{"id":3669,"date":"2025-12-15T12:46:17","date_gmt":"2025-12-15T04:46:17","guid":{"rendered":"https:\/\/tobykskgd.life\/?p=3669"},"modified":"2025-12-23T16:00:11","modified_gmt":"2025-12-23T08:00:11","slug":"123","status":"publish","type":"post","link":"https:\/\/tobykskgd.life\/index.php\/123\/","title":{"rendered":"\u7edf\u8ba1\u5b66\u671f\u672b\u590d\u4e60"},"content":{"rendered":"\n<p>\u7531\u4e8e\u516c\u5f0f\u7b49\u683c\u5f0f\u95ee\u9898\uff0c\u535a\u5ba2\u91cc\u53ea\u653e\u4e86\u524d\u4e24\u7ae0\uff0c\u5b8c\u6574\u7684\u5185\u5bb9\u653e\u5728\u4e0b\u9762\u7684 PDF \u4f9b\u4e0b\u8f7d\u3002<\/p>\n\n\n\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"https:\/\/tobykskgd.life\/wp-content\/uploads\/2025\/12\/\u7edf\u8ba1\u5b66\u671f\u672b\u590d\u4e60.pdf\" type=\"application\/pdf\" style=\"width:100%;height:600px\" aria-label=\"\u5d4c\u5165 \u7edf\u8ba1\u5b66\u671f\u672b\u590d\u4e60\"><\/object><a id=\"wp-block-file--media-ebb1afc7-00ae-446d-9278-cbf3a44a659b\" href=\"https:\/\/tobykskgd.life\/wp-content\/uploads\/2025\/12\/\u7edf\u8ba1\u5b66\u671f\u672b\u590d\u4e60.pdf\">\u7edf\u8ba1\u5b66\u671f\u672b\u590d\u4e60<\/a><a href=\"https:\/\/tobykskgd.life\/wp-content\/uploads\/2025\/12\/\u7edf\u8ba1\u5b66\u671f\u672b\u590d\u4e60.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-ebb1afc7-00ae-446d-9278-cbf3a44a659b\">\u4e0b\u8f7d<\/a><\/div>\n\n\n\n<h2 class=\"wp-block-heading\">\u7b2c 1 \u7ae0\uff1a\u6570\u636e\u7684\u6536\u96c6\u4e0e\u62bd\u6837<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">1.1 \u603b\u4f53\u4e0e\u6837\u672c<\/h3>\n\n\n\n<h4 class=\"wp-block-heading\">1.1.1 \u6570\u636e<\/h4>\n\n\n\n<p>\u6570\u636e\uff1a\u53ef\u4ee5\u662f\u6570\u5b57\u3001\u8868\u683c\u3001\u6587\u5b57\u3001\u8bed\u97f3\u3001\u56fe\u7247\u3001\u89c6\u9891<\/p>\n\n\n\n<p><strong>\u6570\u636e\u96c6<\/strong> (dataset)\uff1a<em>\u5728\u7279\u5b9a\u7814\u7a76\u4e2d\u6536\u96c6<\/em>\u5230\u7684<strong>\u6570\u636e\u96c6\u5408<\/strong><\/p>\n\n\n\n<p>\u5143\u7d20(element)\uff1a\u6570\u636e\u7684\u91c7\u96c6\u5bf9\u8c61<\/p>\n\n\n\n<p>\u53d8\u91cf(variable)\uff1a\u5143\u7d20\u7684\u67d0\u4e2a\u7279\u5f81<\/p>\n\n\n\n<p>\u89c2\u6d4b\u503c(observation)\uff1a\u9488\u5bf9\u67d0\u4e2a\u5143\u7d20\u6240\u91c7\u96c6\u7684\u53d8\u91cf\u53d6\u503c<\/p>\n\n\n\n<p>| <em>\u6570\u636e\u8d8a\u591a\u5e76\u4e0d\u5fc5\u7136\u610f\u5473\u7740\u53ef\u4ee5\u5229\u7528\u7684\u6709\u7528\u4fe1\u606f\u8d8a\u591a\uff0c\u5408\u7406\u7684\u62bd\u6837\u65b9\u6cd5 (sampling method)\u975e\u5e38\u91cd\u8981\u3002<\/em><\/p>\n\n\n\n<h4 class=\"wp-block-heading\">1.1.2 \u62bd\u6837\u65b9\u6cd5<\/h4>\n\n\n\n<p><strong>\u603b\u4f53<\/strong>(population)\uff1a\u6211\u4eec\u7814\u7a76\u4e2d\u611f\u5174\u8da3\u7684\u6240\u6709\u5143\u7d20\u7684\u96c6\u5408<\/p>\n\n\n\n<p><strong>\u6837\u672c<\/strong>(sample)\uff1a\u4ece\u603b\u4f53\u4e2d\u62bd\u53d6\u7684\u90e8\u5206\u4e2a\u4f53\u5f62\u6210\u7684\u96c6\u5408<\/p>\n\n\n\n<p><strong>\u62bd\u6837<\/strong>\uff1a\u63d0\u53d6\u8fc7\u7a0b\u662f\u4e00\u79cd\u62bd\u6837\u3002\u62bd\u6837\u65b9\u6848\u548c\u7814\u7a76\u76ee\u7684\u3001<strong>\u76ee\u6807\u603b\u4f53 (target population)<\/strong> \u7684\u7279\u70b9\u90fd\u6709\u5173\u8054<\/p>\n\n\n\n<p>\u62bd\u6837\u65b9\u6848\u8bbe\u8ba1\u4e0d\u5f53\u4f1a\u5bfc\u81f4\u62bd\u6837\u603b\u4f53(sampled population) \u4e0e\u76ee\u6807\u603b\u4f53\u4e0d\u4e00\u81f4\uff0c\u62bd\u53d6\u7684\u6570\u636e\u5f88\u53ef\u80fd\u5e26\u6765\u7ed3\u8bba\u6027\u8c2c\u8bef<\/p>\n\n\n\n<p><em>\u62bd\u6837\u603b\u4f53\u4e0e\u76ee\u6807\u603b\u4f53\u51fa\u73b0\u504f\u5dee\uff0c\u7ed3\u8bba\u4e5f\u5c31\u53ef\u80fd\u4e0d\u6b63\u786e<\/em><\/p>\n\n\n\n<p><strong>\u53c2\u6570<\/strong>(parameter)\uff1a\u63cf\u8ff0<strong>\u603b\u4f53\u7279\u5f81<\/strong>\u7684\u6982\u62ec\u6027\u5ea6\u91cf<\/p>\n\n\n\n<p><strong>\u7edf\u8ba1\u91cf<\/strong>(statistic)\uff1a\u6839\u636e<strong>\u6837\u672c\u6570\u636e<\/strong>\u8ba1\u7b97\u51fa\u6765\u7528\u4e8e<strong>\u63cf\u8ff0\u6216\u4f30\u8ba1\u603b\u4f53\u7279\u5f81<\/strong>\u7684\u6982\u62ec\u6027\u5ea6\u91cf\u3002<strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\">\u662f\u6837\u672c\u7684\u51fd\u6570\uff0c\u4e0d\u4f9d\u8d56\u4e8e\u4efb\u4f55\u672a\u77e5\u7684\u603b\u4f53\u53c2\u6570\u3002<\/mark><\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/tobykskgd.life\/wp-content\/uploads\/2025\/12\/1_1-1-1024x413.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"413\" data-original=\"https:\/\/tobykskgd.life\/wp-content\/uploads\/2025\/12\/1_1-1-1024x413.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-3674\"  sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/tobykskgd.life\/wp-content\/uploads\/2025\/12\/1_2-1024x369.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"369\" data-original=\"https:\/\/tobykskgd.life\/wp-content\/uploads\/2025\/12\/1_2-1024x369.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-3675\"  sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div><\/figure>\n\n\n\n<p><strong>\u7edf\u8ba1\u63a8\u65ad<\/strong>(statistical inference)\uff1a \u57fa\u4e8e\u6837\u672c\u6570\u636e\u5bf9\u603b\u4f53\u7684\u7279\u5f81\u8fdb\u884c\u63a8\u65ad<\/p>\n\n\n\n<p><strong>\u5b9e\u9a8c\u8bbe\u8ba1 (experimental design)<\/strong>\uff1a\u7edf\u8ba1\u5b66\u5bb6\u901a\u8fc7\u4e00\u4e9b\u8bbe\u8ba1\u65b9\u6848\uff0c\u4ece\u603b\u4f53\u4e2d\u62bd\u53d6\u6837\u672c\u6570\u636e<\/p>\n\n\n\n<p><strong>\u89c2\u5bdf\u6027\u7814\u7a76(observational study)<\/strong>\uff1a\u5728\u5df2\u7ecf\u751f\u6210\u7684\u6570\u636e\u96c6\u4e2d\uff0c\u6309\u7167\u67d0\u79cd\u51c6\u5219\u62bd\u53d6\u90e8\u5206\u6216\u5168\u90e8\u6837\u672c\u6570\u636e\u8fdb\u884c\u5206\u6790<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/tobykskgd.life\/wp-content\/uploads\/2025\/12\/1_1-1024x482.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"482\" data-original=\"https:\/\/tobykskgd.life\/wp-content\/uploads\/2025\/12\/1_1-1024x482.