{"id":29176,"date":"2023-08-28T08:29:01","date_gmt":"2023-08-28T11:29:01","guid":{"rendered":"https:\/\/mindthegraph.com\/blog\/hypothesis-testing-copy\/"},"modified":"2024-12-05T15:51:53","modified_gmt":"2024-12-05T18:51:53","slug":"one-way-anova","status":"publish","type":"post","link":"https:\/\/mindthegraph.com\/blog\/zh\/%e5%8d%95%e5%90%91-%e5%a4%9a%e5%8f%98%e9%87%8f\/","title":{"rendered":"\u5355\u56e0\u5b50\u65b9\u5dee\u5206\u6790\uff1a\u7406\u89e3\u3001\u5b9e\u65bd\u548c\u6f14\u793a"},"content":{"rendered":"<p>\u65b9\u5dee\u5206\u6790 (ANOVA) \u662f\u4e00\u79cd\u7edf\u8ba1\u65b9\u6cd5\uff0c\u7528\u4e8e\u6bd4\u8f83\u4e24\u4e2a\u6216\u591a\u4e2a\u7ec4\u4e4b\u95f4\u7684\u5e73\u5747\u503c\u3002\u7279\u522b\u662f\u5355\u56e0\u5b50\u65b9\u5dee\u5206\u6790\uff0c\u662f\u4e00\u79cd\u5e38\u7528\u7684\u6280\u672f\uff0c\u7528\u4e8e\u5206\u6790\u4e24\u4e2a\u6216\u591a\u4e2a\u5206\u7c7b\u7ec4\u4e4b\u95f4\u5355\u4e00\u8fde\u7eed\u53d8\u91cf\u7684\u65b9\u5dee\u3002\u8be5\u6280\u672f\u5e7f\u6cdb\u5e94\u7528\u4e8e\u5546\u4e1a\u3001\u793e\u4f1a\u79d1\u5b66\u548c\u81ea\u7136\u79d1\u5b66\u7b49\u5404\u4e2a\u9886\u57df\uff0c\u7528\u4e8e\u68c0\u9a8c\u5047\u8bbe\u5e76\u5f97\u51fa\u7ec4\u95f4\u5dee\u5f02\u7684\u7ed3\u8bba\u3002\u4e86\u89e3\u5355\u56e0\u5b50\u65b9\u5dee\u5206\u6790\u7684\u57fa\u672c\u539f\u7406\u6709\u52a9\u4e8e\u7814\u7a76\u4eba\u5458\u548c\u6570\u636e\u5206\u6790\u5e08\u6839\u636e\u7edf\u8ba1\u8bc1\u636e\u505a\u51fa\u660e\u667a\u7684\u51b3\u7b56\u3002\u672c\u6587\u5c06\u8be6\u7ec6\u89e3\u91ca\u5355\u56e0\u7d20\u65b9\u5dee\u5206\u6790\u6280\u672f\uff0c\u5e76\u8ba8\u8bba\u5176\u5e94\u7528\u3001\u5047\u8bbe\u7b49\u3002<\/p>\n\n\n\n<h2 id=\"h-what-is-one-way-anova\"><strong>\u4ec0\u4e48\u662f\u5355\u56e0\u5b50\u65b9\u5dee\u5206\u6790\uff1f<\/strong><\/h2>\n\n\n\n<p>\u5355\u56e0\u5b50\u65b9\u5dee\u5206\u6790\uff08\u65b9\u5dee\u5206\u6790\uff09\u662f\u4e00\u79cd\u7edf\u8ba1\u65b9\u6cd5\uff0c\u7528\u4e8e\u68c0\u9a8c\u5404\u7ec4\u6570\u636e\u7684\u5747\u503c\u4e4b\u95f4\u662f\u5426\u5b58\u5728\u663e\u8457\u5dee\u5f02\u3002\u5b83\u901a\u5e38\u7528\u4e8e\u5b9e\u9a8c\u7814\u7a76\uff0c\u4ee5\u6bd4\u8f83\u4e0d\u540c\u6cbb\u7597\u6216\u5e72\u9884\u63aa\u65bd\u5bf9\u7279\u5b9a\u7ed3\u679c\u7684\u5f71\u54cd\u3002<\/p>\n\n\n\n<p>\u65b9\u5dee\u5206\u6790\u7684\u57fa\u672c\u601d\u60f3\u662f\u5c06\u6570\u636e\u7684\u603b\u53d8\u5f02\u6027\u5206\u4e3a\u4e24\u90e8\u5206\uff1a\u7ec4\u95f4\u53d8\u5f02\uff08\u7531\u4e8e\u5904\u7406\uff09\u548c\u7ec4\u5185\u53d8\u5f02\uff08\u7531\u4e8e\u968f\u673a\u53d8\u5f02\u548c\u4e2a\u4f53\u5dee\u5f02\uff09\u3002\u65b9\u5dee\u5206\u6790\u68c0\u9a8c\u8ba1\u7b97 F \u7edf\u8ba1\u91cf\uff0c\u5373\u7ec4\u95f4\u53d8\u5f02\u4e0e\u7ec4\u5185\u53d8\u5f02\u4e4b\u6bd4\u3002<\/p>\n\n\n\n<p>\u5982\u679c F \u7edf\u8ba1\u91cf\u8db3\u591f\u5927\uff0c\u4e14\u76f8\u5173\u7684 p \u503c\u4f4e\u4e8e\u9884\u5b9a\u7684\u663e\u8457\u6027\u6c34\u5e73\uff08\u5982 0.05\uff09\uff0c\u5219\u8868\u660e\u6709\u786e\u51ff\u8bc1\u636e\u8868\u660e\u81f3\u5c11\u6709\u4e00\u4e2a\u7ec4\u7684\u5e73\u5747\u503c\u4e0e\u5176\u4ed6\u7ec4\u6709\u663e\u8457\u5dee\u5f02\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u53ef\u4ee5\u4f7f\u7528\u8fdb\u4e00\u6b65\u7684\u4e8b\u540e\u68c0\u9a8c\u6765\u786e\u5b9a\u54ea\u4e9b\u7279\u5b9a\u7ec4\u4e4b\u95f4\u5b58\u5728\u5dee\u5f02\u3002\u60a8\u53ef\u4ee5\u5728\u6211\u4eec\u7684 \"Post hoc \"\u5185\u5bb9\u4e2d\u4e86\u89e3\u66f4\u591a\u76f8\u5173\u4fe1\u606f\u3002<a href=\"https:\/\/mindthegraph.com\/blog\/post-hoc-analysis\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u4e8b\u540e\u5206\u6790\u3002\u6d4b\u8bd5\u7684\u8fc7\u7a0b\u548c\u7c7b\u578b<\/a>&#8220;.<\/p>\n\n\n\n<p>\u5355\u56e0\u5b50\u65b9\u5dee\u5206\u6790\u5047\u5b9a\u6570\u636e\u5448\u6b63\u6001\u5206\u5e03\uff0c\u4e14\u5404\u7ec4\u65b9\u5dee\u76f8\u7b49\u3002\u5982\u679c\u4e0d\u7b26\u5408\u8fd9\u4e9b\u5047\u8bbe\uff0c\u5219\u53ef\u4ee5\u4f7f\u7528\u5176\u4ed6\u975e\u53c2\u6570\u68c0\u9a8c\u6765\u4ee3\u66ff\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/researcher.life\/all-access-pricing?utm_source=mtg&amp;utm_campaign=all-access-promotion&amp;utm_medium=blog\"><img decoding=\"async\" loading=\"lazy\" width=\"1024\" height=\"410\" src=\"https:\/\/mindthegraph.com\/blog\/wp-content\/uploads\/2024\/08\/Banner3-1024x410.png\" alt=\"\" class=\"wp-image-55425\" srcset=\"https:\/\/mindthegraph.com\/blog\/wp-content\/uploads\/2024\/08\/Banner3-1024x410.png 1024w, https:\/\/mindthegraph.com\/blog\/wp-content\/uploads\/2024\/08\/Banner3-300x120.png 300w, https:\/\/mindthegraph.com\/blog\/wp-content\/uploads\/2024\/08\/Banner3-768x307.png 768w, https:\/\/mindthegraph.com\/blog\/wp-content\/uploads\/2024\/08\/Banner3-1536x615.png 1536w, https:\/\/mindthegraph.com\/blog\/wp-content\/uploads\/2024\/08\/Banner3-2048x820.png 2048w, https:\/\/mindthegraph.com\/blog\/wp-content\/uploads\/2024\/08\/Banner3-18x7.png 18w, https:\/\/mindthegraph.com\/blog\/wp-content\/uploads\/2024\/08\/Banner3-100x40.png 100w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/a><\/figure>\n\n\n\n<h2 id=\"h-how-is-one-way-anova-used\"><strong>\u5982\u4f55\u4f7f\u7528\u5355\u56e0\u5b50\u65b9\u5dee\u5206\u6790\uff1f<\/strong><\/h2>\n\n\n\n<p>\u5355\u56e0\u5b50\u65b9\u5dee\u5206\u6790\u662f\u4e00\u79cd\u7edf\u8ba1\u68c0\u9a8c\uff0c\u7528\u4e8e\u786e\u5b9a\u4e24\u4e2a\u6216\u591a\u4e2a\u72ec\u7acb\u7ec4\u7684\u5747\u503c\u4e4b\u95f4\u662f\u5426\u5b58\u5728\u663e\u8457\u5dee\u5f02\u3002\u5b83\u7528\u4e8e\u68c0\u9a8c \"\u6240\u6709\u7ec4\u7684\u5747\u503c\u76f8\u7b49 \"\u7684\u96f6\u5047\u8bbe\u548c \"\u81f3\u5c11\u6709\u4e00\u4e2a\u5747\u503c\u4e0e\u5176\u4ed6\u7ec4\u4e0d\u540c \"\u7684\u5907\u62e9\u5047\u8bbe\u3002<\/p>\n\n\n\n<h2 id=\"h-assumptions-of-anova\"><strong>\u65b9\u5dee\u5206\u6790\u7684\u5047\u8bbe<\/strong><\/h2>\n\n\n\n<p>\u65b9\u5dee\u5206\u6790\u5fc5\u987b\u6ee1\u8db3\u51e0\u4e2a\u5047\u8bbe\uff0c\u624d\u80fd\u4f7f\u7ed3\u679c\u6709\u6548\u53ef\u9760\u3002\u8fd9\u4e9b\u5047\u8bbe\u5982\u4e0b\uff1a<\/p>\n\n\n\n<ul>\n<li><strong>\u6b63\u5e38\uff1a<\/strong> \u56e0\u53d8\u91cf\u5728\u5404\u7ec4\u5185\u5e94\u5448\u6b63\u6001\u5206\u5e03\u3002\u53ef\u4ee5\u4f7f\u7528\u76f4\u65b9\u56fe\u3001\u6b63\u6001\u6982\u7387\u56fe\u6216\u7edf\u8ba1\u68c0\u9a8c\uff08\u5982 Shapiro-Wilk \u68c0\u9a8c\uff09\u6765\u68c0\u67e5\u8fd9\u4e00\u70b9\u3002<\/li>\n\n\n\n<li><strong>\u65b9\u5dee\u540c\u8d28\u6027\uff1a <\/strong>\u5404\u7ec4\u56e0\u53d8\u91cf\u7684\u65b9\u5dee\u5e94\u5927\u81f4\u76f8\u7b49\u3002\u8fd9\u53ef\u4ee5\u901a\u8fc7\u7edf\u8ba1\u68c0\u9a8c\uff08\u5982 Levene \u68c0\u9a8c\u6216 Bartlett \u68c0\u9a8c\uff09\u6765\u68c0\u67e5\u3002<\/li>\n\n\n\n<li><strong>\u72ec\u7acb\uff1a <\/strong>\u6bcf\u7ec4\u4e2d\u7684\u89c2\u6d4b\u503c\u5e94\u76f8\u4e92\u72ec\u7acb\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u4e00\u7ec4\u4e2d\u7684\u6570\u503c\u4e0d\u5e94\u4e0e\u5176\u4ed6\u7ec4\u4e2d\u7684\u6570\u503c\u76f8\u5173\uff0c\u4e5f\u4e0d\u5e94\u4f9d\u8d56\u4e8e\u5176\u4ed6\u7ec4\u4e2d\u7684\u6570\u503c\u3002<\/li>\n\n\n\n<li><strong>\u968f\u673a\u62bd\u6837\uff1a<\/strong> \u8fd9\u4e9b\u5c0f\u7ec4\u5e94\u901a\u8fc7\u968f\u673a\u62bd\u6837\u8fc7\u7a0b\u7ec4\u6210\u3002\u8fd9\u6837\u624d\u80fd\u786e\u4fdd\u7ed3\u679c\u53ef\u4ee5\u63a8\u5e7f\u5230\u66f4\u5927\u8303\u56f4\u7684\u4eba\u7fa4\u4e2d\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u5728\u8fdb\u884c\u65b9\u5dee\u5206\u6790\u4e4b\u524d\uff0c\u5fc5\u987b\u68c0\u67e5\u8fd9\u4e9b\u5047\u8bbe\uff0c\u56e0\u4e3a\u8fdd\u53cd\u8fd9\u4e9b\u5047\u8bbe\u53ef\u80fd\u5bfc\u81f4\u4e0d\u51c6\u786e\u7684\u7ed3\u679c\u548c\u4e0d\u6b63\u786e\u7684\u7ed3\u8bba\u3002\u5982\u679c\u8fdd\u53cd\u4e86\u4e00\u4e2a\u6216\u591a\u4e2a\u5047\u8bbe\uff0c\u53ef\u4ee5\u4f7f\u7528\u975e\u53c2\u6570\u68c0\u9a8c\u7b49\u5176\u4ed6\u68c0\u9a8c\u65b9\u6cd5\u6765\u4ee3\u66ff\u3002<\/p>\n\n\n\n<h2 id=\"h-performing-a-one-way-anova\"><strong>\u8fdb\u884c\u5355\u56e0\u5b50\u65b9\u5dee\u5206\u6790<\/strong><\/h2>\n\n\n\n<p>\u8981\u8fdb\u884c\u5355\u56e0\u7d20\u65b9\u5dee\u5206\u6790\uff0c\u53ef\u4ee5\u6309\u7167\u4ee5\u4e0b\u6b65\u9aa4\u64cd\u4f5c\uff1a<\/p>\n\n\n\n<p><strong>\u6b65\u9aa4 