{"id":493,"date":"2023-07-29T17:42:56","date_gmt":"2023-07-29T17:42:56","guid":{"rendered":"https:\/\/statorials.org\/cn\/%e5%8d%95%e5%9b%a0%e7%b4%a0%e6%96%b9%e5%b7%ae%e5%88%86%e6%9e%90\/"},"modified":"2023-07-29T17:42:56","modified_gmt":"2023-07-29T17:42:56","slug":"%e5%8d%95%e5%9b%a0%e7%b4%a0%e6%96%b9%e5%b7%ae%e5%88%86%e6%9e%90","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/%e5%8d%95%e5%9b%a0%e7%b4%a0%e6%96%b9%e5%b7%ae%e5%88%86%e6%9e%90\/","title":{"rendered":"\u5982\u4f55\u5728 r \u4e2d\u6267\u884c\u5355\u5411\u65b9\u5dee\u5206\u6790"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\/cn\/\u5355\u5411\u65b9\u5dee\u5206\u6790\/\" target=\"_blank\" rel=\"noopener\">\u5355\u5411\u65b9\u5dee\u5206\u6790<\/a>\u7528\u4e8e\u786e\u5b9a\u4e09\u4e2a\u6216\u66f4\u591a\u72ec\u7acb\u7ec4\u7684\u5e73\u5747\u503c\u4e4b\u95f4\u662f\u5426\u5b58\u5728\u7edf\u8ba1\u663e\u7740\u5dee\u5f02\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u8fd9\u79cd\u7c7b\u578b\u7684\u68c0\u9a8c\u79f0\u4e3a<em>\u5355\u5411<\/em>\u65b9\u5dee\u5206\u6790\uff0c\u56e0\u4e3a\u6211\u4eec\u5206\u6790\u9884\u6d4b\u53d8\u91cf\u5bf9\u54cd\u5e94\u53d8\u91cf<em>\u7684<\/em>\u5f71\u54cd\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>\u6ce8\u610f<\/strong>\uff1a\u5982\u679c\u6211\u4eec\u5bf9\u4e24\u4e2a\u9884\u6d4b\u53d8\u91cf\u5bf9\u54cd\u5e94\u53d8\u91cf\u7684\u5f71\u54cd\u611f\u5174\u8da3\uff0c\u6211\u4eec\u53ef\u4ee5\u6267\u884c<a href=\"https:\/\/statorials.org\/cn\/\u4e24\u56e0\u7d20\u65b9\u5dee\u5206\u6790\/\" target=\"_blank\" rel=\"noopener\">\u53cc\u5411\u65b9\u5dee\u5206\u6790<\/a>\u3002<\/span><\/p>\n<h2><span style=\"color: #000000;\"><strong>\u5982\u4f55\u5728 R \u4e2d\u6267\u884c\u5355\u5411\u65b9\u5dee\u5206\u6790<\/strong><\/span><\/h2>\n<p><span style=\"color: #000000;\">\u4ee5\u4e0b\u793a\u4f8b\u8bf4\u660e\u4e86\u5982\u4f55\u5728 R \u4e2d\u6267\u884c\u5355\u5411\u65b9\u5dee\u5206\u6790\u3002<\/span><\/p>\n<h3><span style=\"color: #000000;\"><strong>\u80cc\u666f<\/strong><\/span><\/h3>\n<p><span style=\"color: #000000;\">\u5047\u8bbe\u6211\u4eec\u60f3\u8981\u786e\u5b9a\u4e09\u79cd\u4e0d\u540c\u7684\u953b\u70bc\u8ba1\u5212\u662f\u5426\u5bf9\u51cf\u80a5\u6709\u4e0d\u540c\u7684\u5f71\u54cd\u3002\u6211\u4eec\u7814\u7a76\u7684\u9884\u6d4b\u53d8\u91cf\u662f<em>\u953b\u70bc\u8ba1\u5212<\/em>\uff0c<a href=\"https:\/\/statorials.org\/cn\/\u53d8\u91cf\u89e3\u91ca\u6027\u53cd\u5e94\/\" target=\"_blank\" rel=\"noopener\">\u54cd\u5e94\u53d8\u91cf<\/a>\u662f<em>\u4f53\u91cd\u51cf\u8f7b\uff08<\/em>\u4ee5\u78c5\u4e3a\u5355\u4f4d\uff09\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u6211\u4eec\u53ef\u4ee5\u8fdb\u884c\u5355\u5411\u65b9\u5dee\u5206\u6790\uff0c\u4ee5\u786e\u5b9a\u8fd9\u4e09\u4e2a\u8ba1\u5212\u6240\u5e26\u6765\u7684\u4f53\u91cd\u51cf\u8f7b\u662f\u5426\u5b58\u5728\u7edf\u8ba1\u4e0a\u7684\u663e\u7740\u5dee\u5f02\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u6211\u4eec\u62db\u52df 