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-3670\"  sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u6982\u7387\u62bd\u6837\uff1a\u80fd\u8c08\u201c\u62bd\u6837\u8bef\u5dee\/\u63a8\u65ad\u201d\uff0c\u66f4\u6b63\u89c4\n<ul class=\"wp-block-list\">\n<li><strong>\u7b80\u5355\u968f\u673a\u62bd\u6837\uff08SRS\uff09<\/strong>\uff1a\u603b\u4f53\u4e2d\u6bcf\u4e2a\u5143\u7d20<strong>\u4ee5\u76f8\u540c\u6982\u7387<\/strong>\u88ab\u72ec\u7acb\u62bd\u53d6\uff1b\u5206<strong>\u6709\u653e\u56de\/\u65e0\u653e\u56de<\/strong>\u3002\n<ul class=\"wp-block-list\">\n<li>\u91cd\u590d\u62bd\u6837\uff1a\u91cd\u590d\u62bd\u6837\u8868\u793a\u4e00\u4e2a\u5143\u7d20\u88ab\u62bd\u4e2d\u4e4b\u540e\uff0c\u8fd8\u6709\u53ef\u80fd\u88ab\u7ee7\u7eed\u62bd\u53d6\u51fa\u6765<\/li>\n\n\n\n<li>\u4e0d\u91cd\u590d\u62bd\u6837\uff1a\u4e0d\u91cd\u590d\u62bd\u6837\u5219\u4e0d\u4f1a\u5982\u6b64<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>\u7cfb\u7edf\u968f\u673a\u62bd\u6837<\/strong>\uff1a\u5148\u7f16\u53f7\uff0c<strong>\u968f\u673a\u5b9a\u7b2c\u4e00\u4e2a<\/strong>\uff0c<strong>\u518d\u6309\u56fa\u5b9a\u95f4\u9694\u62bd<\/strong>\uff1b\u4f18\u70b9\u662f\u7701\u4e8b\/\u7ecf\u6d4e\uff0c\u4f46\u82e5\u603b\u4f53\u5b58\u5728<strong>\u5468\u671f\u6027<\/strong>\u4f1a\u51fa\u95ee\u9898\u3002<\/li>\n\n\n\n<li><strong>\u5206\u5c42\u968f\u673a\u62bd\u6837<\/strong>\uff1a<strong>\u5148\u5206\u5c42\uff08Stratum\uff09<\/strong>\uff0c<strong>\u6bcf\u5c42\u5185\u518d\u505a\u7b80\u5355\u968f\u673a\u62bd\u6837<\/strong>\uff1b\u5173\u952e\u662f<strong>\u5c42\u5185\u5dee\u5f02\u5c0f<\/strong>\u65f6\u8d28\u91cf\u9ad8\uff0c\u4e14\u9002\u5408\u201c\u4e0d\u5e73\u8861\u7ec4\u201d\u3002<\/li>\n\n\n\n<li><strong>\u6574\u7fa4\u62bd\u6837\uff08Cluster\uff09<\/strong>\uff1a\u5148\u5206\u6210\u4e92\u4e0d\u76f8\u4ea4\u7684<strong>\u7fa4<\/strong>\uff0c\u518d\u968f\u673a\u62bd\u82e5\u5e72\u4e2a\u7fa4\uff1b\u5e0c\u671b<strong>\u7fa4\u5185\u5dee\u5f02\u5927<\/strong>\u3001\u4e14\u62bd\u5230\u7684\u7fa4\u6574\u4f53\u5206\u5e03\u50cf\u603b\u4f53\u65f6\u6548\u679c\u597d\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u975e\u6982\u7387\u62bd\u6837\uff1a\u5feb\uff0c\u4f46\u4ee3\u8868\u6027\/\u63a8\u65ad\u80fd\u529b\u5f31\n<ul class=\"wp-block-list\">\n<li><strong>\u4fbf\u5229\u62bd\u6837<\/strong>\uff1a<strong>\u56fe\u65b9\u4fbf\uff0c\u4e0d\u6309\u6982\u7387<\/strong>\uff1b\u75ab\u82d7\u4eba\u4f53\u8bd5\u9a8c\u62db\u52df\u5fd7\u613f\u8005\u7684\u4f8b\u5b50\uff1a\u4f26\u7406\u4e0a\u53ef\u884c\uff0c\u4f46\u4ee3\u8868\u6027\u53ef\u80fd\u4e0d\u8db3\u3002<\/li>\n\n\n\n<li><strong>\u5224\u65ad\u62bd\u6837<\/strong>\uff1a\u6309\u7814\u7a76\u8005\u7ecf\u9a8c\/\u51c6\u5219\u6311\u6837\u672c\uff08\u4f8b\u5982\u201c\u4e24\u4f1a\u201d\u8bb0\u8005\u6311\u4ee3\u8868\u63d0\u95ee\uff09\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p>\u5206\u5c42 vs \u6574\u7fa4\uff08\u6613\u6df7\uff09<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u5206\u5c42\u62bd\u6837<\/strong>\uff1a\u8ffd\u6c42\u201c\u5c42\u5185\u540c\u8d28\u201d\uff08\u5c42\u5185\u5dee\u5f02\u5c0f\uff09<\/li>\n\n\n\n<li><strong>\u6574\u7fa4\u62bd\u6837<\/strong>\uff1a\u5e0c\u671b\u201c\u7fa4\u5185\u5f02\u8d28\u201d\uff08\u7fa4\u5185\u5dee\u5f02\u5927\uff09\u4e14\u7fa4\u7684\u5206\u5e03\u50cf\u603b\u4f53<\/li>\n<\/ul>\n\n\n\n<p><em><strong>\u5206\u5c42\u662f\u4e3a\u4e86\u66f4\u7cbe\u786e\uff08\u63a7\u5dee\u5f02\uff09\uff0c\u6574\u7fa4\u662f\u4e3a\u4e86\u66f4\u7701\u6210\u672c\uff08\u62bd\u4e00\u7247\uff09<\/strong>\u3002<\/em><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">1.2 \u62bd\u6837\u65b9\u6cd5\u5728\u5927\u6570\u636e\u65f6\u4ee3\u7684\u5e94\u7528<\/h3>\n\n\n\n<p><strong>\u6d77\u91cf\u6570\u636e\u5206\u5e03\u5f0f\u5b58\u50a8<\/strong> + <strong>\u9690\u79c1\u8981\u6c42\u9ad8<\/strong>\uff0c\u5bfc\u81f4\u4e0d\u80fd\u628a\u6570\u636e\u5168\u6c47\u603b\u5230\u4e00\u8d77\u5206\u6790\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u5206\u5e03\u5f0f\u7edf\u8ba1\u63a8\u65ad<\/strong>\uff1a\u4e0d\u5408\u5e76\u539f\u59cb\u6570\u636e\uff0c\u4f20\u9012\u201c\u6c47\u603b\u91cf\u201d\uff08\u4f8b\u5982\u5404\u57ce\u5e02\u6837\u672c\u548c\uff09\u6765\u4f30\u8ba1\u53c2\u6570\uff08\u5982\u6b63\u6001\u603b\u4f53\u7684\u5747\u503c\uff09\u3002<\/li>\n\n\n\n<li>\u5f53\u6570\u636e\u5927\u5230\u8fde\u7b97\u5747\u503c\u90fd\u6210\u672c\u9ad8\u65f6\uff0c\u53ef\u4ee5\u5728\u6bcf\u4e2a\u8282\u70b9<strong>\u968f\u673a\u62bd\u6837<\/strong>\uff08\u598210\u4e07\u62bd1000\uff09\u6765\u964d\u8ba1\u7b97\u6210\u672c\u3002<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">\u7b2c 2 \u7ae0\uff1a\u6570\u636e\u7684\u6574\u7406\u4e0e\u53ef\u89c6\u5316<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">2.1 \u6570\u636e\u7684\u5206\u7c7b<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u6309<strong>\u8ba1\u91cf\u5c3a\u5ea6<\/strong>\u5206\u7c7b<\/li>\n\n\n\n<li><strong>\u5b9a\u6027\u6570\u636e\uff08qualitative data\uff09\/ \u5c5e\u6027\u6570\u636e\uff08categorical data\uff09<\/strong>\uff1a\u53ea\u80fd\u5f52\u4e8e\u67d0\u4e00\u7c7b\u522b\u7684<strong>\u975e\u6570\u5b57<\/strong>\u578b\u6570\u636e\n<ul class=\"wp-block-list\">\n<li><strong>\u540d\u4e49\u6570\u636e\uff08nominal data\uff09<\/strong>\uff1a\u5404\u7c7b\u522b\u4e4b\u95f4<strong>\u6ca1\u6709\u5e8f<\/strong>\u7684\u5173\u7cfb\u3002\u4f8b\u5982\uff0c\u6027\u522b (\u7537\u3001\u5973)\u3001\u5a5a\u59fb\u72b6\u51b5\uff08\u672a\u5a5a\u3001\u5df2\u5a5a\uff09\u7b49\u3002<\/li>\n\n\n\n<li><strong>\u5b9a\u5e8f\u6570\u636e\uff08ordinal data\uff09<\/strong>\uff1a\u5404\u7c7b\u522b\u4e4b\u95f4<strong>\u6709\u5e8f<\/strong>\u7684\u5173\u7cfb\u3002\u4f8b\u5982\uff0c\u6587\u5316\u7a0b\u5ea6\uff08\u6587\u76f2\u3001\u5c0f\u5b66\u3001\u521d\u4e2d\u3001\u9ad8\u4e2d\u3001\u5927\u5b66\uff09\u7b49\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>\u5b9a\u91cf\u6570\u636e\uff08quantitative data\uff09\/ \u6570\u503c\u6570\u636e\uff08numerical data\uff09<\/strong>\uff1a\u6309<strong>\u6570\u5b57<\/strong>\u5c3a\u5ea6\u6d4b\u91cf\u7684\u6570\u636e\u3002\u4f8b\u5982\uff0c\u8eab\u9ad8\u3001\u4f53\u91cd\uff08\u8fde\u7eed\u6570\u636e\uff09\uff0c\u67d0\u5730\u533a\u6bcf\u5929\u7684\u4ea4\u901a\u4e8b\u6545\u6570\uff08\u8ba1\u6570\u6570\u636e\uff09\u3002<\/li>\n\n\n\n<li>\u6309<strong>\u6536\u96c6\u65b9\u6cd5<\/strong>\u5206\u7c7b<\/li>\n\n\n\n<li><strong>\u89c2\u6d4b\u6570\u636e\uff08observational data\uff09<\/strong>\uff1a\u901a\u8fc7\u8c03\u67e5\u6216\u89c2\u6d4b\u6536\u96c6\u5230\u7684\u6570\u636e\uff0c<strong>\u65e0\u4eba\u4e3a\u63a7\u5236<\/strong>\u3002\u4f8b\u5982\uff0c\u793e\u4f1a\u7ecf\u6d4e\u7684\u5927\u591a\u6570\u6570\u636e\u3002<\/li>\n\n\n\n<li><strong>\u5b9e\u9a8c\u6570\u636e\uff08experimental data\uff09<\/strong>\uff1a\u5728\u5b9e\u9a8c\u4e2d<strong>\u63a7\u5236\u5b9e\u9a8c\u5bf9\u8c61<\/strong>\u800c\u6536\u96c6\u5230\u7684\u6570\u636e\u3002\u4f8b\u5982\uff0c\u81ea\u7136\u79d1\u5b66\u3001\u533b\u5b66\u7b49\u9886\u57df\u7684\u5927\u591a\u6570\u6570\u636e\u3002<\/li>\n\n\n\n<li>\u6309<strong>\u63cf\u8ff0\u5bf9\u8c61\u4e0e\u65f6\u95f4\u5173\u7cfb<\/strong>\u5206\u7c7b<\/li>\n\n\n\n<li><strong>\u622a\u9762\u6570\u636e\uff08cross-sectional