1\uff1a<\/strong> \u63d0\u51fa\u5047\u8bbe<\/p>\n\n\n\n<p>\u5b9a\u4e49\u96f6\u5047\u8bbe\u548c\u5907\u62e9\u5047\u8bbe\u3002\u96f6\u5047\u8bbe\u662f\u6307\u5404\u7ec4\u5e73\u5747\u503c\u4e4b\u95f4\u6ca1\u6709\u663e\u8457\u5dee\u5f02\u3002\u5907\u62e9\u5047\u8bbe\u662f\u81f3\u5c11\u6709\u4e00\u4e2a\u7ec4\u7684\u5e73\u5747\u503c\u4e0e\u5176\u4ed6\u7ec4\u6709\u663e\u8457\u5dee\u5f02\u3002<\/p>\n\n\n\n<p><strong>\u6b65\u9aa4 2\uff1a<\/strong> \u6536\u96c6\u6570\u636e<\/p>\n\n\n\n<p>\u6536\u96c6\u8981\u6bd4\u8f83\u7684\u5404\u7ec4\u6570\u636e\u3002\u6bcf\u4e2a\u7ec4\u90fd\u5e94\u8be5\u662f\u72ec\u7acb\u7684\uff0c\u5e76\u4e14\u6837\u672c\u91cf\u76f8\u4f3c\u3002<\/p>\n\n\n\n<p><strong>\u6b65\u9aa4 3\uff1a<\/strong> \u8ba1\u7b97\u5404\u7ec4\u7684\u5e73\u5747\u6570\u548c\u65b9\u5dee<\/p>\n\n\n\n<p>\u5229\u7528\u6536\u96c6\u5230\u7684\u6570\u636e\u8ba1\u7b97\u5404\u7ec4\u7684\u5e73\u5747\u503c\u548c\u65b9\u5dee\u3002<\/p>\n\n\n\n<p><strong>\u7b2c4\u6b65\u3002<\/strong> \u8ba1\u7b97\u603b\u4f53\u5747\u503c\u548c\u65b9\u5dee<\/p>\n\n\n\n<p>\u53d6\u5404\u7ec4\u5e73\u5747\u503c\u548c\u65b9\u5dee\u7684\u5e73\u5747\u503c\uff0c\u8ba1\u7b97\u603b\u5e73\u5747\u503c\u548c\u65b9\u5dee\u3002<\/p>\n\n\n\n<p><strong>\u6b65\u9aa4 5\uff1a<\/strong> \u8ba1\u7b97\u7ec4\u95f4\u5e73\u65b9\u548c (SSB)<\/p>\n\n\n\n<p>\u7528\u516c\u5f0f\u8ba1\u7b97\u7ec4\u95f4\u5e73\u65b9\u548c\uff08SSB\uff09\uff1a<\/p>\n\n\n\n<p>SSB = \u03a3ni (x\u0304i - x\u0304)^2<\/p>\n\n\n\n<p>\u5176\u4e2d\uff0cni \u662f\u7b2c i \u7ec4\u7684\u6837\u672c\u91cf\uff0cx\u0304i \u662f\u7b2c i \u7ec4\u7684\u5e73\u5747\u6570\uff0cx\u0304 \u662f\u603b\u4f53\u5e73\u5747\u6570\u3002<\/p>\n\n\n\n<p><strong>\u6b65\u9aa4 6\uff1a<\/strong> \u8ba1\u7b97\u7ec4\u5185\u5e73\u65b9\u548c (SSW)<\/p>\n\n\n\n<p>\u7528\u516c\u5f0f\u8ba1\u7b97\u7ec4\u5185\u5e73\u65b9\u548c\uff08SSW\uff09\uff1a<\/p>\n\n\n\n<p>SSW = \u03a3\u03a3(xi - x\u0304i)^2<\/p>\n\n\n\n<p>\u5176\u4e2d\uff0cxi \u662f\u7b2c j \u7ec4\u4e2d\u7684\u7b2c i \u4e2a\u89c2\u6d4b\u503c\uff0cx\u0304i \u662f\u7b2c j \u7ec4\u7684\u5e73\u5747\u503c\uff0cj \u4ecb\u4e8e 1 \u5230 k \u7ec4\u4e4b\u95f4\u3002<\/p>\n\n\n\n<p><strong>\u6b65\u9aa4 7\uff1a <\/strong>\u8ba1\u7b97 F \u7edf\u8ba1\u91cf<\/p>\n\n\n\n<p>\u7528\u7ec4\u95f4\u65b9\u5dee\uff08SSB\uff09\u9664\u4ee5\u7ec4\u5185\u65b9\u5dee\uff08SSW\uff09\uff0c\u8ba1\u7b97 F \u7edf\u8ba1\u91cf\uff1a<\/p>\n\n\n\n<p>F = (SSB \/ (k - 1)) \/ (SSW \/ (n - k))<\/p>\n\n\n\n<p>\u5176\u4e2d\uff0ck \u4e3a\u7ec4\u6570\uff0cn \u4e3a\u6837\u672c\u603b\u91cf\u3002<\/p>\n\n\n\n<p><strong>\u6b65\u9aa4 