{"id":2249,"date":"2023-07-23T02:17:28","date_gmt":"2023-07-23T02:17:28","guid":{"rendered":"https:\/\/statorials.org\/cn\/%e8%a7%a3%e9%87%8a-cramers-v\/"},"modified":"2023-07-23T02:17:28","modified_gmt":"2023-07-23T02:17:28","slug":"%e8%a7%a3%e9%87%8a-cramers-v","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/%e8%a7%a3%e9%87%8a-cramers-v\/","title":{"rendered":"\u5982\u4f55\u89e3\u91ca cramer \u7684 v\uff08\u9644\u793a\u4f8b\uff09"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>Cramer \u7684 V<\/strong>\u662f\u4e24\u4e2a\u540d\u4e49\u53d8\u91cf\u4e4b\u95f4\u5173\u8054\u5f3a\u5ea6\u7684\u5ea6\u91cf\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u5b83\u4ece 0 \u5230 1\uff0c\u5176\u4e2d\uff1a<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>0<\/strong>\u8868\u793a\u4e24\u4e2a\u53d8\u91cf\u4e4b\u95f4\u6ca1\u6709\u5173\u8054\u3002<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>1<\/strong>\u8868\u793a\u4e24\u4e2a\u53d8\u91cf\u4e4b\u95f4\u5b8c\u7f8e\u5173\u8054\u3002<\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000;\">\u8ba1\u7b97\u65b9\u6cd5\u5982\u4e0b\uff1a<\/span><\/p>\n<p><strong><span style=\"color: #000000;\">\u514b\u83b1\u9ed8\u7684 V = \u221a <span style=\"border-top: 1px solid black;\">(X <sup>2<\/sup> \/n) \/ min(c-1, r-1)<\/span><\/span><\/strong><\/p>\n<p><span style=\"color: #000000;\">\u91d1\u5b50\uff1a<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>X <sup>2<\/sup> \uff1a<\/strong>\u5361\u65b9\u7edf\u8ba1\u91cf<\/span><\/li>\n<li><span style=\"color: #000000;\"><strong>n\uff1a<\/strong>\u603b\u6837\u672c\u91cf<\/span><\/li>\n<li><span style=\"color: #000000;\"><strong>r\uff1a<\/strong>\u884c\u6570<\/span><\/li>\n<li><span style=\"color: #000000;\"><strong>c:<\/strong>\u5217\u6570<\/span><\/li>\n<\/ul>\n<h3><span style=\"color: #000000;\"><strong>\u5982\u4f55\u89e3\u91ca\u514b\u83b1\u9ed8\u7684 V<\/strong><\/span><\/h3>\n<p><span style=\"color: #000000;\">\u4e0b\u8868\u663e\u793a\u4e86\u5982\u4f55\u6839\u636e\u81ea\u7531\u5ea6\u89e3\u91ca Cramer V\uff1a<\/span><\/p>\n<table>\n<tbody>\n<tr>\n<th style=\"text-align: center;\"><span style=\"color: #000000;\"><strong>\u81ea\u7531\u7a0b\u5ea6<\/strong><\/span><\/th>\n<th style=\"text-align: center;\"><span style=\"color: #000000;\"><strong>\u5c0f\u7684<\/strong><\/span><\/th>\n<th style=\"text-align: center;\"><span style=\"color: #000000;\"><strong>\u5e73\u5747\u7684<\/strong><\/span><\/th>\n<th style=\"text-align: center;\"><span style=\"color: #000000;\"><strong>\u5927\u7684<\/strong><\/span><\/th>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\"><strong>1<\/strong><\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">0.10<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">0.30<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">0.50<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\"><strong>2<\/strong><\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">0.07<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">0.21<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">0.35<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\"><b>3<\/b><\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">0.06<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