data\uff09<\/strong>\uff1a\u5728<strong>\u540c\u4e00\u65f6\u95f4\u622a\u9762<\/strong>\u4e0a\u6536\u96c6\u7684\u4e0d\u540c\u5bf9\u8c61\u7684\u6570\u636e\u3002<strong>\u9759\u6001\u6570\u636e\uff08\u540c\u4e00\u65f6\u95f4\uff0c\u4e0d\u540c\u7a7a\u95f4\uff09<\/strong>\u3002\u4f8b\u5982\uff0c2010\u5e74\u6211\u56fd\u5404\u7701\u533a\u7684\u56fd\u5185\u751f\u4ea7\u603b\u503c\u3002<\/li>\n\n\n\n<li><strong>\u65f6\u95f4\u5e8f\u5217\u6570\u636e\uff08time series data\uff09<\/strong>\uff1a\u5728<strong>\u4e0d\u540c\u65f6\u70b9<\/strong>\u4e0a\u6536\u96c6\u5230\u7684\u6570\u636e\u3002<strong>\u52a8\u6001\u6570\u636e\uff08\u4e0d\u540c\u65f6\u95f4\uff0c\u540c\u4e00\u7a7a\u95f4\uff09<\/strong>\u3002\u4f8b\u5982\uff0c\u4e0a\u6d77\u5e02\u8fc7\u53bb\u4e00\u5e74\u7684\u6bcf\u65e5\u6c14\u6e29\u3002<\/li>\n\n\n\n<li><strong>\u9762\u677f (\u6216\u7eb5\u5411) \u6570\u636e\uff08panel\/longitudinal data\uff09<\/strong> \/ \u65f6\u95f4\u5e8f\u5217\u4e0e\u622a\u9762\u6df7\u5408\u6570\u636e\uff1a\u5177\u6709<strong>\u6a2a\u622a\u9762\u548c\u65f6\u95f4\u5e8f\u5217<\/strong>\u4e24\u4e2a\u7ef4\u5ea6<strong>\uff08\u4e0d\u540c\u65f6\u95f4\uff0c\u4e0d\u540c\u7a7a\u95f4\uff09<\/strong>\u3002\u4f8b\u5982\uff0c2010\u5e74\u223c2023\u5e74\u6211\u56fd\u5404\u7701\u533a\u6bcf\u5e74\u4eba\u5747\u56fd\u6c11\u751f\u4ea7\u603b\u503c\u3002<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-large\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/tobykskgd.life\/wp-content\/uploads\/2025\/12\/2_1-1024x560.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"560\" data-original=\"https:\/\/tobykskgd.life\/wp-content\/uploads\/2025\/12\/2_1-1024x560.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-3681\"  sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">2.2 \u6570\u636e\u7684\u6574\u7406<\/h3>\n\n\n\n<h4 class=\"wp-block-heading\">2.2.1 \u5b9a\u6027\u6570\u636e\u7684\u6574\u7406<\/h4>\n\n\n\n<p>\u5bf9\u4e8e\u5c5e\u6027\u6570\u636e \/ \u5b9a\u6027\u6570\u636e\uff0c\u4e3b\u8981\u6c47\u603b\u6bcf\u4e00\u4e2a\u7c7b\u7684\u9891\u6570\u3001\u9891\u7387\u3001\u767e\u5206\u6bd4\u9891\u7387\uff0c\u4ee5\u4fbf\u4e86\u89e3\u9891\u6570\u5206\u5e03\u548c\u5404\u7c7b\u95f4\u7684\u5dee\u5f02\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u9891\u6570\uff1a\u843d\u5728\u67d0\u4e00\u7279\u5b9a\u7c7b\u522b\u6216\u7ec4\u4e2d\u7684\u6570\u636e\u4e2a\u6570\u79f0\u4e3a\u9891\u6570<\/li>\n\n\n\n<li>\u9891\u6570\u5206\u5e03\uff1a\u628a\u5404\u4e2a\u7c7b\u522b\u53ca\u843d\u5728\u5176\u4e2d\u7684\u76f8\u5e94\u9891\u6570\u5168\u90e8\u5217\u51fa\uff0c\u5e76\u4e14\u7528\u8868\u683c\u8868\u793a\uff0c\u79f0\u4e3a\u9891\u6570\u5206\u5e03<\/li>\n\n\n\n<li>\u7b80\u5355\u9891\u6570\u8868\uff1a\u9488\u5bf9\u4e00\u4e2a\u5206\u7c7b\u53d8\u91cf\u751f\u6210\u7684\u9891\u6570\u5206\u5e03\u8868<\/li>\n\n\n\n<li>\u5217\u8054\u8868\uff1a\u6839\u636e\u4e24\u4e2a\u5206\u7c7b\u53d8\u91cf\u751f\u6210\u7684\u9891\u6570\u5206\u5e03\u8868\uff0c\u4e5f\u79f0\u4e3a\u4ea4\u53c9\u8868<\/li>\n<\/ul>\n\n\n\n<h5 class=\"wp-block-heading\">2.2.1.1 \u9891\u6570\u8868<\/h5>\n\n\n\n<p><strong>\u7b80\u5355\u9891\u6570\u5206\u5e03\u8868<\/strong>\u5982\u4e0b\u6240\u793a\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-resized\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/tobykskgd.life\/wp-content\/uploads\/2025\/12\/2_2-1024x347.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"347\" data-original=\"https:\/\/tobykskgd.life\/wp-content\/uploads\/2025\/12\/2_2-1024x347.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-3683\" style=\"aspect-ratio:2.951089641543613;width:711px;height:auto\"  sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div><\/figure>\n\n\n\n<p><strong>\u9891\u6570\u9891\u7387\u5206\u5e03\u8868<\/strong>\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-resized\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/tobykskgd.life\/wp-content\/uploads\/2025\/12\/2_3-1024x408.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"408\" data-original=\"https:\/\/tobykskgd.life\/wp-content\/uploads\/2025\/12\/2_3-1024x408.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-3684\" style=\"aspect-ratio:2.5099210980904805;width:685px;height:auto\"  sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div><\/figure>\n\n\n\n<h5 class=\"wp-block-heading\">2.2.1.2 \u5217\u8054\u8868<\/h5>\n\n\n\n<p>\u5bf9\u4e8e<strong>\u4e24\u4e2a(\u6216\u591a\u4e2a)\u5c5e\u6027\u6570\u636e<\/strong>\uff0c\u901a\u8fc7<strong>\u5217\u8054\u8868\uff08contingency table\uff09<\/strong>\u5c06\u5404\u4e2a\u5c5e\u6027\u7684<strong>\u4ea4\u53c9\u5206\u7c7b\u8054\u5408\u8ba1\u6570<\/strong>\uff0c\u4ee5\u4fbf\u4e86\u89e3\u53d8\u91cf\u4e4b\u95f4\u662f\u5426\u5b58\u5728\u5173\u8054\u6027\u3002<\/p>\n\n\n\n<p>\u5728\u4e24\u4e2a\u5c5e\u6027\u6570\u636e\u7684\u5217\u8054\u8868\u4e2d\uff0c\u4e24\u4e2a\u53d8\u91cf\u5206\u522b\u79f0\u4e3a<strong>\u884c\u53d8\u91cf<\/strong>\u548c<strong>\u5217\u53d8\u91cf<\/strong><\/p>\n\n\n\n<p>\u5982\u679c\u884c\u53d8\u91cf\u6709r\u7c7b\uff0c\u5217\u53d8\u91cf\u6709c\u7c7b\uff0c\u4ea4\u53c9\u5206\u7c7b\u540e\u5f97\u5230\u7684\u5217\u8054\u8868\u79f0\u4e3a r \u00d7 c \u5217\u8054\u8868<\/p>\n\n\n\n<p>\u5355\u5143\u683c\u7684\u6570\u503c ??? \u8868\u793a\u884c\u53d8\u91cf\u7b2c i \u7c7b\u4e0e\u5217\u53d8\u91cf\u7b2c j \u7c7b\u7684\u8054\u5408\u9891\u6570<\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-resized\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/tobykskgd.life\/wp-content\/uploads\/2025\/12\/2_4-1024x579.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"579\" data-original=\"https:\/\/tobykskgd.life\/wp-content\/uploads\/2025\/12\/2_4-1024x579.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-3685\" style=\"aspect-ratio:1.7685955850906339;width:624px;height:auto\"  sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div><\/figure>\n\n\n\n<p>\u5217\u8054\u8868\u7ecf\u5e38\u7528<strong>\u767e\u5206\u6bd4\u5f62\u5f0f<\/strong>\u8868\u793a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u5355\u5143\u683c\u9891\u6570\u5360\u603b\u6570\u7684\u6bd4\u4f8b???\/?\u79f0\u4e3a\u603b\u548c\u767e\u5206\u6bd4<\/li>\n\n\n\n<li>\u5355\u5143\u683c\u9891\u6570\u5360\u884c\u603b\u6570\u7684\u6bd4\u4f8b???\/??