u6587\u4f5c\u8005\u88fd\uff09<\/p>\n\n\n\n\n\n\n
<\/td>\n\u597d\u5403<\/td>\n\u666e\u901a<\/td>\n\u96e3\u5403<\/td>\n\u7e3d\u548c<\/td>\n<\/tr>\n
\uff21<\/td>\n11<\/td>\n23<\/td>\n19<\/td>\n53<\/td>\n<\/tr>\n
\uff22<\/td>\n5<\/td>\n32<\/td>\n10<\/td>\n47<\/td>\n<\/tr>\n
\u7e3d\u548c<\/td>\n16<\/td>\n55<\/td>\n29<\/td>\n100<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\\(H_0\\)\uff1a\u5169\u7a2e\u70f9\u716e\u65b9\u5f0f\u5c0d\u65bc\u9867\u5ba2\u6eff\u610f\u5ea6\u76f8\u540c
\n\\(H_a\\)\uff1a\u5169\u7a2e\u70f9\u716e\u65b9\u5f0f\u5c0d\u65bc\u9867\u5ba2\u6eff\u610f\u5ea6\u4e0d\u540c<\/p>\n

\u7d71\u8a08\u6aa2\u5b9a\u91cf\u503c\u8a08\u7b97\u5982\u4e0b\uff1a<\/p>\n

\\(\\chi^2_0=\\frac{(11-8.48)^2}{8.48}+\\frac{(23-29.15)^2}{29.15}+\\frac{(19-15.37)^2}{15.37}+\\frac{(5-7.52)^2}{7.52}+\\frac{(32-25.85)^2}{25.85}+\\frac{(10-13.63)^2}{13.63}=6.1781\\)<\/p>\n

\u5728 \\(\\alpha= 0.05\\)\u00a0\u4e0b\uff0c\u6aa2\u5b9a\u7d71\u8a08\u91cf\u503c\u670d\u5f9e\u81ea\u7531\u5ea6\u70ba \\((2-1)(3-1) = 2\\) \u7684\u5361\u65b9\u5206\u5e03\uff0c\u81ea\u7531\u5ea6\u70ba \\(2\\) \u4e4b\u5361\u65b9\u5206\u5e03\u7684 \\(95\\%\\) \u767e\u5206\u4f4d\u6578\u53ef\u67e5\u8868\u6216\u7531 Excel \u51fd\u5f0f\u6c42\u5f97\uff08\u8b80\u8005\u53ef\u53c3\u8003\u300a\u5361\u65b9\u5206\u5e03\u5728 Excel \u7684\u61c9\u7528\uff08\u4e0a\uff09\u3001\uff08\u4e0b\uff09\u300b\u5169\u7bc7\u6587\u7ae0\uff09\u70ba \\(5.99\\)\u3002\u56e0\u70ba\u6aa2\u5b9a\u7d71\u8a08\u91cf \\(= 6.1781 > 5.99\\)\uff0c\u6545\u5728 \\(\\alpha= 0.05\\) \u4e0b\uff0cA \u548c B \u70f9\u716e\u65b9\u5f0f\u5c0d\u65bc\u9867\u5ba2\u6eff\u610f\u5ea6\u4e26\u4e0d\u76f8\u540c\u3002<\/p>\n

\n

\u53c3\u8003\u6587\u737b<\/strong><\/p>\n

    \n
  1. \u6c88\u660e\u4f86 (2014)\u3002\u751f\u7269\u7d71\u8a08\u5b78\u5165\u9580\u3002\u4e5d\u5dde\u3002<\/li>\n
  2. \u90ed\u5bf6\u931a\u3001\u9673\u7389\u654f (2011)\u3002\u751f\u7269\u7d71\u8a08\u5b78\u3002\u4e94\u5357\u3002<\/li>\n
  3. Hogg, R. V., Tanis, E., & Zimmerman, D. (2015). Probability and statistical inference (9th<\/sup> edition). Pearson Higher Ed.<\/li>\n<\/ol>\n<\/div>","protected":false},"excerpt":{"rendered":"

    \u985e\u5225\u8cc7\u6599\u5206\u6790\u2014\u540c\u8cea\u6027\u6aa2\u5b9a(Categorical Data Analysis \u2013 Test of Homoge…<\/p>\n","protected":false},"author":50,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[111,230,229],"tags":[10369,10375,10419,10373,10420,10418,10374,10368],"class_list":["post-73318","post","type-post","status-publish","format-standard","hentry","category-mathematics00","category-math06-01","category-math06","tag-categorical-data-analysis","tag-chi-square-test","tag-chi-square-test-of-homogeneity","tag-r-x-c-contingency-table","tag-r-x-c","tag-10418","tag-10374","tag-10368","loop-entry","cat-111","cat-230","cat-229","no-thumbnail"],"views":8386,"_links":{"self":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/73318","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/users\/50"}],"replies":[{"embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/comments?post=73318"}],"version-history":[{"count":1,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/73318\/revisions"}],"predecessor-version":[{"id":86029,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/73318\/revisions\/86029"}],"wp:attachment":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/media?parent=73318"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/categories?post=73318"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/tags?post=73318"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}