{"id":3507,"date":"2020-04-07T22:34:18","date_gmt":"2020-04-07T20:34:18","guid":{"rendered":"https:\/\/myoceane.fr\/?p=3507"},"modified":"2020-04-12T15:59:13","modified_gmt":"2020-04-12T13:59:13","slug":"fisher-exact-test","status":"publish","type":"post","link":"https:\/\/myoceane.fr\/index.php\/fisher-exact-test\/","title":{"rendered":"[\u7d71\u8a08] Fisher Exact Test"},"content":{"rendered":"
<\/div>\n\n

Fisher Exact Test \u662f\u4e00\u500b\u6aa2\u9a57\u5169\u500b\u8b8a\u6578\u662f\u5426\u76f8\u95dc\u7684\u65b9\u6cd5\uff1f\u5728\u57fa\u56e0\u5927\u6578\u64da\u7684\u9818\u57df\u88e1\u9762\u7b97\u662f\u5f88\u5e38\u898b\u7684\u65b9\u6cd5\u4e4b\u4e00\uff0c\u8a73\u7d30\u53ef\u4ee5\u53c3\u8003\u9023\u7d50<\/a>\uff0c\u7531\u65bc\u5728\u7814\u8b80 Fisher Exact Test \u7684\u6642\u5019\uff0c\u6211\u5011\u767c\u73fe\u5927\u90e8\u5206\u7db2\u8def\u4e0a\u53ef\u4ee5\u627e\u5230\u7684\u8a0a\u606f\u4f8b\u5982\u9023\u7d50\u4e00<\/a>\uff0c\u9023\u7d50\u4e8c<\/a>\u90fd\u53ea\u6709\u76f4\u63a5\u5c55\u793a\u8a08\u7b97\u7684\u7d50\u679c\u4f46\u662f\u6c92\u6709\u63a8\u5c0e\u6240\u4ee5\u6211\u5011\u5f88\u96e3\u771f\u6b63\u7406\u89e3\u9019\u4e9b\u6578\u5b78\u5f0f\u80cc\u5f8c\u7684\u610f\u7fa9\uff0c\u672c\u7bc7\u7684\u63a8\u5c0e\u53c3\u8003 Michael J. Evans and Jeffrey S.Rosenthal \u8457\u4f5c\u7684 Probability and Statistic, The Science of Uncertainty<\/a> \u4e00\u66f8\u3002<\/p>\n\n\n\n

\u4f7f\u7528 Fisher Exact Test \u7684\u65b9\u6cd5<\/h5>\n\n\n\n\n\u4ee5\u4e0b\u6211\u5011\u5c55\u793a Fisher Exact Test \u662f\u600e\u9ebc\u9a57\u8b49\u5169\u500b\u96a8\u6a5f\u8b8a\u6578 \"A\", \"B\" \u4e4b\u9593\u662f\u5426\u6709\u95dc\u806f\u6027\u7684\uff1f\u5047\u8a2d \"A\" \u8207 \"B\" \u5404\u6709 \"[1,\cdots,M]\" \u8207 \"[1,\cdots,K]\" \u500b\u96e2\u6563\u72c0\u614b\uff0c\u800c\u4e14\u5047\u8a2d \"A,B\" \u7684\u6a5f\u7387\u5206\u4f48\u70ba Multinominal \u5206\u4f48\uff1a\n

(1) <\/span>   <\/span>\"\begin{align*}<\/p>\n

(2) <\/span>   <\/span>\"\begin{equation*}<\/p>\nFisher Exact Test \u7684 null hypothesis \u5047\u5b9a \"A,B\" \u70ba\u7368\u7acb\u7684\u96a8\u6a5f\u8b8a\u6578\uff0c\u5728\u6b64\u5047\u8a2d\u4e0b\n

(3) <\/span>   <\/span>\"\begin{align*}<\/p>\n\u7576\u53d6\u6a23\u6a23\u672c\u6578\u70ba \"n\"\uff0c\u4e14 \"X_{mk}\" \u4ee3\u8868\u6a23\u672c\u70ba \"a_i=m,b_i=k\" \u7684\u500b\u6578\uff0c\u5247 \n