\u2219\u79f0\u4e3a\u884c\u767e\u5206\u6bd4<\/li>\n\n\n\n<li>\u5355\u5143\u683c\u9891\u6570\u5360\u5217\u603b\u6570\u7684\u6bd4\u4f8b???\/?\u2219?\u79f0\u4e3a\u5217\u767e\u5206\u6bd4<\/li>\n<\/ul>\n\n\n\n<p>\u76f8\u8f83\u4e8e\u8ba1\u6570\u5f62\u5f0f\uff0c\u767e\u5206\u6bd4\u5217\u8054\u8868\u66f4\u5bb9\u6613\u89c2\u5bdf\u53d8\u91cf\u95f4\u7684\u5173\u7cfb<\/p>\n\n\n\n<p><strong>\u603b\u548c\u767e\u5206\u6bd4\u5217\u8054\u8868<\/strong>\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-resized\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/tobykskgd.life\/wp-content\/uploads\/2025\/12\/2_5-1024x432.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"432\" data-original=\"https:\/\/tobykskgd.life\/wp-content\/uploads\/2025\/12\/2_5-1024x432.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-3687\" style=\"aspect-ratio:2.3685949684980394;width:727px;height:auto\"  sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div><\/figure>\n\n\n\n<p><strong>\u5217\u767e\u5206\u6bd4\u5217\u8054\u8868<\/strong>\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-resized\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/tobykskgd.life\/wp-content\/uploads\/2025\/12\/2_6-1024x488.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"488\" data-original=\"https:\/\/tobykskgd.life\/wp-content\/uploads\/2025\/12\/2_6-1024x488.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-3688\" style=\"aspect-ratio:2.0999179719542207;width:731px;height:auto\"  sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\">2.2.2 \u5b9a\u91cf\u6570\u636e\u7684\u6574\u7406<\/h4>\n\n\n\n<p>\u5b9a\u91cf\u6570\u636e\u540c\u6837\u53ef\u4ee5\u6574\u7406\u6c47\u603b\u6210\u9891\u6570\u5206\u5e03\u8868\u3002\u5bf9<strong>\u5b9a\u91cf\u6570\u636e\u7f16\u5236\u9891\u6570\u5206\u5e03\u8868<\/strong>\u7684\u4e00\u822c\u6b65\u9aa4\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u786e\u5b9a\u533a\u95f4\u6570\u548c\u533a\u95f4\u5bbd\u5ea6<\/strong>\uff1a\u5148\u786e\u5b9a\u533a\u95f4\u6570\uff0c\u518d\u786e\u5b9a\u533a\u95f4\u5bbd\u5ea6\uff08\u7ec4\u8ddd\uff09 \u533a\u95f4\u6570\u901a\u5e38\u4e3a 5 \u223c 20 \u4e2a\uff0c\u533a\u95f4\u901a\u5e38\u53d6\u4e3a\u7b49\u5bbd \u7b49\u5bbd\u60c5\u5f62\u4e0b\uff0c\u5bbd\u5ea6\u53ef\u4ee5\u901a\u8fc7\u201c\u6570\u636e\u6781\u5dee\/\u533a\u95f4\u6570\u201d\u6765\u8fd1\u4f3c <strong>\u7ec4\u8ddd d = (\u6700\u5927\u503c &#8211; \u6700\u5c0f\u503c) \u00f7 \u7ec4\u6570<\/strong><\/li>\n\n\n\n<li><strong>\u8bbe\u5b9a\u533a\u95f4\u7aef\u70b9<\/strong>\uff1a\u7b2c\u4e00\u7ec4\u4e0b\u9650\u7565\u5c0f\u4e8e\u6700\u5c0f\u503c\uff0c\u6700\u540e\u4e00\u7ec4\u4e0a\u9650\u7565\u5927\u4e8e\u6700\u5927\u503c\uff0c\u786e\u4fdd\u6240\u6709\u6570\u636e\u5747\u88ab\u8986\u76d6\uff0c\u4e14\u6bcf\u4e2a\u503c\u53ea\u5c5e\u4e8e\u4e00\u4e2a\u533a\u95f4\u3002<\/li>\n\n\n\n<li><strong>\u7edf\u8ba1\u9891\u6570<\/strong>\uff1a\u8ba1\u7b97\u5404\u7ec4\u7684\u9891\u6570\uff0c\u5e76\u5217\u51fa\u9891\u6570\u5206\u5e03\u8868<\/li>\n<\/ol>\n\n\n\n<figure class=\"wp-block-image size-large is-resized\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/tobykskgd.life\/wp-content\/uploads\/2025\/12\/2_7-1024x497.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"497\" data-original=\"https:\/\/tobykskgd.life\/wp-content\/uploads\/2025\/12\/2_7-1024x497.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-3689\" style=\"aspect-ratio:2.0616658996778647;width:753px;height:auto\"  sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">2.3 \u63cf\u8ff0\u6027\u5ea6\u91cf<\/h3>\n\n\n\n<p>\u5bf9\u4e8e\u6574\u7406\u597d\u7684\u6570\u636e\uff0c\u901a\u8fc7\u63cf\u8ff0\u6027\u7edf\u8ba1\u5206\u6790\uff0c\u53ef\u4ee5\u6316\u6398\u51fa\u53d8\u91cf\u7684\u5f88\u591a\u7279\u5f81\uff0c\u4f8b\u5982\u96c6\u4e2d\u8d8b\u52bf\u3001\u79bb\u6563\u7a0b\u5ea6\u548c\u5206\u5e03\u5f62\u6001\u7b49\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">2.3.1 \u96c6\u4e2d\u8d8b\u52bf\u7684\u5ea6\u91cf<\/h4>\n\n\n\n<p><strong>\u96c6\u4e2d\u8d8b\u52bf<\/strong>\u53cd\u6620\u6570\u636e\u5411\u67d0\u4e00\u4e2d\u5fc3\u503c\u805a\u96c6\u7684\u7279\u6027\u3002\u6839\u636e\u4e2d\u5fc3\u503c\u7684\u786e\u5b9a\u65b9\u6cd5\uff0c\u53ef\u5c06\u5176\u6307\u6807\u5206\u4e3a\u4e24\u7c7b\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u6570\u503c\u5e73\u5747\u6570<\/strong>\uff1a\u5229\u7528\u5168\u90e8\u6570\u636e\u8ba1\u7b97\u5f97\u5230\u7684\u5e73\u5747\u6c34\u5e73\uff0c\u4e3b\u8981\u6709\uff1a<\/li>\n\n\n\n<li><strong>\u7b97\u672f\u5e73\u5747\u6570\u3001\u52a0\u6743\u5e73\u5747\u6570\u3001\u51e0\u4f55\u5e73\u5747\u6570<\/strong><\/li>\n\n\n\n<li><strong>\u4f4d\u7f6e\u5e73\u5747\u6570<\/strong>\uff1a\u6839\u636e\u6570\u636e\u7684\u987a\u5e8f\u6216\u9891\u6570\u786e\u5b9a\u7684\u4ee3\u8868\u503c\uff0c\u4e3b\u8981\u6709\uff1a<\/li>\n\n\n\n<li><strong>\u4f17\u6570\u3001\u4e2d\u4f4d\u6570\u3001\u56db\u5206\u4f4d\u6570<\/strong><\/li>\n<\/ul>\n\n\n\n<h5 class=\"wp-block-heading\">2.3.1.1 \u6570\u503c\u5e73\u5747\u6570<\/h5>\n\n\n\n<h6 class=\"wp-block-heading\">\u7b97\u6570\u5e73\u5747\u6570<\/h6>\n\n\n\n<p><strong>\u7b97\u672f\u5e73\u5747\u6570\uff08arithmetic mean\uff09<\/strong>\uff0c\u7b80\u79f0\u4e3a<strong>\u5747\u503c\uff08mean\uff09<\/strong><\/p>\n\n\n\n<p>?\u4e2a\u6837\u672c\u89c2\u6d4b\u503c ?1,?2,\u2026,?? \u7684\u5747\u503c ? <em>hat<\/em> \u5b9a\u4e49\u4e3a\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-resized\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/tobykskgd.life\/wp-content\/uploads\/2025\/12\/2_8-1024x287.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"287\" data-original=\"https:\/\/tobykskgd.life\/wp-content\/uploads\/2025\/12\/2_8-1024x287.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-3690\" style=\"aspect-ratio:3.5678258561189273;width:592px;height:auto\"  sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u6240\u6709\u6570\u636e\u5bf9\u5747\u503c\u7684\u5f71\u54cd\u76f8\u540c\uff0c\u6743\u91cd\u90fd\u662f <strong>1 \/ n<\/strong><\/li>\n\n\n\n<li>\u5747\u503c<strong>\u5bb9\u6613\u53d7\u5230\u6781\u7aef\u503c\u7684\u5f71\u54cd<\/strong><\/li>\n<\/ul>\n\n\n\n<h6 class=\"wp-block-heading\">\u51e0\u4f55\u5e73\u5747\u6570<\/h6>\n\n\n\n<p><strong>\u51e0\u4f55\u5e73\u5747\u6570\uff08geometric mean\uff09<\/strong>\uff1a? \u4e2a\u6837\u672c\u89c2\u6d4b\u503c ?1, ?2,\u2026,?? \u4e58\u79ef\u7684 ? \u6b21\u65b9\u6839<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/tobykskgd.life\/wp-content\/uploads\/2025\/12\/2_9.