">0.17<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">0.29<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\"><b>4<\/b><\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">0.05<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">0.15<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">0.25<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\"><strong>5<\/strong><\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">0.04<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">0.13<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">0.22<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><span style=\"color: #000000;\">\u4ee5\u4e0b\u793a\u4f8b\u5c55\u793a\u4e86\u5982\u4f55\u5728\u4e0d\u540c\u60c5\u51b5\u4e0b\u89e3\u91ca Cramer \u7684 V\u3002<\/span><\/p>\n<h3><span style=\"color: #000000;\"><strong>\u793a\u4f8b 1\uff1a\u89e3\u91ca 2&#215;3 \u6570\u7ec4\u7684 Cramer V<\/strong><\/span><\/h3>\n<p><span style=\"color: #000000;\">\u5047\u8bbe\u6211\u4eec\u60f3\u77e5\u9053\u773c\u775b\u989c\u8272\u548c\u6027\u522b\u4e4b\u95f4\u662f\u5426\u5b58\u5728\u5173\u8054\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u8be2\u95ee\u4e86 50 \u4e2a\u4eba\u5e76\u5f97\u5230\u4ee5\u4e0b\u7ed3\u679c\uff1a<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-20463 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/poly12.png\" alt=\"\" width=\"370\" height=\"111\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p><span style=\"color: #000000;\">\u6211\u4eec\u53ef\u4ee5\u5728 R \u4e2d\u4f7f\u7528\u4ee5\u4e0b\u4ee3\u7801\u6765\u8ba1\u7b97\u8fd9\u4e24\u4e2a\u53d8\u91cf\u7684 Cramer&#8217;s V\uff1a<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008000;\">library<\/span> (rcompanion)\n\n<span style=\"color: #008080;\">#create table\n<\/span>data = matrix(c(6, 9, 8, 5, 12, 10), nrow= <span style=\"color: #008000;\">2<\/span> )\n\n<span style=\"color: #008080;\">#view table\n<\/span>data\n\n     [,1] [,2] [,3]\n[1,] 6 8 12\n[2,] 9 5 10\n\n<span style=\"color: #008080;\">#calculate Cramer's V\n<\/span>cramerV(data)\n\nCramer V \n  0.1671<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Cramer \u7684 V \u7ed3\u679c\u4e3a<strong>0.1671<\/strong> \u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u81ea\u7531\u5ea6\u8ba1\u7b97\u5982\u4e0b\uff1a<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">df = min(#rows-1, #columns-1)<\/span><\/li>\n<li> <span style=\"color: #000000;\">df = \u5206\u949f(1, 2)<\/span><\/li>\n<li> <span style=\"color: #000000;\">df = <strong>1<\/strong><\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000;\">\u53c2\u8003\u4e0a\u8868\uff0c\u6211\u4eec\u53ef\u4ee5\u770b\u5230 Cramer&#8217;s V \u4e3a<strong>0.1671<\/strong>\u4e14\u81ea\u7531\u5ea6 = <strong>1<\/strong>\u8868\u660e\u773c\u775b\u989c\u8272\u548c\u6027\u522b\u4e4b\u95f4\u7684\u5173\u8054\u8f83\u5c0f\uff08\u6216\u201c\u5f31\u201d\uff09\u3002<\/span><\/p>\n<h3><span style=\"color: #000000;\"><strong>\u793a\u4f8b 2\uff1a\u89e3\u91ca 3\u00d73 \u8868\u7684 Cramer V<\/strong><\/span><\/h3>\n<p><span style=\"color: #000000;\">\u5047\u8bbe\u6211\u4eec\u60f3\u77e5\u9053\u773c\u775b\u989c\u8272\u548c\u5bf9\u653f\u515a\u7684\u504f\u597d\u4e4b\u95f4\u662f\u5426\u5b58\u5728\u5173\u8054\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u8be2\u95ee\u4e86 