(4) <\/span>   <\/span>\"\begin{align*}<\/p>\n\u6b64\u6642\u6839\u64da\u7368\u7acb\u6027\u7684\u5047\u8a2d\u6211\u5011\u5f97\u5230 Likelihood \u51fd\u5f0f\u70ba\n

(5) <\/span>   <\/span>\"\begin{align*}<\/p>\n\u5728\u6b64\u70ba\u4e86\u65b9\u4fbf\u8d77\u898b\u6211\u5011\u5229\u7528 \"X_{m\cdot}=\sum^{K}_{k=1}X_{mk}, X_{\cdot k}=\sum^{M}_{m=1}X_{mk}\" \u7c21\u5316\u6578\u5b78\u5f0f\uff0c\u4e26\u4e14\u5c07 \"\alpha_M, \beta_K\" \u53d6\u4ee3\u3002\n\u6700\u5927\u5316 Likelihood \u51fd\u5f0f\u7684\u8a71\u6211\u5011\u53ef\u4ee5\u5c0d\u6240\u6709 \"\alpha_m,\beta_k\" \u505a\u504f\u5fae\u5206\uff1a\n

(6) <\/span>   <\/span>\"\begin{align*}<\/p>\n\u5f97\u5230\u4ee5\u4e0b \"M-1\" \u500b\u806f\u7acb\u65b9\u7a0b\u5f0f\n

(7) <\/span>   <\/span>\"\begin{align*}<\/p>\n\u6c42\u89e3\u53ef\u4ee5\u5f97\u5230\n

(8) <\/span>   <\/span>\"\begin{align*}<\/p>\n\u4ee5\u4e0a\u6211\u5011\u8b49\u660e \"X_{m\cdot}, X_{\cdot k}\" \u662f minimal sufficient statistic (\u6700\u5c0f\u5145\u5206\u7d71\u8a08\u91cf)\u3002\n\n\n\n

\u00a0<\/p>\n

Fisher Exact Test \u5047\u8a2d\u6aa2\u5b9a\u7684\u7cbe\u795e\u662f\u89c0\u5bdf\u53d6\u6a23\u7684 P value \u662f\u5426\u8db3\u5920\u4f4e\uff0c\u8db3\u5920\u53bb\u63a8\u7ffb\u6211\u5011\u505a\u7684\u7368\u7acb\u6027\u5047\u8a2d\uff0c<\/p>\n\n\n\n\u5728\u4e00\u500b \"2\times 2\" contingency table \u88e1\u9762\uff0c\u5047\u8a2d\u662f\u7368\u7acb\u767c\u751f\u7684\uff0c\u5247\u6bcf\u4e00\u500b\u53ef\u80fd\u6027\u6a5f\u7387\u4e00\u6a23\uff0c\u90a3\u9ebc \"X_{11}, X_{12}, X_{21}, X_{22}\" \u767c\u751f\u7684\u6a5f\u7387\u5247\u70ba\uff1a\n

(9) <\/span>   <\/span>\"\begin{equation*}<\/p>\n\n\u63a8\u5ee3\u5230\u4e00\u822c\u60c5\u6cc1 \"P\" \u503c\u7531\u4ee5\u4e0b\u65b9\u5f0f\u8a08\u7b97\uff1a\n

(10) <\/span>   <\/span>\"\begin{align*}<\/p>\n\n\n\n

\u8981\u5224\u65b7 P \u503c\u662f\u5426\u5c0f\u65bc\u4e00\u500b\u95be\u503c\u9084\u9700\u8981\u628a\u6240\u6709\u5c0f\u65bc\u9019\u500b P \u503c\u7684\u6240\u6709\u60c5\u6cc1\u52a0\u7e3d\u8d77\u4f86\uff0c\u5728 2×2 \u4ee5\u5916\u7684\u60c5\u6cc1\u6bd4\u8f03\u96e3\u505a\u8a08\u7b97\uff0c\u56e0\u70ba\u5f88\u96e3\u7aae\u8209\uff0c\u9023\u7d50\u6587\u7ae0<\/a>\u5728\u4ecb\u7d39\u9019\u500b\u505a\u6cd5\uff01<\/p>\n","protected":false},"excerpt":{"rendered":"