90 \u4eba\u53c2\u52a0\u4e00\u9879\u5b9e\u9a8c\uff0c\u968f\u673a\u5206\u914d 30 \u4eba\u9075\u5faa\u8ba1\u5212 A\u3001\u8ba1\u5212 B \u6216\u8ba1\u5212 C\uff0c\u4e3a\u671f\u4e00\u4e2a\u6708\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u4ee5\u4e0b\u4ee3\u7801\u521b\u5efa\u6211\u4eec\u5c06\u4f7f\u7528\u7684\u6570\u636e\u6846\uff1a<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#make this example reproducible\n<span style=\"color: #000000;\">set.seed(0)\n<\/span>\n#create data frame\n<span style=\"color: #000000;\">data &lt;- data.frame(program = rep(c(\"A\", \"B\", \"C\"), each = 30),\n                   weight_loss = c(runif(30, 0, 3),\n                                   runif(30, 0, 5),\n                                   runif(30, 1, 7)))<\/span>\n\n#view first six rows of data frame\n<span style=\"color: #000000;\">head(data)\n<\/span>\n<span style=\"color: #000000;\"># program weight_loss\n#1 A 2.6900916\n#2 A 0.7965260\n#3 A 1.1163717\n#4 A 1.7185601\n#5 A 2.7246234\n#6 A 0.6050458<\/span>\n<\/span><\/strong><\/pre>\n<p><span style=\"color: #000000;\">\u6570\u636e\u6846\u7684\u7b2c\u4e00\u5217\u663e\u793a\u8be5\u4eba\u53c2\u52a0\u4e00\u4e2a\u6708\u7684\u8ba1\u5212\uff0c\u7b2c\u4e8c\u5217\u663e\u793a\u8be5\u4eba\u5728\u8ba1\u5212\u7ed3\u675f\u65f6\u7ecf\u5386\u7684\u603b\u4f53\u91cd\u51cf\u8f7b\uff08\u4ee5\u78c5\u4e3a\u5355\u4f4d\uff09\u3002<\/span><\/p>\n<h3><span style=\"color: #000000;\"><strong>\u63a2\u7d22\u6570\u636e<\/strong><\/span><\/h3>\n<p><span style=\"color: #000000;\">\u5728\u62df\u5408\u5355\u5411\u65b9\u5dee\u5206\u6790\u6a21\u578b\u4e4b\u524d\uff0c\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u4f7f\u7528<strong>dplyr<\/strong>\u5305\u67e5\u627e\u4e09\u4e2a\u7a0b\u5e8f\u4e2d\u6bcf\u4e00\u4e2a\u7684\u51cf\u80a5\u5e73\u5747\u503c\u548c\u6807\u51c6\u5dee\u6765\u66f4\u597d\u5730\u7406\u89e3\u6570\u636e\uff1a<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#load <em>dplyr<\/em> package<\/span>\n<span style=\"color: #008000;\">library<\/span> (dplyr)\n\n<span style=\"color: #008080;\">#find mean and standard deviation of weight loss for each treatment group<\/span>\ndata %&gt;%\n  <span style=\"color: #800080;\">group_by<\/span> (program) %&gt;%\n  <span style=\"color: #800080;\">summarize<\/span> (mean = mean(weight_loss),\n            sd = sd(weight_loss))\n\n# A tibble: 3 x 3\n# program mean