50 \u4e2a\u4eba\u5e76\u5f97\u5230\u4ee5\u4e0b\u7ed3\u679c\uff1a<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-20548 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/cramer1.png\" alt=\"\" width=\"423\" height=\"131\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p><span style=\"color: #000000;\">\u6211\u4eec\u53ef\u4ee5\u5728 R \u4e2d\u4f7f\u7528\u4ee5\u4e0b\u4ee3\u7801\u6765\u8ba1\u7b97\u8fd9\u4e24\u4e2a\u53d8\u91cf\u7684 Cramer&#8217;s V\uff1a<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008000;\">library<\/span> (rcompanion)\n\n<span style=\"color: #008080;\">#create table\n<\/span>data = matrix(c(8, 2, 4, 5, 8, 6, 6, 3, 8), nrow= <span style=\"color: #008000;\">3<\/span> )\n\n<span style=\"color: #008080;\">#view table\n<\/span>data\n\n     [,1] [,2] [,3]\n[1,] 8 5 6\n[2,] 2 8 3\n[3,] 4 6 8\n\n<span style=\"color: #008080;\">#calculate Cramer's V\n<\/span>cramerV(data)\n\nCramer V \n  0.246<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Cramer \u7684 V \u7ed3\u679c\u4e3a<strong>0.246<\/strong> \u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u81ea\u7531\u5ea6\u8ba1\u7b97\u5982\u4e0b\uff1a<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">df = min(#rows-1, #columns-1)<\/span><\/li>\n<li> <span style=\"color: #000000;\">df = \u5206\u949f(2, 2)<\/span><\/li>\n<li> <span style=\"color: #000000;\">df = <strong>2<\/strong><\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000;\">\u53c2\u8003\u4e0a\u8868\uff0c\u6211\u4eec\u53ef\u4ee5\u770b\u5230 Cramer&#8217;s V \u4e3a<strong>0.246<\/strong>\u4e14\u81ea\u7531\u5ea6 = <strong>2<\/strong>\u8868\u660e\u773c\u775b\u989c\u8272\u548c\u653f\u515a\u504f\u597d\u4e4b\u95f4\u5b58\u5728\u4e2d\u7b49\uff08\u6216\u201c\u4e2d\u7b49\u201d\uff09\u5173\u8054\u3002<\/span><\/p>\n<h3><span style=\"color: #000000;\"><strong>\u5176\u4ed6\u8d44\u6e90<\/strong><\/span><\/h3>\n<p><span style=\"color: #000000;\">\u4ee5\u4e0b\u6559\u7a0b\u89e3\u91ca\u4e86\u5982\u4f55\u5728\u4e0d\u540c\u7684\u7edf\u8ba1\u8f6f\u4ef6\u4e2d\u8ba1\u7b97 Cramer&#8217;s V\uff1a<\/span><\/p>\n<p><a href=\"https:\/\/statorials.org\/cn\/excel\u4e2d\u7684\u514b\u62c9\u9ed8\u65afv\/\" target=\"_blank\" rel=\"noopener\">\u5982\u4f55\u5728 Excel \u4e2d\u8ba1\u7b97 Cramer \u7684 V<\/a><br \/><a href=\"https:\/\/statorials.org\/cn\/\u514b\u62c9\u9ed8\u65af-v-in-r\/\" target=\"_blank\" rel=\"noopener\">\u5982\u4f55\u5728 R \u4e2d\u8ba1\u7b97 Cramer \u7684 V<\/a><br \/><a href=\"https:\/\/statorials.org\/cn\/python-\u4e2d\u7684cramers-v\/\" target=\"_blank\" rel=\"noopener\">\u5982\u4f55\u7528 Python \u8ba1\u7b97 Cramer \u7684 V<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Cramer \u7684 V\u662f\u4e24\u4e2a\u540d\u4e49\u53d8\u91cf\u4e4b\u95f4\u5173\u8054\u5f3a\u5ea6\u7684\u5ea6\u91cf\u3002 \u5b83\u4ece 0 \u5230 1\uff0c\u5176\u4e2d\uff1a 0\u8868\u793a\u4e24\u4e2a\u53d8\u91cf\u4e4b\u95f4\u6ca1\u6709\u5173\u8054\u3002 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11],"tags":[],"class_list":["post-2249","post","type-post","status-publish","format-standard","hentry","category-11"],"yoast_head":"<!-- This site is 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