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"653\" height=\"158\" data-original=\"https:\/\/tobykskgd.life\/wp-content\/uploads\/2025\/12\/2_9.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-3691\" style=\"width:579px;height:auto\"  sizes=\"auto, (max-width: 653px) 100vw, 653px\" \/><\/div><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u51e0\u4f55\u5e73\u5747\u6570\u5e38\u7528\u4e8e<strong>\u6bd4\u7387\u578b\u6570\u636e<\/strong>\uff0c\u9002\u5408\u8ba1\u7b97\u5e73\u5747\u589e\u957f\uff08\u6216\u53d8\u5316\uff09\u7387<\/li>\n\n\n\n<li>\u51e0\u4f55\u5e73\u5747\u6570<strong>\u53d7\u6781\u7aef\u503c\u5f71\u54cd\u8f83\u7b97\u672f\u5e73\u5747\u6570\u66f4\u5c0f<\/strong><\/li>\n<\/ul>\n\n\n\n<h5 class=\"wp-block-heading\">2.3.1.2 \u4f4d\u7f6e\u5e73\u5747\u6570<\/h5>\n\n\n\n<h6 class=\"wp-block-heading\">\u4f17\u6570<\/h6>\n\n\n\n<p><strong>\u4f17\u6570\uff08mode\uff09<\/strong>\uff1a\u4e00\u7ec4\u6570\u636e\u4e2d\u51fa\u73b0\u6b21\u6570\u6700\u591a\u7684\u6570\u503c<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u4f17\u6570<strong>\u53ef\u80fd\u4e0d\u552f\u4e00\uff0c\u4e5f\u53ef\u80fd\u4e0d\u5b58\u5728<\/strong><\/li>\n\n\n\n<li>\u4f17\u6570<strong>\u9002\u7528\u4e8e\u5b9a\u6027\u6570\u636e<\/strong>\u3002<strong>\u5b9a\u91cf\u6570\u636e\u53ef\u80fd\u4e0d\u5b58\u5728\u4f17\u6570<\/strong><\/li>\n\n\n\n<li>\u4f17\u6570<strong>\u4e0d\u6613\u53d7\u6781\u7aef\u503c\u5f71\u54cd<\/strong>\u3002<\/li>\n<\/ul>\n\n\n\n<h6 class=\"wp-block-heading\">\u4e2d\u4f4d\u6570<\/h6>\n\n\n\n<p><strong>\u4e2d\u4f4d\u6570\uff08Median\uff09<\/strong> \uff1a\u6307\u4e00\u7ec4\u6570\u636e\u4ece\u5c0f\u5230\u5927<strong>\u6392\u5e8f<\/strong>\u540e\u5904\u5728<strong>\u4e2d\u95f4\u4f4d\u7f6e\u7684\u6570<\/strong>\u3002\u89c2\u6d4b\u503c ?1,?2,\u2026,?? \u4ece\u5c0f\u5230\u5927\u6392\u5e8f\u4e4b\u540e\u8bb0\u4f5c ?(1) \u2264 ?(2) \u2264 \u22ef \u2264 ?(?)\uff0c\u4e2d\u4f4d\u6570\u4e3a\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/tobykskgd.life\/wp-content\/uploads\/2025\/12\/2_10.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"1023\" height=\"340\" data-original=\"https:\/\/tobykskgd.life\/wp-content\/uploads\/2025\/12\/2_10.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-3692\" style=\"aspect-ratio:3.0088990877035875;width:647px;height:auto\"  sizes=\"auto, (max-width: 1023px) 100vw, 1023px\" \/><\/div><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u4e2d\u4f4d\u6570<strong>\u4e0d\u53d7\u6781\u7aef\u503c\u5f71\u54cd<\/strong><\/li>\n<\/ul>\n\n\n\n<h6 class=\"wp-block-heading\">?-\u5206\u4f4d\u6570<\/h6>\n\n\n\n<p>\u6837\u672c <strong>?-\u5206\u4f4d\u6570\uff08q-quantile\uff09<\/strong>\uff1a\u628a\u987a\u5e8f\u6392\u5217\u7684\u6837\u672c ?(1) \u2264 ?(2) \u2264 \u22ef \u2264 ?(?) \u8fdb\u884c?\u7b49\u5206\u7684\u5206\u5272\u70b9\u5bf9\u5e94\u7684\u6570\u503c\u3002<\/p>\n\n\n\n<p>?-\u5206\u4f4d\u6570\u5c06\u6570\u636e\u5206\u4e3a ? \u4efd\uff0c\u5171\u6709 ?\u22121 \u4e2a\u5206\u5272\u70b9\u3002\u7b2c ? \u4e2a\u5206\u5272\u70b9\u79f0\u4e3a\u7b2c ? \u4e2a ?-\u5206\u4f4d\u6570\uff0c\u8bb0\u4f5c ??(? =1,2,\u2026,? \u22121)\uff0c\u5176\u5b9a\u4e49\u5982\u4e0b\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-resized\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/tobykskgd.life\/wp-content\/uploads\/2025\/12\/2_11-1024x283.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"283\" data-original=\"https:\/\/tobykskgd.life\/wp-content\/uploads\/2025\/12\/2_11-1024x283.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-3693\" style=\"aspect-ratio:3.61508977203954;width:651px;height:auto\"  sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div><\/figure>\n\n\n\n<h6 class=\"wp-block-heading\">\u56db\u5206\u4f4d\u6570<\/h6>\n\n\n\n<p><strong>\u56db\u5206\u4f4d\u6570(quartile)<\/strong>\uff1a\u5c06\u4ece\u5c0f\u5230\u5927\u6392\u5e8f\u540e\u7684\u6570\u636e\u56db\u7b49\u5206\u7684\u4e09\u4e2a\u5206\u5272\u70b9\u5bf9\u5e94\u7684\u6570\u503c\uff0c\u5206\u522b\u79f0\u4e3a\u7b2c\u4e00\u56db\u5206\u4f4d\u6570 ?1\u3001\u7b2c\u4e8c\u56db\u5206\u4f4d\u6570 ?2\uff08\u4e2d\u4f4d\u6570\uff09\u548c\u7b2c\u4e09\u56db\u5206\u4f4d\u6570 ?3\u3002<strong>\u8ba1\u7b97\u516c\u5f0f\u53ef\u4ee5\u5e26\u5165 ?-\u5206\u4f4d\u6570\u7684\uff0c? = 4<\/strong>\u3002<\/p>\n\n\n\n<p>\u4f8b\u5b50\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-resized\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/tobykskgd.life\/wp-content\/uploads\/2025\/12\/2_12-1024x514.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"514\" data-original=\"https:\/\/tobykskgd.life\/wp-content\/uploads\/2025\/12\/2_12-1024x514.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-3694\" style=\"aspect-ratio:1.9928086888831227;width:658px;height:auto\"  sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\">2.3.2 \u79bb\u6563\u7a0b\u5ea6\u7684\u5ea6\u91cf<\/h4>\n\n\n\n<p>\u7528\u6765\u8861\u91cf\u6570\u636e\u7684<strong>\u6563\u5e03\u7a0b\u5ea6<\/strong>\u7684\u7edf\u8ba1\u91cf\u5305\u62ec\uff1a<strong>\u6781\u5dee\u3001\u56db\u5206\u4f4d\u8ddd\u3001\u65b9\u5dee\u548c\u6807\u51c6\u5dee\u3001\u53d8\u5f02\u7cfb\u6570<\/strong>\u7b49\u3002<\/p>\n\n\n\n<h5 class=\"wp-block-heading\">2.3.2.1 \u6781\u5dee<\/h5>\n\n\n\n<p><strong>\u6781\u5dee(range)\uff08\u4e5f\u79f0\u5168\u8ddd\uff09<\/strong>\uff1a\u6570\u636e\u4e2d<strong>\u6700\u5927\u503c\u4e0e\u6700\u5c0f\u503c\u4e4b\u5dee<\/strong>\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/tobykskgd.life\/wp-content\/uploads\/2025\/12\/2_13.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"650\" height=\"161\" data-original=\"https:\/\/tobykskgd.life\/wp-content\/uploads\/2025\/12\/2_13.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-3695\" style=\"width:363px;height:auto\"  sizes=\"auto, (max-width: 650px) 100vw, 650px\" \/><\/div><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u6781\u5dee\u53ea\u6307\u660e\u4e86<strong>\u6837\u672c\u7684\u6700\u5927\u79bb\u6563\u8303\u56f4\uff0c\u672a\u5229\u7528\u5168\u90e8\u6837\u672c\u7684\u4fe1\u606f<\/strong><\/li>\n\n\n\n<li><strong>\u4f18\u70b9<\/strong>\uff1a\u8ba1\u7b97\u7b80\u5355\uff0c\u542b\u4e49\u76f4\u89c2\uff0c\u8fd0\u7528\u65b9\u4fbf<\/li>\n\n\n\n<li><strong>\u7f3a\u70b9<\/strong>\uff1a<strong>\u6613\u53d7\u6781\u7aef\u503c\u5f71\u54cd<\/strong>\uff0c\u4e14\u4e0d\u80fd\u63ed\u793a\u4e2d\u95f4\u6570\u636e\u7684\u5206\u5e03\u60c5\u51b5<\/li>\n<\/ul>\n\n\n\n<h5 class=\"wp-block-heading\">2.3.2.2 \u56db\u5206\u4f4d\u8ddd<\/h5>\n\n\n\n<p><strong>\u56db\u5206\u4f4d\u8ddd(interquartile range)<\/strong>\uff1a\u4e0a\u3001\u4e0b\u56db\u5206\u4f4d\u6570\u4e4b\u5dee\uff0c\u901a\u5e38\u8bb0\u4f5c <strong>???