sd\n#      \n#1 A 1.58 0.905\n#2 B 2.56 1.24 \n#3 C 4.13 1.57  \n<\/strong><\/pre>\n<p><span style=\"color: #000000;\">\u6211\u4eec\u8fd8\u53ef\u4ee5\u4e3a\u8fd9\u4e09\u4e2a\u8ba1\u5212\u4e2d\u7684\u6bcf\u4e00\u4e2a\u521b\u5efa\u4e00\u4e2a<a href=\"https:\/\/statorials.org\/cn\/\u7edf\u8ba1\u5b66\u4ee5\u7b80\u5355\u76f4\u63a5\u7684\u65b9\u5f0f\u89e3\u91ca\u6982\u5ff5\uff0c\u6211\u4eec\u4f7f\u5b66\u4e60\u7edf\u8ba1\u53d8\u5f97\u66f4\u5bb9\u6613\/\" target=\"_blank\" rel=\"noopener\">\u7bb1\u7ebf\u56fe<\/a>\uff0c\u4ee5\u53ef\u89c6\u5316\u6bcf\u4e2a\u8ba1\u5212\u7684\u51cf\u80a5\u5206\u5e03\uff1a<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#create boxplots\n<\/span>boxplot(weight_loss ~ program,\ndata = data,\nmain = \"Weight Loss Distribution by Program\",\nxlab = \"Program\",\nylab = \"Weight Loss\",\ncol = \"steelblue\",\nborder = \"black\")<\/strong><\/pre>\n<p><span style=\"color: #000000;\">\u4ece\u8fd9\u4e9b\u7bb1\u7ebf\u56fe\u4e2d\uff0c\u6211\u4eec\u53ef\u4ee5\u770b\u5230\uff0c\u8ba1\u5212 C \u7684\u53c2\u4e0e\u8005\u7684\u5e73\u5747\u4f53\u91cd\u51cf\u8f7b\u6700\u9ad8\uff0c\u8ba1\u5212 A \u7684\u53c2\u4e0e\u8005\u7684\u5e73\u5747\u4f53\u91cd\u51cf\u8f7b\u6700\u4f4e\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u6211\u4eec\u8fd8\u53ef\u4ee5\u770b\u5230\uff0c\u4e0e\u5176\u4ed6\u4e24\u4e2a\u7a0b\u5e8f\u76f8\u6bd4\uff0c\u7a0b\u5e8f C \u4e2d\u7684\u51cf\u80a5\u6807\u51c6\u5dee\uff08\u7bb1\u7ebf\u56fe\u7684\u201c\u957f\u5ea6\u201d\uff09\u7a0d\u9ad8\u4e00\u4e9b\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u5c06\u5355\u5411\u65b9\u5dee\u5206\u6790\u6a21\u578b\u4e0e\u6211\u4eec\u7684\u6570\u636e\u8fdb\u884c\u62df\u5408\uff0c\u770b\u770b\u8fd9\u4e9b\u89c6\u89c9\u5dee\u5f02\u5b9e\u9645\u4e0a\u662f\u5426\u5177\u6709\u7edf\u8ba1\u663e\u7740\u6027\u3002<\/span><\/p>\n<h3><span style=\"color: #000000;\"><strong>\u5355\u5411\u65b9\u5dee\u5206\u6790\u6a21\u578b\u62df\u5408<\/strong><\/span><\/h3>\n<p><span style=\"color: #000000;\">\u5728 R \u4e2d\u62df\u5408\u5355\u5411\u65b9\u5dee\u5206\u6790\u6a21\u578b\u7684\u4e00\u822c\u8bed\u6cd5\u662f\uff1a<\/span><\/p>\n<p style=\"text-align: left;\"> <strong><span style=\"color: #000000;\">aov\uff08\u54cd\u5e94\u53d8\u91cf~\u9884\u6d4b\u53d8\u91cf\uff0c\u6570\u636e=\u6570\u636e\u96c6\uff09<\/span><\/strong><\/p>\n<p><span style=\"color: #000000;\">\u5728\u6211\u4eec\u7684\u793a\u4f8b\u4e2d\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u4ee5\u4e0b\u4ee3\u7801\u6765\u62df\u5408\u5355\u5411\u65b9\u5dee\u5206\u6790\u6a21\u578b\uff0c\u4f7f\u7528<em>weight_loss<\/em>\u4f5c\u4e3a\u54cd\u5e94\u53d8\u91cf\uff0c\u4f7f\u7528<em>program<\/em>\u4f5c\u4e3a\u9884\u6d4b\u53d8\u91cf\u3002\u7136\u540e\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528<strong>summary()<\/strong>\u51fd\u6570\u6765\u663e\u793a\u6a21\u578b\u7684\u7ed3\u679c\uff1a<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#fit