Fisher Exact Test \u662f\u4e00\u500b\u6aa2\u9a57\u5169\u500b\u8b8a\u6578\u662f\u5426\u76f8\u95dc\u7684\u65b9\u6cd5\uff1f\u5728\u57fa\u56e0\u5927\u6578\u64da\u7684\u9818\u57df\u88e1\u9762\u7b97\u662f\u5f88\u5e38\u898b\u7684\u65b9\u6cd5\u4e4b\u4e00\uff0c\u8a73\u7d30\u53ef\u4ee5\u53c3\u8003\u9023\u7d50\uff0c\u7531\u65bc\u5728\u7814\u8b80 Fisher Exact Test \u7684\u6642\u5019\uff0c\u6211\u5011\u767c\u73fe\u5927\u90e8\u5206\u7db2\u8def\u4e0a\u53ef\u4ee5\u627e\u5230\u7684\u8a0a\u606f\u4f8b\u5982\u9023\u7d50\u4e00\uff0c\u9023\u7d50\u4e8c\u90fd\u53ea\u6709\u76f4\u63a5\u5c55\u793a\u8a08\u7b97\u7684\u7d50\u679c\u4f46\u662f\u6c92\u6709\u63a8\u5c0e\u6240\u4ee5\u6211\u5011\u5f88\u96e3\u771f\u6b63\u7406\u89e3\u9019\u4e9b\u6578\u5b78\u5f0f\u80cc\u5f8c\u7684\u610f\u7fa9\uff0c\u672c\u7bc7\u7684\u63a8\u5c0e\u53c3\u8003\u00a0Michael J. Evans and Jeffrey S.Rosenthal \u8457\u4f5c\u7684\u00a0Probability and Statistic, The Science of Uncertainty \u4e00\u66f8\u3002<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[14,158],"tags":[171,172],"class_list":["post-3507","post","type-post","status-publish","format-standard","hentry","category-it-technology","category-probability-and-statistics","tag-fisher-exact-test","tag-p-value"],"yoast_head":"\n[\u7d71\u8a08] Fisher Exact Test - \u60f3\u65b9\u6d89\u6cd5 - \u91cf\u74f6\u5916\u7684\u5929\u7a7a M-Y-Oceane<\/title>\n<meta name=\"description\" content=\"Fisher Exact Test \u662f\u4e00\u500b\u6aa2\u9a57\u5169\u500b\u8b8a\u6578\u662f\u5426\u76f8\u95dc\u7684\u65b9\u6cd5\uff1f\u5728\u57fa\u56e0\u5927\u6578\u64da\u7684\u9818\u57df\u88e1\u9762\u7b97\u662f\u5f88\u5e38\u898b\u7684\u65b9\u6cd5\u4e4b\u4e00\uff0c\u8a73\u7d30\u53ef\u4ee5\u53c3\u8003\u9023\u7d50\uff0c\u7531\u65bc\u5728\u7814\u8b80 Fisher Exact Test \u7684\u6642\u5019\uff0c\u6211\u5011\u767c\u73fe\u5927\u90e8\u5206\u7db2\u8def\u4e0a\u53ef\u4ee5\u627e\u5230\u7684\u8a0a\u606f\u4f8b\u5982\u9023\u7d50\u4e00\uff0c\u9023\u7d50\u4e8c\u90fd\u53ea\u6709\u76f4\u63a5\u5c55\u793a\u8a08\u7b97\u7684\u7d50\u679c\u4f46\u662f\u6c92\u6709\u63a8\u5c0e\u6240\u4ee5\u6211\u5011\u5f88\u96e3\u771f\u6b63\u7406\u89e3\u9019\u4e9b\u6578\u5b78\u5f0f\u80cc\u5f8c\u7684\u610f\u7fa9\uff0c\u672c\u7bc7\u7684\u63a8\u5c0e\u53c3\u8003\u00a0Michael J. 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