<\/strong>\u3002\u5176\u8ba1\u7b97\u516c\u5f0f\u4e3a\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/tobykskgd.life\/wp-content\/uploads\/2025\/12\/2_14.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"600\" height=\"150\" data-original=\"https:\/\/tobykskgd.life\/wp-content\/uploads\/2025\/12\/2_14.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-3696\" style=\"width:372px;height:auto\"  sizes=\"auto, (max-width: 600px) 100vw, 600px\" \/><\/div><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u56db\u5206\u4f4d\u8ddd<strong>\u53cd\u6620\u4e2d\u95f4 50% \u6570\u636e\u7684\u79bb\u6563\u7a0b\u5ea6<\/strong>\uff0c<strong>\u6570\u503c\u8d8a\u5c0f\u8868\u793a\u96c6\u4e2d\u5ea6\u8d8a\u9ad8\uff0c\u8d8a\u5927\u8868\u793a\u5206\u6563\u5ea6\u8d8a\u5927<\/strong><\/li>\n\n\n\n<li>\u56db\u5206\u4f4d\u8ddd\u5728<strong>\u4e00\u5b9a\u7a0b\u5ea6\u4e0a\u4f53\u73b0\u4e86\u4e2d\u4f4d\u6570\u5bf9\u6570\u636e\u7684\u4ee3\u8868\u6027<\/strong><\/li>\n\n\n\n<li>\u56db\u5206\u4f4d\u8ddd<strong>\u4e0d\u53d7\u6781\u503c\u7684\u5f71\u54cd<\/strong><\/li>\n<\/ul>\n\n\n\n<h5 class=\"wp-block-heading\">2.3.2.3 \u65b9\u5dee\u548c\u6807\u51c6\u5dee<\/h5>\n\n\n\n<p><strong>\u65b9\u5dee(variance)<\/strong>\uff1a\u5bf9\u4e8e\u4e00\u7ec4\u6837\u672c ?1,?2,\u2026,??\uff0c\u5176\u65b9\u5dee ?2 \u7684\u8ba1\u7b97\u516c\u5f0f\u4e3a\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-resized\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/tobykskgd.life\/wp-content\/uploads\/2025\/12\/2_15-1024x196.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"196\" data-original=\"https:\/\/tobykskgd.life\/wp-content\/uploads\/2025\/12\/2_15-1024x196.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-3697\" style=\"aspect-ratio:5.22093813732155;width:616px;height:auto\"  sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u65b9\u5dee\u8861\u91cf<strong>\u6570\u636e\u79bb\u6563\u7a0b\u5ea6<\/strong>\uff0c\u4e5f\u662f\u53cd\u6620\u7cbe\u786e\u5ea6\u7684\u91cd\u8981\u91cf\u5316\u5f62\u5f0f\u3002<\/li>\n\n\n\n<li>\u65b9\u5dee\u7684\u5355\u4f4d\u4e0e\u539f\u59cb\u6570\u636e\u4e0d\u4e00\u81f4\uff0c\u89e3\u91ca\u4e0d\u4fbf\uff0c\u56e0\u6b64\u5e38\u7528<strong>\u65b9\u5dee\u7684\u5e73\u65b9\u6839<\/strong>\u2014\u2014<strong>\u6807\u51c6\u5dee\uff08standard deviation\uff0c\u8bb0\u4f5cs\uff09<\/strong>\u8868\u793a\u6570\u636e\u7684\u5dee\u5f02\u7a0b\u5ea6\u3002<\/li>\n\n\n\n<li>\u65b9\u5dee\u4e3a\u5404\u89c2\u6d4b\u503c\u4e0e\u6837\u672c\u5747\u503c\u7684<strong>\u79bb\u5dee\u5e73\u65b9\u548c\u7684\u5e73\u5747<\/strong>\u3002<\/li>\n\n\n\n<li>\u4e4b\u6240\u4ee5<strong>\u9664\u4ee5 ?\u22121<\/strong> \u800c\u4e0d\u662f ?\uff0c\u662f\u4e3a\u4e86\u5728\u4f30\u8ba1\u603b\u4f53\u65b9\u5dee\u65f6\u66f4\u4e3a\u7cbe\u786e\uff08\u5177\u4f53\u5c06\u5728\u540e\u7eed\u7ae0\u8282\u89e3\u91ca\uff09\u3002<\/li>\n\n\n\n<li><strong>\u65b9\u5dee\u548c\u6807\u51c6\u5dee\u8d8a\u5927\uff0c\u89c2\u6d4b\u503c\u5206\u5e03\u8d8a\u5206\u6563\uff0c\u96c6\u4e2d\u8d8b\u52bf\u8d8a\u5f31\uff1b\u53cd\u4e4b\uff0c\u65b9\u5dee\u548c\u6807\u51c6\u5dee\u8d8a\u5c0f\uff0c\u89c2\u6d4b\u503c\u8d8a\u96c6\u4e2d\uff0c\u96c6\u4e2d\u8d8b\u52bf\u8d8a\u5f3a\u3002<\/strong><\/li>\n<\/ul>\n\n\n\n<h5 class=\"wp-block-heading\">2.3.2.4 \u53d8\u5f02\u7cfb\u6570<\/h5>\n\n\n\n<p><strong>\u53d8\u5f02\u7cfb\u6570(coefficient of variation)\uff08\u4e5f\u79f0\u79bb\u6563\u7cfb\u6570\uff09<\/strong>\uff1a<strong>\u6837\u672c\u7684\u6807\u51c6\u5dee\u4e0e\u5747\u503c\u7684\u6bd4<\/strong>\uff0c\u5373\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/tobykskgd.life\/wp-content\/uploads\/2025\/12\/2_16.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"481\" height=\"203\" data-original=\"https:\/\/tobykskgd.life\/wp-content\/uploads\/2025\/12\/2_16.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-3698\" style=\"width:329px;height:auto\"  sizes=\"auto, (max-width: 481px) 100vw, 481px\" \/><\/div><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u53d8\u5f02\u7cfb\u6570\u662f\u4e00\u79cd<strong>\u76f8\u5bf9\u79bb\u6563\u5ea6\u91cf\uff0c\u65e0\u91cf\u7eb2<\/strong>\u3002\u4e3b\u8981\u7528\u4e8e<strong>\u6bd4\u8f83\u91cf\u7eb2\u4e0d\u540c\u7684\u53d8\u91cf<\/strong>\uff0c\u6216<strong>\u91cf\u7eb2\u76f8\u540c\u4f46\u5747\u503c\u5dee\u5f02\u8f83\u5927<\/strong>\u7684\u53d8\u91cf\u4e4b\u95f4\u7684<strong>\u79bb\u6563\u7a0b\u5ea6<\/strong><\/li>\n\n\n\n<li><strong>\u53d8\u5f02\u7cfb\u6570\u8d8a\u5927\uff0c\u6570\u636e\u8d8a\u5206\u6563\uff1b\u8d8a\u5c0f\uff0c\u6570\u636e\u8d8a\u96c6\u4e2d<\/strong><\/li>\n\n\n\n<li>\u6781\u5dee\u3001\u65b9\u5dee\u548c\u6807\u51c6\u5dee\u5c5e\u4e8e<strong>\u7edd\u5bf9\u79bb\u6563\u6307\u6807<\/strong>\uff0c\u5176\u5927\u5c0f\u4e0d\u4ec5\u53d7\u53d8\u91cf\u6c34\u5e73\u548c\u8ba1\u91cf\u5355\u4f4d\u5f71\u54cd\uff0c\u8fd8<strong>\u53d6\u51b3\u4e8e\u6570\u636e\u7684\u53d8\u5f02\u7a0b\u5ea6<\/strong><\/li>\n<\/ul>\n\n\n\n<p><strong>\u65b9\u5dee VS \u53d8\u5f02\u7cfb\u6570\uff1a<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u4e8c\u8005\u90fd\u53ef\u4ee5\u63cf\u8ff0\u6570\u636e\u7684\u79bb\u6563\u7a0b\u5ea6<\/li>\n\n\n\n<li><strong>\u5747\u503c\u76f8\u540c\u65f6<\/strong>\uff0c\u7528<strong>\u65b9\u5dee<\/strong>\u53ef\u4ee5\u63cf\u8ff0\u79bb\u6563\u7a0b\u5ea6<\/li>\n\n\n\n<li><strong>\u5747\u503c\u4e0d\u540c\u65f6<\/strong>\uff0c\u7528<strong>\u53d8\u5f02\u7cfb\u6570<\/strong>\u63cf\u8ff0\u79bb\u6563\u7a0b\u5ea6<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">2.3.3 \u5206\u5e03\u5f62\u6001\u7684\u5ea6\u91cf<\/h4>\n\n\n\n<h6 class=\"wp-block-heading\">\u504f\u5ea6<\/h6>\n\n\n\n<p><strong>\u504f\u5ea6\uff08skewness\uff09<\/strong>\uff1a\u53c8\u79f0\u504f\u6001\u7cfb\u6570\uff0c\u7528\u4e8e<strong>\u523b\u753b\u6570\u636e\u5206\u5e03\u7684\u504f\u659c\u65b9\u5411\u4e0e\u7a0b\u5ea6<\/strong>\uff0c\u662f<strong>\u8861\u91cf\u5206\u5e03\u975e\u5bf9\u79f0\u6027<\/strong>\u7684\u7edf\u8ba1\u91cf\u3002<\/p>\n\n\n\n<p>\u504f\u5ea6\u5b9a\u4e49\u4e3a\u6837\u672c\u7684\u4e09\u9636\u6807\u51c6\u5316\u77e9\uff0c\u5373\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/tobykskgd.life\/wp-content\/uploads\/2025\/12\/2_17.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"934\" height=\"318\" data-original=\"https:\/\/tobykskgd.life\/wp-content\/uploads\/2025\/12\/2_17.