the one-way ANOVA model<\/span>\nmodel &lt;- aov(weight_loss ~ program, data = data)\n\n<span style=\"color: #008080;\">#view the model output<\/span>\nsummary(model)\n\n# Df Sum Sq Mean Sq F value Pr(&gt;F)    \n#program 2 98.93 49.46 30.83 7.55e-11 ***\n#Residuals 87 139.57 1.60                     \n#---\n#Significant. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n<\/strong><\/pre>\n<p><span style=\"color: #000000;\">\u4ece\u6a21\u578b\u7ed3\u679c\u4e2d\u6211\u4eec\u53ef\u4ee5\u770b\u51fa\uff0c\u9884\u6d4b\u53d8\u91cf<em>\u7a0b\u5e8f<\/em>\u5728 0.05 \u663e\u7740\u6027\u6c34\u5e73\u4e0a\u5177\u6709\u7edf\u8ba1\u663e\u7740\u6027\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u6362\u53e5\u8bdd\u8bf4\uff0c\u8fd9\u4e09\u4e2a\u8ba1\u5212\u7684\u5e73\u5747\u4f53\u91cd\u51cf\u8f7b\u4e4b\u95f4\u5b58\u5728\u7edf\u8ba1\u4e0a\u7684\u663e\u7740\u5dee\u5f02\u3002<\/span><\/p>\n<h3><span style=\"color: #000000;\"><strong>\u68c0\u67e5\u6a21\u578b\u5047\u8bbe<\/strong><\/span><\/h3>\n<p><span style=\"color: #000000;\">\u5728\u8fdb\u4e00\u6b65\u8fdb\u884c\u4e4b\u524d\uff0c\u6211\u4eec\u9700\u8981\u9a8c\u8bc1\u6a21\u578b\u7684<a href=\"https:\/\/statorials.org\/cn\/\u8fbe\u8bfa\u74e6\u5047\u8bbe\/\" target=\"_blank\" rel=\"noopener\">\u5047\u8bbe<\/a>\u662f\u5426\u5f97\u5230\u6ee1\u8db3\uff0c\u4ee5\u4fbf\u6a21\u578b\u7ed3\u679c\u53ef\u9760\u3002\u7279\u522b\u662f\uff0c\u5355\u5411\u65b9\u5dee\u5206\u6790\u5047\u8bbe\uff1a<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1. \u72ec\u7acb\u6027<\/strong>\u2014\u2014\u6bcf\u7ec4\u7684\u89c2\u5bdf\u7ed3\u679c\u5fc5\u987b\u76f8\u4e92\u72ec\u7acb\u3002\u7531\u4e8e\u6211\u4eec\u4f7f\u7528\u4e86<\/span><span style=\"color: #000000;\">\u968f\u673a\u8bbe\u8ba1\uff08\u5373\u5c06\u53c2\u4e0e\u8005\u968f\u673a\u5206\u914d\u5230\u953b\u70bc\u8ba1\u5212\uff09\uff0c\u56e0\u6b64\u5e94\u8be5\u6ee1\u8db3\u8fd9\u4e2a\u5047\u8bbe\uff0c\u8fd9\u6837\u6211\u4eec\u5c31\u4e0d\u5fc5\u5bf9\u6b64\u8fc7\u4e8e\u62c5\u5fc3\u3002<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>2. \u6b63\u6001\u6027<\/strong>\u2014\u2014\u56e0\u53d8\u91cf\u5bf9\u4e8e\u9884\u6d4b\u53d8\u91cf\u7684\u6bcf\u4e2a\u6c34\u5e73\u90fd\u5e94\u5177\u6709\u8fd1\u4f3c\u6b63\u6001\u5206\u5e03\u3002<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>3. \u65b9\u5dee\u76f8\u7b49<\/strong>\u2014\u2014\u6bcf\u7ec4\u7684\u65b9\u5dee\u76f8\u7b49\u6216\u8fd1\u4f3c\u76f8\u7b49\