8\uff1a<\/strong> \u786e\u5b9a F \u4e34\u754c\u503c\u548c p \u503c<\/p>\n\n\n\n<p>\u6839\u636e\u6240\u9700\u7684\u663e\u8457\u6027\u6c34\u5e73\u548c\u81ea\u7531\u5ea6\uff0c\u786e\u5b9a F \u7684\u4e34\u754c\u503c\u548c\u76f8\u5e94\u7684 p \u503c\u3002<\/p>\n\n\n\n<p><strong>\u6b65\u9aa4 9\uff1a<\/strong> \u5c06\u8ba1\u7b97\u51fa\u7684 F \u7edf\u8ba1\u91cf\u4e0e F \u4e34\u754c\u503c\u8fdb\u884c\u6bd4\u8f83<\/p>\n\n\n\n<p>\u5982\u679c\u8ba1\u7b97\u51fa\u7684 F \u7edf\u8ba1\u91cf\u5927\u4e8e F \u4e34\u754c\u503c\uff0c\u5219\u62d2\u7edd\u96f6\u5047\u8bbe\uff0c\u5e76\u5f97\u51fa\u81f3\u5c11\u4e24\u7ec4\u5747\u503c\u4e4b\u95f4\u5b58\u5728\u663e\u8457\u5dee\u5f02\u7684\u7ed3\u8bba\u3002\u5982\u679c\u8ba1\u7b97\u51fa\u7684 F \u7edf\u8ba1\u91cf\u5c0f\u4e8e\u6216\u7b49\u4e8e F \u7684\u4e34\u754c\u503c\uff0c\u5219\u4e0d\u80fd\u62d2\u7edd\u96f6\u5047\u8bbe\uff0c\u5e76\u5f97\u51fa\u7ed3\u8bba\u8ba4\u4e3a\u5404\u7ec4\u4e4b\u95f4\u7684\u5747\u503c\u6ca1\u6709\u663e\u8457\u5dee\u5f02\u3002<\/p>\n\n\n\n<p><strong>\u6b65\u9aa4 10\uff1a<\/strong> \u4e8b\u540e\u5206\u6790\uff08\u5982\u6709\u5fc5\u8981\uff09<\/p>\n\n\n\n<p>\u5982\u679c\u62d2\u7edd\u4e86\u96f6\u5047\u8bbe\uff0c\u5219\u8fdb\u884c\u4e8b\u540e\u5206\u6790\uff0c\u4ee5\u786e\u5b9a\u54ea\u4e9b\u7ec4\u522b\u4e4b\u95f4\u5b58\u5728\u663e\u8457\u5dee\u5f02\u3002\u5e38\u89c1\u7684\u4e8b\u540e\u68c0\u9a8c\u5305\u62ec Tukey's HSD \u68c0\u9a8c\u3001Bonferroni \u6821\u6b63\u548c Scheffe \u68c0\u9a8c\u3002<\/p>\n\n\n\n<h2 id=\"h-interpreting-the-results\"><strong>\u89e3\u8bfb\u7ed3\u679c<\/strong><\/h2>\n\n\n\n<p>\u5728\u8fdb\u884c\u5355\u56e0\u7d20\u65b9\u5dee\u5206\u6790\u540e\uff0c\u7ed3\u679c\u53ef\u89e3\u91ca\u5982\u4e0b\uff1a<\/p>\n\n\n\n<p><strong>F \u7edf\u8ba1\u91cf\u548c p \u503c\uff1a <\/strong>F \u7edf\u8ba1\u91cf\u8861\u91cf\u7ec4\u95f4\u65b9\u5dee\u4e0e\u7ec4\u5185\u65b9\u5dee\u4e4b\u6bd4\u3002p \u503c\u8868\u793a\u5728\u96f6\u5047\u8bbe\u6210\u7acb\u7684\u60c5\u51b5\u4e0b\uff0c\u83b7\u5f97\u4e0e\u89c2\u5bdf\u5230\u7684 F \u7edf\u8ba1\u91cf\u4e00\u6837\u6781\u7aef\u7684 F \u7edf\u8ba1\u91cf\u7684\u6982\u7387\u3002\u5c0f\u7684 p \u503c\uff08\u5c0f\u4e8e\u6240\u9009\u7684\u663e\u8457\u6027\u6c34\u5e73\uff0c\u901a\u5e38\u4e3a 0.05\uff09\u8868\u660e\u53cd\u5bf9\u96f6\u5047\u8bbe\u7684\u8bc1\u636e\u786e\u51ff\uff0c\u8868\u660e\u81f3\u5c11\u4e24\u7ec4\u7684\u5747\u503c\u4e4b\u95f4\u5b58\u5728\u663e\u8457\u5dee\u5f02\u3002<\/p>\n\n\n\n<p><strong>\u81ea\u7531\u5ea6 <\/strong>\u7ec4\u95f4\u56e0\u5b50\u548c\u7ec4\u5185\u56e0\u5b50\u7684\u81ea\u7531\u5ea6\u5206\u522b\u4e3a k-1 \u548c N-k\uff0c\u5176\u4e2d k \u4e3a\u7ec4\u6570\uff0cN \u4e3a\u6837\u672c\u603b\u91cf\u3002<\/p>\n\n\n\n<p><strong>\u5747\u65b9\u8bef\u5dee\uff1a<\/strong><em> <\/em>\u5747\u65b9\u8bef\u5dee\uff08MSE\uff09\u662f\u7ec4\u5185\u5e73\u65b9\u548c\u4e0e\u7ec4\u5185\u81ea\u7531\u5ea6\u4e4b\u6bd4\u3002\u8fd9\u8868\u793a\u5728\u8003\u8651\u7ec4\u95f4\u5dee\u5f02\u540e\uff0c\u5404\u7ec4\u5185\u7684\u4f30\u8ba1\u65b9\u5dee\u3002<\/p>\n\n\n\n<p><strong>\u6548\u679c\u5927\u5c0f\u3002<\/strong> \u6548\u5e94\u5927\u5c0f\u53ef\u4ee5\u7528\u7b49\u65b9\u503c (\u03b7\u00b2)\u6765\u8861\u91cf\uff0c\u7b49\u65b9\u503c\u8868\u793a\u56e0\u53d8\u91cf\u603b\u53d8\u5f02\u4e2d\u7531\u7ec4\u95f4\u5dee\u5f02\u5f15\u8d77\u7684\u53d8\u5f02\u6240\u5360\u7684\u6bd4\u4f8b\u3002\u7b49\u65b9\u503c\u7684\u5e38\u89c1\u89e3\u91ca\u5982\u4e0b<\/p>\n\n\n\n<p>\u5c0f\u5f71\u54cd\uff1a\u03b7\u00b2 &lt; 0.01<\/p>\n\n\n\n<p>\u4e2d\u7b49\u6548\u5e94\uff1a0.01 \u2264 \u03b7\u00b2 &lt; 0.06<\/p>\n\n\n\n<p>\u5927\u6548\u5e94\uff1a\u03b7\u00b2 \u2265 0.06<\/p>\n\n\n\n<p><a href=\"https:\/\/mindthegraph.com\/blog\/post-hoc-analysis\/\"><strong>\u4e8b\u540e\u5206\u6790\uff1a<\/strong><\/a> \u5982\u679c\u5426\u5b9a\u4e86\u96f6\u5047\u8bbe\uff0c\u5219\u53ef\u4ee5\u8fdb\u884c\u4e8b\u540e\u5206\u6790\uff0c\u4ee5\u786e\u5b9a\u54ea\u4e9b\u7ec4\u4e4b\u95f4\u5b58\u5728\u663e\u8457\u5dee\u5f02\u3002\u8fd9\u53ef\u4ee5\u901a\u8fc7\u5404\u79cd\u68c0\u9a8c\u6765\u5b8c\u6210\uff0c\u5982 Tukey's HSD \u68c0\u9a8c\u3001Bonferroni \u6821\u6b63\u6216 Scheffe \u68c0\u9a8c\u3002<\/p>\n\n\n\n<p>\u5e94\u6839\u636e\u7814\u7a76\u95ee\u9898\u548c\u5206\u6790\u5047\u8bbe\u6765\u89e3\u91ca\u7ed3\u679c\u3002\u5982\u679c\u5047\u8bbe\u4e0d\u6210\u7acb\u6216\u7ed3\u679c\u65e0\u6cd5\u89e3\u91ca\uff0c\u53ef\u80fd\u9700\u8981\u8fdb\u884c\u5176\u4ed6\u6d4b\u8bd5\u6216\u4fee\u6539\u5206\u6790\u3002<\/p>\n\n\n\n<h2 id=\"h-post-hoc-testing\"><strong>\u4e8b\u540e\u6d4b\u8bd5<\/strong><\/h2>\n\n\n\n<p>\u5728\u7edf\u8ba1\u5b66\u4e2d\uff0c\u5355\u56e0\u7d20\u65b9\u5dee\u5206\u6790\u662f\u4e00\u79cd\u7528\u4e8e\u6bd4\u8f83\u4e09\u4e2a\u6216\u66f4\u591a\u7ec4\u5747\u503c\u7684\u6280\u672f\u3002\u4e00\u65e6\u8fdb\u884c\u4e86\u65b9\u5dee\u5206\u6790\u68c0\u9a8c\uff0c\u5982\u679c\u62d2\u7edd\u4e86\u96f6\u5047\u8bbe\uff0c\u5373\u6709\u91cd\u8981\u8bc1\u636e\u8868\u660e\u81f3\u5c11\u6709\u4e00\u4e2a\u7ec4\u7684\u5e73\u5747\u503c\u4e0e\u5176\u4ed6\u7ec4\u4e0d\u540c\uff0c\u5c31\u53ef\u4ee5\u8fdb\u884c\u4e8b\u540e\u68c0\u9a8c\uff0c\u4ee5\u786e\u5b9a\u54ea\u4e9b\u7ec4\u4e4b\u95f4\u5b58\u5728\u663e\u8457\u5dee\u5f02\u3002<\/p>\n\n\n\n<p>\u4e8b\u540e\u68c0\u9a8c\u7528\u4e8e\u786e\u5b9a\u7ec4\u95f4\u5747\u503c\u7684\u5177\u4f53\u5dee\u5f02\u3002\u4e00\u4e9b\u5e38\u89c1\u7684\u4e8b\u540e\u68c0\u9a8c\u5305\u62ec