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-3699\" style=\"aspect-ratio:2.9372234059990165;width:514px;height:auto\"  sizes=\"auto, (max-width: 934px) 100vw, 934px\" \/><\/div><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u5f53 SK <strong>\u63a5\u8fd1\u4e8e 0 \u65f6<\/strong>\uff0c\u6570\u636e\u5728\u5747\u503c\u5de6\u53f3<strong>\u5927\u81f4\u5bf9\u79f0<\/strong>\n<ul class=\"wp-block-list\">\n<li>\u5bf9\u4e8e\u5bf9\u79f0\u5206\u5e03\uff0c\u5747\u503c\u4e0e\u4e2d\u4f4d\u6570\u5e94\u975e\u5e38\u63a5\u8fd1<\/li>\n\n\n\n<li><strong>\u6b63\u6001\u5206\u5e03\u7684 SK \u4e3a 0<\/strong><\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u5f53\u6570\u636e\u4e2d\u5b58\u5728\u51e0\u4e2a\u660e\u663e\u504f\u5927\u7684\u503c\u65f6\uff0c<strong>?? &gt;0<\/strong> \n<ul class=\"wp-block-list\">\n<li>\u4ece\u5f62\u6001\u4e0a\u770b\uff0c\u6b64\u65f6\u5206\u5e03\u5411\u53f3\u5ef6\u4f38\u7684\u7a0b\u5ea6\u8fdc\u8fdc\u5927\u4e8e\u5176\u5411\u5de6\u5ef6\u4f38\u7684\u7a0b\u5ea6\uff0c\u6211\u4eec\u79f0\u5206\u5e03\u5448<strong>\u53f3\u504f<\/strong>\uff0c\u4e5f\u79f0<strong>\u6b63\u504f<\/strong><\/li>\n\n\n\n<li>\u5bf9\u4e8e\u53f3\u504f\u5206\u5e03\uff0c\u7531\u4e8e\u5b58\u5728\u6781\u5927\u503c\uff0c\u5747\u503c\u901a\u5e38\u5927\u4e8e\u4e2d\u4f4d\u6570<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u6570\u636e\u4e2d\u5b58\u5728\u51e0\u4e2a\u660e\u663e\u504f\u5c0f\u7684\u503c\u65f6\uff0c<strong>??&lt;0<\/strong> \n<ul class=\"wp-block-list\">\n<li>\u4ece\u5f62\u6001\u4e0a\u770b\uff0c\u6b64\u65f6\u5206\u5e03\u5411\u5de6\u5ef6\u4f38\u7684\u7a0b\u5ea6\u8fdc\u8fdc\u5927\u4e8e\u5176\u5411\u53f3\u5ef6\u4f38\u7684\u7a0b\u5ea6\uff0c\u6211\u4eec\u79f0\u5206\u5e03\u5448<strong>\u5de6\u504f<\/strong>\uff0c\u4e5f\u79f0<strong>\u8d1f\u504f<\/strong><\/li>\n\n\n\n<li>\u5bf9\u4e8e\u5de6\u504f\u5206\u5e03\uff0c\u7531\u4e8e\u5b58\u5728\u6781\u5c0f\u503c\uff0c\u5747\u503c\u901a\u5e38\u5c0f\u4e8e\u4e2d\u4f4d\u6570<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-large\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/tobykskgd.life\/wp-content\/uploads\/2025\/12\/2_18-1024x339.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"339\" data-original=\"https:\/\/tobykskgd.life\/wp-content\/uploads\/2025\/12\/2_18-1024x339.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-3700\"  sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div><\/figure>\n\n\n\n<p><strong><em>\u504f\u5ea6\u63cf\u8ff0\u7684\u662f\u5206\u5e03\u7684\u4e0d\u5bf9\u79f0\u6027\uff1b\u201c\u5de6\u504f\/\u53f3\u504f\u201d\u6307\u7684\u662f\u54ea\u4e00\u4fa7\u7684\u5c3e\u5df4\u66f4\u957f\uff08\u66f4\u6781\u7aef\u3001\u66f4\u62d6\u5c3e\uff09\u3002<\/em><\/strong><\/p>\n\n\n\n<p><strong>\u770b\u201c\u5c3e\u5df4\u201d\u4e0d\u770b\u201c\u5c71\u5cf0\u201d<\/strong><\/p>\n\n\n\n<h6 class=\"wp-block-heading\">\u5cf0\u5ea6<\/h6>\n\n\n\n<p><strong>\u5cf0\u5ea6\uff08kurtosis\uff09<\/strong>\uff1a\u5ea6\u91cf\u6570\u636e\u5206\u5e03\u5728<strong>\u5e73\u5747\u503c\u5904\u5cf0\u503c\u9ad8\u4f4e<\/strong>\u7684\u6570\u5b57\u7279\u5f81<\/p>\n\n\n\n<p>\u5cf0\u5ea6\u5b9a\u4e49\u4e3a<strong>\u6837\u672c\u7684\u56db\u9636\u6807\u51c6\u5316\u77e9\u51cf 3<\/strong>\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/tobykskgd.life\/wp-content\/uploads\/2025\/12\/2_19.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"864\" height=\"272\" data-original=\"https:\/\/tobykskgd.life\/wp-content\/uploads\/2025\/12\/2_19.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-3701\" style=\"aspect-ratio:3.1765540061451194;width:575px;height:auto\"  sizes=\"auto, (max-width: 864px) 100vw, 864px\" \/><\/div><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u5cf0\u5ea6\u662f<strong>\u76f8\u8f83\u4e8e\u6b63\u6001\u5206\u5e03\u800c\u8a00<\/strong>\u7684\uff0c<strong>\u6b63\u6001\u5206\u5e03\u7684\u5cf0\u5ea6\u7b49\u4e8e 0<\/strong><\/li>\n\n\n\n<li>\u82e5 <strong>?&gt;0\uff0c\u5206\u5e03\u8f83\u6b63\u6001\u66f4\u9661\u5ced\uff0c\u79f0\u4e3a\u5c16\u5cf0<\/strong><\/li>\n\n\n\n<li>\u82e5 <strong>?&lt;0\uff0c\u5206\u5e03\u8f83\u6b63\u6001\u66f4\u5e73\u5766\uff0c\u79f0\u4e3a\u5e73\u5cf0<\/strong><\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-large is-resized\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/tobykskgd.life\/wp-content\/uploads\/2025\/12\/2_20-1024x497.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"497\" data-original=\"https:\/\/tobykskgd.life\/wp-content\/uploads\/2025\/12\/2_20-1024x497.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-3702\" style=\"aspect-ratio:2.058350562830232;width:585px;height:auto\"  sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u5c16\u5cf0\u5206\u5e03\u4e24\u7aef\u6781\u503c\u51fa\u73b0\u7684\u6982\u7387\u66f4\u9ad8\uff0c\u56e0\u6b64\u5448\u73b0\u51fa\u539a\u5c3e\u7279\u5f81<\/li>\n\n\n\n<li>\u201c\u5cf0\u5ea6\u9ad8\u201d\u901a\u5e38\u8868\u73b0\u4e3a\uff1a\u66f4\u5c16\u7684\u5cf0 + \u66f4\u539a\u7684\u5c3e<\/li>\n\n\n\n<li>\u76f4\u89c2\u7406\u89e3\uff1a\u5cf0\u5ea6\u9ad8 \u2248 \u201c\u66f4\u5bb9\u6613\u51fa\u73b0\u79bb\u8c31\u503c\uff08outlier\uff09\u201d\u3002<\/li>\n\n\n\n<li><strong>\u539a\u5c3e<\/strong>\u4e0d\u662f\u8bf4\u201c\u5c3e\u5df4\u66f4\u957f\u5f97\u51fa\u53bb\u201d\uff0c\u800c\u662f\u8bf4\uff1a<\/li>\n\n\n\n<li>\u5728\u540c\u6837\u79bb\u5747\u503c\u5f88\u8fdc\u7684\u5730\u65b9\uff0c<strong>\u5c3e\u90e8\u6982\u7387\u66f4\u5927 \/ \u4e0b\u964d\u66f4\u6162<\/strong>\u3002<\/li>\n\n\n\n<li>\u4e0a\u56fe\u6309\u201c<strong>\u5c3e\u90e8\u539a\u8584\uff08\u6781\u7aef\u503c\u51fa\u73b0\u6982\u7387\u5927\u5c0f\/\u8870\u51cf\u901f\u5ea6\u5feb\u6162\uff09<\/strong>\u201d<strong>\u4ece\u539a\u5230\u8584<\/strong>\uff0c<strong>\u5cf0\u5ea6\u4ece\u5927\u5230\u5c0f<\/strong>\u5c31\u662f\uff1a<\/li>\n\n\n\n<li><strong>\u62c9\u666e\u62c9\u65af\uff08\u9ed1\uff09 &gt; \u6b63\u6001\uff08\u7ea2\uff09 &gt; \u5747\u5300\uff08\u7eff\uff09<\/strong>\u3002<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">2.3.4 \u4e24\u4e2a\u53d8\u91cf\u5173\u7cfb\u7684\u63cf\u8ff0<\/h4>\n\n\n\n<p>\u5bf9\u4e8e\u4e24\u4e2a\u5b9a\u91cf\u6570\u636e\uff0c\u6211\u4eec\u53ef\u4ee5\u5b9a\u4e49\u6837\u672c\u534f\u65b9\u5dee\u548c\u6837\u672c\u76f8\u5173\u7cfb\u6570\u6765\u8868\u5f81\u8fd9\u4e24\u4e2a\u5b9a\u91cf\u53d8\u91cf\u95f4\u7ebf\u6027\u76f8\u5173\u5173\u7cfb\u7684\u5f3a\u5f31\u3002<\/p>\n\n\n\n<h6 class=\"wp-block-heading\">\u534f\u65b9\u5dee<\/h6>\n\n\n\n<p>\u5bf9\u4e8e ? \u4e2a\u6837\u672c (?1, ?1), \u2026, (?n, ?n)\uff0c<strong>\u6837\u672c\u534f\u65b9\u5dee\uff08sample covariance\uff09<\/strong>\u5b9a\u4e49\u4e3a\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-resized\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/tobykskgd.life\/wp-content\/uploads\/2025\/12\/2_21-1024x207.