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u68c0\u67e5<strong>\u6b63\u6001\u6027<\/strong>\u548c<strong>\u7b49\u65b9\u5dee\u5047\u8bbe<\/strong>\u7684\u4e00\u79cd\u65b9\u6cd5\u662f\u4f7f\u7528<strong>plot()<\/strong>\u51fd\u6570\uff0c\u8be5\u51fd\u6570\u4f1a\u751f\u6210\u56db\u4e2a\u6a21\u578b\u68c0\u67e5\u56fe\u3002\u7279\u522b\u662f\uff0c\u6211\u4eec\u5bf9\u4ee5\u4e0b\u4e24\u4e2a\u56fe\u7279\u522b\u611f\u5174\u8da3\uff1a<\/span><\/p>\n<ul>\n<li><span style=\"color: #000000;\"><strong>\u6b8b\u5dee\u5bf9\u6bd4\u62df\u5408<\/strong>&#8211; \u8be5\u56fe\u663e\u793a\u6b8b\u5dee\u548c\u62df\u5408\u503c\u4e4b\u95f4\u7684\u5173\u7cfb\u3002\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u8be5\u56fe\u6765\u7c97\u7565\u8bc4\u4f30\u7ec4\u4e4b\u95f4\u7684\u65b9\u5dee\u662f\u5426\u8fd1\u4f3c\u76f8\u7b49\u3002<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>QQ \u56fe<\/strong>\u2013 \u8be5\u56fe\u663e\u793a\u76f8\u5bf9\u4e8e\u7406\u8bba\u5206\u4f4d\u6570\u7684\u6807\u51c6\u5316\u6b8b\u5dee\u3002\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u8be5\u56fe\u6765\u7c97\u7565\u8bc4\u4f30\u662f\u5426\u6ee1\u8db3\u6b63\u6001\u6027\u5047\u8bbe\u3002<\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000;\">\u4ee5\u4e0b\u4ee3\u7801\u53ef\u7528\u4e8e\u751f\u6210\u8fd9\u4e9b\u6a21\u578b\u68c0\u67e5\u56fe\uff1a<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <span style=\"color: #000000;\"><strong><span style=\"color: #000000;\">plot(model)<\/span><\/strong><\/span><\/pre>\n<p><span style=\"color: #000000;\">\u4e0a\u9762\u7684<em>QQ\u56fe<\/em>\u8ba9\u6211\u4eec\u9a8c\u8bc1\u4e86\u6b63\u6001\u6027\u5047\u8bbe\u3002\u7406\u60f3\u60c5\u51b5\u4e0b\uff0c\u6807\u51c6\u5316\u6b8b\u5dee\u5c06\u6cbf\u7740\u56fe\u7684\u76f4\u7ebf\u5bf9\u89d2\u7ebf\u5206\u5e03\u3002\u7136\u800c\uff0c\u5728\u4e0a\u56fe\u4e2d\u6211\u4eec\u53ef\u4ee5\u770b\u5230\u6b8b\u5dee\u5728\u5f00\u59cb\u548c\u7ed3\u675f\u65f6\u4e0e\u76f4\u7ebf\u7565\u6709\u504f\u5dee\u3002\u8fd9\u8868\u660e\u6211\u4eec\u7684\u6b63\u6001\u6027\u5047\u8bbe\u53ef\u80fd\u88ab\u8fdd\u53cd\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\"><em>\u6b8b\u5dee\u5bf9\u6bd4<\/em>\u4e0a\u9762<em>\u8c03\u6574\u540e\u7684\u56fe\u8868<\/em>\u4f7f\u6211\u4eec\u80fd\u591f\u9a8c\u8bc1\u65b9\u5dee\u76f8\u7b49\u7684\u5047\u8bbe\u3002\u7406\u60f3\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u5e0c\u671b\u6b8b\u5dee\u5bf9\u4e8e\u62df\u5408\u503c\u7684\u6bcf\u4e2a\u7ea7\u522b\u5747\u7b49\u5206\u5e03\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u6211\u4eec\u53ef\u4ee5\u770b\u5230\uff0c\u5bf9\u4e8e\u8f83\u9ad8\u7684\u62df\u5408\u503c\uff0c\u6b8b\u5dee\u66f4\u52a0\u5206\u6563\uff0c\u8fd9\u8868\u660e\u6211\u4eec\u7684<a