Tukey \u7684\u8bda\u5b9e\u663e\u8457\u6027\u5dee\u5f02 (HSD)\u3001Bonferroni \u6821\u6b63\u3001Scheffe \u65b9\u6cd5\u548c Dunnett \u68c0\u9a8c\u3002\u6bcf\u79cd\u68c0\u9a8c\u90fd\u6709\u81ea\u5df1\u7684\u5047\u8bbe\u3001\u4f18\u52bf\u548c\u5c40\u9650\u6027\uff0c\u9009\u62e9\u4f7f\u7528\u54ea\u79cd\u68c0\u9a8c\u53d6\u51b3\u4e8e\u5177\u4f53\u7684\u7814\u7a76\u95ee\u9898\u548c\u6570\u636e\u7684\u7279\u70b9\u3002<\/p>\n\n\n\n<p>\u603b\u7684\u6765\u8bf4\uff0c\u4e8b\u540e\u68c0\u9a8c\u6709\u52a9\u4e8e\u63d0\u4f9b\u6709\u5173\u5355\u56e0\u7d20\u65b9\u5dee\u5206\u6790\u4e2d\u7279\u5b9a\u7fa4\u4f53\u5dee\u5f02\u7684\u66f4\u8be6\u7ec6\u4fe1\u606f\u3002\u4e0d\u8fc7\uff0c\u5728\u4f7f\u7528\u8fd9\u4e9b\u68c0\u9a8c\u65f6\u4e00\u5b9a\u8981\u8c28\u614e\uff0c\u8981\u6839\u636e\u7814\u7a76\u95ee\u9898\u548c\u6570\u636e\u7684\u5177\u4f53\u7279\u70b9\u6765\u89e3\u91ca\u68c0\u9a8c\u7ed3\u679c\u3002<\/p>\n\n\n\n<p>\u5728\u6211\u4eec\u7684\u5185\u5bb9\u4e2d\u4e86\u89e3\u66f4\u591a\u6709\u5173\u4e8b\u540e\u5206\u6790\u7684\u4fe1\u606f \"<a href=\"https:\/\/mindthegraph.com\/blog\/post-hoc-analysis\/\">\u4e8b\u540e\u5206\u6790\u3002\u6d4b\u8bd5\u7684\u8fc7\u7a0b\u548c\u7c7b\u578b<\/a>&#8220;.<\/p>\n\n\n\n<h2 id=\"h-reporting-the-results-of-anova\"><strong>\u62a5\u544a\u65b9\u5dee\u5206\u6790\u7ed3\u679c<\/strong><\/h2>\n\n\n\n<p>\u5728\u62a5\u544a\u65b9\u5dee\u5206\u6790\u7ed3\u679c\u65f6\uff0c\u5e94\u5305\u62ec\u51e0\u9879\u4fe1\u606f\uff1a<\/p>\n\n\n\n<p><strong>F \u7edf\u8ba1\u91cf\uff1a <\/strong>\u8fd9\u662f\u65b9\u5dee\u5206\u6790\u7684\u68c0\u9a8c\u7edf\u8ba1\u91cf\uff0c\u8868\u793a\u7ec4\u95f4\u65b9\u5dee\u4e0e\u7ec4\u5185\u65b9\u5dee\u7684\u6bd4\u7387\u3002<\/p>\n\n\n\n<p><strong>F \u7edf\u8ba1\u91cf\u7684\u81ea\u7531\u5ea6\uff1a<\/strong> \u8fd9\u5305\u62ec\u5206\u5b50\uff08\u7ec4\u95f4\u53d8\u5f02\uff09\u548c\u5206\u6bcd\uff08\u7ec4\u5185\u53d8\u5f02\uff09\u7684\u81ea\u7531\u5ea6\u3002<\/p>\n\n\n\n<p><strong>p \u503c\uff1a <\/strong>\u8fd9\u8868\u793a\u5047\u8bbe\u96f6\u5047\u8bbe\u4e3a\u771f\uff0c\u4ec5\u51ed\u5076\u7136\u673a\u4f1a\u83b7\u5f97\u89c2\u6d4b\u5230\u7684 F \u7edf\u8ba1\u91cf\uff08\u6216\u66f4\u6781\u7aef\u7684\u503c\uff09\u7684\u6982\u7387\u3002<\/p>\n\n\n\n<p><strong>\u5173\u4e8e\u662f\u5426\u62d2\u7edd\u96f6\u5047\u8bbe\u7684\u58f0\u660e\uff1a<\/strong> \u8fd9\u5e94\u57fa\u4e8e p \u503c\u548c\u6240\u9009\u7684\u663e\u8457\u6027\u6c34\u5e73\uff08\u5982 alpha = 0.05\uff09\u3002<\/p>\n\n\n\n<p><strong>\u4e8b\u540e\u6d4b\u8bd5\uff1a<\/strong> \u5982\u679c\u5426\u5b9a\u4e86\u96f6\u5047\u8bbe\uff0c\u5219\u5e94\u62a5\u544a\u4e8b\u540e\u68c0\u9a8c\u7684\u7ed3\u679c\uff0c\u4ee5\u786e\u5b9a\u54ea\u4e9b\u7ec4\u522b\u4e4b\u95f4\u5b58\u5728\u663e\u8457\u5dee\u5f02\u3002<\/p>\n\n\n\n<p>\u4f8b\u5982\uff0c\u62a5\u544a\u6837\u672c\u53ef\u4ee5\u662f<\/p>\n\n\n\n<p>\u5bf9\u4e09\u7ec4\uff08A \u7ec4\u3001B \u7ec4\u548c C \u7ec4\uff09\u5728\u8bb0\u5fc6\u4fdd\u6301\u6d4b\u8bd5\u4e2d\u7684\u5e73\u5747\u5f97\u5206\u8fdb\u884c\u4e86\u5355\u56e0\u7d20\u65b9\u5dee\u5206\u6790\u6bd4\u8f83\u3002F \u7edf\u8ba1\u91cf\u4e3a 4.58\uff0c\u81ea\u7531\u5ea6\u4e3a 2\uff0c87\uff0cP \u503c\u4e3a 0.01\u3002\u4f7f\u7528 Tukey's HSD \u8fdb\u884c\u7684\u4e8b\u540e\u68c0\u9a8c\u8868\u660e\uff0cA \u7ec4\u7684\u5e73\u5747\u5206\uff08M = 83.4\uff0cSD = 4.2\uff09\u660e\u663e\u9ad8\u4e8e B \u7ec4\uff08M = 76.9\uff0cSD = 5.5\uff09\u548c C \u7ec4\uff08M = 77.6\uff0cSD = 5.3\uff09\uff0c\u800c B \u7ec4\u548c C \u7ec4\u4e4b\u95f4\u6ca1\u6709\u660e\u663e\u5dee\u5f02\u3002<\/p>\n\n\n\n<h2 id=\"h-find-the-perfect-infographic-template-for-you\"><strong>\u627e\u5230\u6700\u9002\u5408\u60a8\u7684\u4fe1\u606f\u56fe\u8868\u6a21\u677f<\/strong><\/h2>\n\n\n\n<p><a href=\"https:\/\/mindthegraph.com\/\" target=\"_blank\" rel=\"noreferrer noopener\">Mind the Graph<\/a> \u662f\u4e00\u4e2a\u63d0\u4f9b\u5927\u91cf\u9884\u8bbe\u8ba1\u4fe1\u606f\u56fe\u8868\u6a21\u677f\u7684\u5e73\u53f0\uff0c\u53ef\u5e2e\u52a9\u79d1\u5b66\u5bb6\u548c\u7814\u7a76\u4eba\u5458\u521b\u5efa\u53ef\u89c6\u5316\u8f85\u52a9\u5de5\u5177\uff0c\u6709\u6548\u4f20\u8fbe\u79d1\u5b66\u6982\u5ff5\u3002\u8be5\u5e73\u53f0\u63d0\u4f9b\u5927\u91cf\u79d1\u5b66\u63d2\u56fe\u5e93\uff0c\u786e\u4fdd\u79d1\u5b66\u5bb6\u548c\u7814\u7a76\u4eba\u5458\u53ef\u4ee5\u8f7b\u677e\u627e\u5230\u5b8c\u7f8e\u7684\u4fe1\u606f\u56fe\u8868\u6a21\u677f\uff0c\u76f4\u89c2\u5730\u4f20\u8fbe\u4ed6\u4eec\u7684\u7814\u7a76\u6210\u679c\u3002<\/p>\n\n\n\n<div style=\"height:21px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><a href=\"https:\/\/mindthegraph.com\/offer-trial\"><img decoding=\"async\" loading=\"lazy\" width=\"651\" height=\"174\" src=\"https:\/\/mindthegraph.com\/blog\/wp-content\/uploads\/2023\/02\/banner-blog-trial-04.jpg\" alt=\"\" class=\"wp-image-26792\" srcset=\"https:\/\/mindthegraph.com\/blog\/wp-content\/uploads\/2023\/02\/banner-blog-trial-04.jpg 651w, https:\/\/mindthegraph.com\/blog\/wp-content\/uploads\/2023\/02\/banner-blog-trial-04-300x80.jpg 300w, https:\/\/mindthegraph.com\/blog\/wp-content\/uploads\/2023\/02\/banner-blog-trial-04-18x5.jpg 18w, https:\/\/mindthegraph.com\/blog\/wp-content\/uploads\/2023\/02\/banner-blog-trial-04-100x27.jpg 100w\" sizes=\"(max-width: 651px) 100vw, 651px\" \/><\/a><\/figure><\/div>\n\n\n<div style=\"height:44px\" aria-hidden=\"true\" 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