href=\"https:\/\/statorials.org\/cn\/\u7b49\u65b9\u5dee\u5047\u8bbe\/\" target=\"_blank\" rel=\"noopener\">\u65b9\u5dee\u9f50\u6027\u5047\u8bbe<\/a>\u53ef\u80fd\u88ab\u8fdd\u53cd\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u4e3a\u4e86\u6b63\u5f0f\u6d4b\u8bd5\u7b49\u65b9\u5dee\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528<strong>car<\/strong>\u5305\u6267\u884c Levene \u6d4b\u8bd5\uff1a<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#load car package\n<\/span><span style=\"color: #008000;\">library<\/span> (car)\n\n<span style=\"color: #008080;\">#conduct Levene's Test for equality of variances\n<\/span>leveneTest(weight_loss ~ program, data = data)\n\n#Levene's Test for Homogeneity of Variance (center = median)\n# Df F value Pr(&gt;F)  \n#group 2 4.1716 0.01862 *\n#87                  \n#---\n#Significant. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n<\/strong><\/pre>\n<p><span style=\"color: #000000;\">\u68c0\u9a8c\u7684 p \u503c\u4e3a<strong>0.01862<\/strong> \u3002\u5982\u679c\u6211\u4eec\u4f7f\u7528 0.05 \u7684\u663e\u7740\u6027\u6c34\u5e73\uff0c\u6211\u4eec\u5c06\u62d2\u7edd\u4e09\u4e2a\u7a0b\u5e8f\u4e4b\u95f4\u65b9\u5dee\u76f8\u7b49\u7684\u539f\u5047\u8bbe\u3002\u4f46\u662f\uff0c\u5982\u679c\u6211\u4eec\u4f7f\u7528 0.01 \u7684\u663e\u7740\u6027\u6c34\u5e73\uff0c\u6211\u4eec\u5c06\u4e0d\u4f1a\u62d2\u7edd\u539f\u5047\u8bbe\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u5c3d\u7ba1\u6211\u4eec\u53ef\u4ee5\u5c1d\u8bd5\u8f6c\u6362\u6570\u636e\u4ee5\u786e\u4fdd\u6ee1\u8db3\u6b63\u6001\u6027\u548c\u65b9\u5dee\u76f8\u7b49\u7684\u5047\u8bbe\uff0c\u4f46\u76ee\u524d\u6211\u4eec\u4e0d\u4f1a\u592a\u62c5\u5fc3\u5b83\u3002<\/span><\/p>\n<h3><span style=\"color: #000000;\"><strong>\u5206\u6790\u6cbb\u7597\u5dee\u5f02<\/strong><\/span><\/h3>\n<p><span style=\"color: #000000;\">\u4e00\u65e6\u6211\u4eec\u9a8c\u8bc1\u4e86\u6a21\u578b\u5047\u8bbe\u5f97\u5230\u6ee1\u8db3\uff08\u6216\u5408\u7406\u6ee1\u8db3\uff09\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u8fdb\u884c<a href=\"https:\/\/statorials.org\/cn\/\u7edf\u8ba1\u5b66\u4ee5\u7b80\u5355\u76f4\u63a5\u7684\u65b9\u5f0f\u89e3\u91ca\u6982\u5ff5\uff0c\u6211\u4eec\u4f7f\u5b66\u4e60\u7edf\u8ba1\u53d8\u5f97\u66f4\u5bb9\u6613\/\" target=\"_blank\" rel=\"noopener\">\u4e8b\u540e\u6d4b\u8bd5<\/a>\u6765\u51c6\u786e\u786e\u5b9a\u54ea\u4e9b\u6cbb\u7597\u7ec4\u5f7c\u6b64\u4e0d\u540c\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u5bf9\u4e8e\u6211\u4eec\u7684\u4e8b\u540e\u6d4b\u8bd5\uff0c\u6211\u4eec\u5c06\u4f7f\u7528<strong>TukeyHSD()<\/strong>\u51fd\u6570\u6267\u884c Tukey \u6d4b\u8bd5\u4ee5\u8fdb\u884c\u591a\u91cd\u6bd4\u8f83\uff1a<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#perform Tukey's Test for multiple comparisons\n<\/span>TukeyHSD(model, conf.level=.95) \n\n#Tukey multiple comparisons of means\n# 95% family-wise confidence level\n#\n#Fit: aov(formula = weight_loss ~ program, data = data)\n#\n#$program\n# diff lwr upr p adj\n#BA 0.9777414 0.1979466 1.757536 0.0100545\n#CA 2.5454024 1.7656076 3.325197 0.0000000\n#CB 1.5676610 0.7878662 2.347456 0.0000199\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">p \u503c\u8868\u793a\u6bcf\u4e2a\u7a0b\u5e8f\u4e4b\u95f4\u662f\u5426\u5b58\u5728\u7edf\u8ba1\u663e\u7740\u5dee\u5f02\u3002\u7ed3\u679c\u663e\u793a\uff0c\u5404\u65b9\u6848\u7684\u5e73\u5747\u51cf\u80a5\u6548\u679c\u57280.05\u663e\u7740\u6027\u6c34\u5e73\u4e0a\u5b58\u5728\u7edf\u8ba1\u5b66\u4e0a\u7684\u663e\u7740\u5dee\u5f02\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u6211\u4eec\u8fd8\u53ef\u4ee5\u4f7f\u7528 R \u4e2d\u7684<strong>plot(TukeyHSD())<\/strong>\u51fd\u6570\u53ef\u89c6\u5316 Tukey \u6d4b\u8bd5\u4ea7\u751f\u7684 95% \u7f6e\u4fe1\u533a\u95f4\uff1a<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#create confidence interval for each comparison\n<\/span>plot(TukeyHSD(model, conf.level=.95), las = 2)\n<\/strong><\/pre>\n<p><span style=\"color: #000000;\">\u7f6e\u4fe1\u533a\u95f4\u7684\u7ed3\u679c\u4e0e\u5047\u8bbe\u68c0\u9a8c\u7684\u7ed3\u679c\u4e00\u81f4\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u7279\u522b\u662f\uff0c\u6211\u4eec\u53ef\u4ee5\u770b\u5230\uff0c\u7a0b\u5e8f\u4e4b\u95f4\u7684\u5e73\u5747\u4f53\u91cd\u51cf\u8f7b\u7684\u7f6e\u4fe1\u533a\u95f4\u90fd\u4e0d\u5305\u542b\u503c<em>0<\/em> \uff0c\u8fd9\u8868\u660e\u4e09\u4e2a\u7a0b\u5e8f\u4e4b\u95f4\u7684\u5e73\u5747\u4f53\u91cd\u51cf\u8f7b\u5b58\u5728\u7edf\u8ba1\u4e0a\u7684\u663e\u7740\u5dee\u5f02\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u8fd9\u4e0e\u6211\u4eec<a href=\"https:\/\/statorials.org\/cn\/\u5047\u8bbe\u68c0\u9a8c1\/\" target=\"_blank\" rel=\"noopener\">\u5047\u8bbe\u68c0\u9a8c<\/a>\u7684\u6240\u6709<a href=\"https:\/\/statorials.org\/cn\/p\u503c\u7edf\u8ba1\u663e\u7740\u6027\/\" target=\"_blank\" rel=\"noopener\">p \u503c<\/a>\u5747\u5c0f\u4e8e 0.05 \u4e00\u81f4\u3002<\/span><\/p>\n<h3><strong><span style=\"color: #000000;\">\u62a5\u544a\u5355\u5411\u65b9\u5dee\u5206\u6790\u7ed3\u679c<\/span><\/strong><\/h3>\n<p><span style=\"color: #000000;\">\u6700\u540e\uff0c\u6211\u4eec\u53ef\u4ee5\u7528\u4e00\u79cd\u603b\u7ed3\u7ed3\u679c\u7684\u65b9\u5f0f\u62a5\u544a\u5355\u5411\u65b9\u5dee\u5206\u6790\u7684\u7ed3\u679c\uff1a<\/span><\/p>\n<p><span style=\"color: #000000;\">\u8fdb\u884c\u5355\u5411\u65b9\u5dee\u5206\u6790\u6765\u68c0\u67e5\u953b\u70bc\u8ba1\u5212\u7684\u6548\u679c<em>&nbsp;<\/em>\u5173\u4e8e\u51cf\u80a5<em>\uff08\u4ee5\u78c5\u4e3a\u5355\u4f4d\uff09\u3002<\/em>\u4e09\u4e2a\u8ba1\u5212\u7684\u51cf\u80a5\u6548\u679c\u4e4b\u95f4\u5b58\u5728\u7edf\u8ba1\u5b66\u4e0a\u7684\u663e\u7740\u5dee\u5f02\uff08F(2, 87) = 30.83, p = 7.55e-11\uff09\u3002<\/span><span style=\"color: #000000;\">\u8fdb\u884c\u4e8b\u540e Tukey \u7684 HSD \u6d4b\u8bd5\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u8ba1\u5212 C \u53c2\u4e0e\u8005\u7684\u5e73\u5747\u4f53\u91cd\u51cf\u8f7b\u660e\u663e\u5927\u4e8e\u8ba1\u5212 B \u53c2\u4e0e\u8005\u7684\u5e73\u5747\u4f53\u91cd\u51cf\u8f7b (p &lt; 0.0001)\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u8ba1\u5212 C \u53c2\u4e0e\u8005\u7684\u5e73\u5747\u4f53\u91cd\u51cf\u8f7b\u660e\u663e\u5927\u4e8e\u8ba1\u5212 A \u53c2\u4e0e\u8005\u7684\u5e73\u5747\u4f53\u91cd\u51cf\u8f7b (p &lt; 0.0001)\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u6b64\u5916\uff0c\u8ba1\u5212 B \u53c2\u4e0e\u8005\u7684\u5e73\u5747\u4f53\u91cd\u51cf\u8f7b\u660e\u663e\u5927\u4e8e\u8ba1\u5212 A \u53c2\u4e0e\u8005\u7684\u5e73\u5747\u4f53\u91cd\u51cf\u8f7b (p = 0.01)\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\u63d0\u4f9b\u6709\u5173\u5355\u5411\u65b9\u5dee\u5206\u6790\u7684\u66f4\u591a\u4fe1\u606f\uff1a<\/span><\/p>\n<p><a href=\"https:\/\/statorials.org\/cn\/\u5355\u5411\u65b9\u5dee\u5206\u6790\/\" target=\"_blank\" rel=\"noopener\">\u5355\u5411\u65b9\u5dee\u5206\u6790\u7b80\u4ecb<\/a><br \/><a href=\"https:\/\/statorials.org\/cn\/\u4e8b\u540e\u65b9\u5dee\u5206\u6790\u68c0\u9a8c\/\" target=\"_blank\" rel=\"noopener\">\u4f7f\u7528\u65b9\u5dee\u5206\u6790\u8fdb\u884c\u4e8b\u540e\u6d4b\u8bd5\u7684\u6307\u5357<\/a><br \/> <a href=\"https:\/\/statorials.org\/cn\/\u5982\u4f55\u62a5\u544a\u65b9\u5dee\u5206\u6790\u7ed3\u679c\/\" target=\"_blank\" rel=\"noopener\">\u5b8c\u6574\u6307\u5357\uff1a\u5982\u4f55\u62a5\u544a\u65b9\u5dee\u5206\u6790\u7ed3\u679c<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5355\u5411\u65b9\u5dee\u5206\u6790\u7528\u4e8e\u786e\u5b9a\u4e09\u4e2a\u6216\u66f4\u591a\u72ec\u7acb\u7ec4\u7684\u5e73\u5747\u503c\u4e4b\u95f4\u662f\u5426\u5b58\u5728\u7edf\u8ba1\u663e\u7740\u5dee\u5f02\u3002 \u8fd9\u79cd\u7c7b\u578b\u7684\u68c0\u9a8c\u79f0\u4e3a\u5355\u5411\u65b9\u5dee\u5206\u6790\uff0c\u56e0\u4e3a\u6211 [&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-493","post","type-post","status-publish","format-standard","hentry","category-11"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin 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