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"207\" data-original=\"https:\/\/tobykskgd.life\/wp-content\/uploads\/2025\/12\/2_21-1024x207.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-3703\" style=\"aspect-ratio:4.9366391184573;width:666px;height:auto\"  sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u6837\u672c\u534f\u65b9\u5dee\u662f\u4e00\u4e2a\u6807\u91cf\uff0c\u7528\u4e8e\u63cf\u8ff0\u4e24\u4e2a\u53d8\u91cf<strong>\u7ebf\u6027\u5173\u7cfb<\/strong>\u7684\u65b9\u5411\u548c\u5f3a\u5ea6\uff1a<\/li>\n\n\n\n<li>\u82e5 <strong>??? &gt; 0<\/strong>\uff0c\u8868\u793a<strong>\u6b63\u76f8\u5173<\/strong>\u5173\u7cfb<\/li>\n\n\n\n<li>\u5982\u679c <strong>??? &lt; 0<\/strong>\uff0c\u8868\u793a<strong>\u8d1f\u76f8\u5173<\/strong>\u5173\u7cfb<\/li>\n\n\n\n<li>\u82e5 <strong>??? \u63a5\u8fd1 0<\/strong>\uff0c\u5219\u8bf4\u660e\u4e24\u8005<strong>\u51e0\u4e4e\u65e0\u7ebf\u6027\u5173\u7cfb<\/strong><\/li>\n\n\n\n<li>\u534f\u65b9<strong>\u5dee\u53d7\u91cf\u7eb2\u5f71\u54cd\u8f83\u5927<\/strong>\u3002<\/li>\n\n\n\n<li>\u4f8b\u5982\uff0c\u7814\u7a76\u8eab\u9ad8\u4e0e\u4f53\u91cd\u65f6\uff0c\u5c06\u8eab\u9ad8\u5355\u4f4d\u7531\u7c73\u6539\u4e3a\u5398\u7c73\uff0c\u534f\u65b9\u5dee\u4f1a\u6269\u5927 100 \u500d<\/li>\n\n\n\n<li>\u534f\u65b9\u5dee\u53ef\u4ee5\u53d6\u4efb\u610f\u5b9e\u6570\uff0c<strong>\u65e0\u6cd5\u76f4\u63a5\u53cd\u6620\u76f8\u5173\u5173\u7cfb\u7684\u5f3a\u5f31<\/strong>\u3002 \u56e0\u6b64\uff0c\u7edf\u8ba1\u5b66\u5bb6\u76ae\u5c14\u900a\u63d0\u51fa\u4e86<strong>\u76f8\u5173\u7cfb\u6570<\/strong>\u7684\u6982\u5ff5<\/li>\n<\/ul>\n\n\n\n<h6 class=\"wp-block-heading\">\u76f8\u5173\u7cfb\u6570<\/h6>\n\n\n\n<p><strong>\u6837\u672c\u76f8\u5173\u7cfb\u6570 (sample coefficient of correlation)<\/strong>\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-resized\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/tobykskgd.life\/wp-content\/uploads\/2025\/12\/2_22-1024x408.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"408\" data-original=\"https:\/\/tobykskgd.life\/wp-content\/uploads\/2025\/12\/2_22-1024x408.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-3704\" style=\"aspect-ratio:2.5120321480304657;width:590px;height:auto\"  sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u6837\u672c\u76f8\u5173\u7cfb\u6570\u662f<strong>\u6570\u636e\u6807\u51c6\u5316\u540e\u7684\u534f\u65b9\u5dee<\/strong>\uff0c\u662f\u5254\u9664\u4e86\u4e24\u4e2a\u53d8\u91cf\u91cf\u7eb2\u5f71\u54cd\u540e\u5f97\u5230\u7684\u7edf\u8ba1\u91cf<\/li>\n\n\n\n<li>\u76f8\u5173\u7cfb\u6570\uff1a<\/li>\n\n\n\n<li><strong>\u5927\u4e8e 0 \u8868\u793a\u6b63\u76f8\u5173<\/strong><\/li>\n\n\n\n<li><strong>\u5c0f\u4e8e 0 \u8868\u793a\u8d1f\u76f8\u5173<\/strong><\/li>\n\n\n\n<li><strong>\u63a5\u8fd1 0 \u8868\u793a\u65e0\u7ebf\u6027\u5173\u7cfb<\/strong><\/li>\n\n\n\n<li>\u76f8\u5173\u7cfb\u6570\u7684<strong>\u53d6\u503c\u8303\u56f4\u56fa\u5b9a\u5728 [-1,1]<\/strong>\uff1a<\/li>\n\n\n\n<li>\u5176<strong>\u7edd\u5bf9\u503c\u8d8a\u63a5\u8fd1 1\uff0c\u7ebf\u6027\u76f8\u5173\u6027\u8d8a\u5f3a<\/strong><\/li>\n\n\n\n<li><strong>\u8d8a\u63a5\u8fd1 0\uff0c\u7ebf\u6027\u76f8\u5173\u6027\u8d8a\u5f31<\/strong><\/li>\n\n\n\n<li>\u76f8\u5173\u7cfb\u6570\u53ef\u901a\u8fc7\u7edf\u8ba1\u8f6f\u4ef6\uff08\u5982 R \u8bed\u8a00\uff09\u8ba1\u7b97<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">2.4 \u6570\u636e\u7684\u53ef\u89c6\u5316<\/h3>\n\n\n\n<h4 class=\"wp-block-heading\">2.4.1 \u5b9a\u6027\u6570\u636e\u7684\u53ef\u89c6\u5316<\/h4>\n\n\n\n<h6 class=\"wp-block-heading\">\u6761\u5f62\u56fe<\/h6>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u6761\u5f62\u56fe\uff08bar plot\uff09<\/strong><\/li>\n\n\n\n<li>\u53c8\u79f0\u67f1\u72b6\u56fe\uff0c\u7528<strong>\u77e9\u5f62\u6761<\/strong>\u8868\u793a\u5b9a\u6027\u6570\u636e\u5404\u6c34\u5e73\uff0c\u5176<strong>\u9ad8\u5ea6\u5bf9\u5e94\u4e8e\u8be5\u6c34\u5e73\u7684\u9891\u6570\u3001\u9891\u7387\u6216\u767e\u5206\u6bd4<\/strong>\uff0c\u662f\u9891\u6570\u5206\u5e03\u8868\u7684\u56fe\u5f62\u5316\u5c55\u793a<\/li>\n<\/ul>\n\n\n\n<h6 class=\"wp-block-heading\">\u997c\u56fe<\/h6>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u997c\u56fe\uff08pie chart\uff09<\/strong><\/li>\n\n\n\n<li>\u4ee5\u5706\u5f62\u4e3a\u6574\u4f53\uff0c\u6309\u6bd4\u4f8b\u5212\u5206\u6210\u82e5\u5e72\u6247\u5f62\uff0c\u6bcf\u4e2a\u6247\u5f62\u5bf9\u5e94\u4e00\u4e2a\u6c34\u5e73\uff0c\u5176<strong>\u9762\u79ef\u53cd\u6620\u9891\u7387\u6216\u767e\u5206\u6bd4<\/strong> \u5728\u6bd4\u8f83\u4e0d\u540c\u6c34\u5e73\uff0c\u5c24\u5176\u662f\u9891\u6570\u63a5\u8fd1\u65f6\uff0c<strong>\u6761\u5f62\u56fe\u6bd4\u997c\u56fe\u66f4\u76f4\u89c2\u6e05\u6670<\/strong><\/li>\n<\/ul>\n\n\n\n<h6 class=\"wp-block-heading\">\u5357\u4e01\u683c\u5c14\u73ab\u7470\u56fe<\/h6>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u5357\u4e01\u683c\u5c14\u73ab\u7470\u56fe\uff08nightingale rose diagram\uff09<\/strong><\/li>\n\n\n\n<li>\u53c8\u79f0\u6781\u5750\u6807\u533a\u57df\u56fe\u6216\u9e21\u51a0\u82b1\u56fe\uff0c\u662f\u5f17\u7f57\u4f26\u65af\u00b7\u5357\u4e01\u683c\u5c14\u53d1\u660e\u7684\u6781\u5750\u6807\u67f1\u72b6\u56fe\uff0c\u7528\u4ee5\u8868\u8fbe\u519b\u961f\u533b\u9662\u5b63\u8282\u6027\u6b7b\u4ea1\u7387<\/li>\n\n\n\n<li>\u5176\u4ee5<strong>\u6247\u5f62\u534a\u5f84\u8868\u793a\u9891\u6570\u6216\u9891\u7387<\/strong>\uff0c\u7531\u4e8e\u9762\u79ef\u4e0e\u534a\u5f84\u5e73\u65b9\u6210\u6b63\u6bd4\uff0c\u6bd4\u4f8b\u5dee\u5f02\u4f1a\u88ab\u653e\u5927<\/li>\n\n\n\n<li><strong>\u9002\u5408\u6bd4\u8f83\u6570\u503c\u63a5\u8fd1\u7684\u6c34\u5e73<\/strong>\uff0c<strong>\u82e5\u5dee\u8ddd\u8fc7\u5927\u5219\u5bb9\u6613\u5938\u5927\u5dee\u5f02<\/strong><\/li>\n\n\n\n<li>\u56e0\u5706\u5f62\u5177\u6709\u5468\u671f\u7279\u6027\uff0c\u8be5\u56fe\u4e5f\u5e38\u7528\u4e8e<strong>\u8868\u793a\u5468\u671f\u6027\u65f6\u95f4\u6570\u636e<\/strong>\uff0c\u5982\u661f\u671f\u6216\u6708\u4efd<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-large\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/tobykskgd.life\/wp-content\/uploads\/2025\/12\/2_23-1024x278.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"278\" data-original=\"https:\/\/tobykskgd.life\/wp-content\/uploads\/2025\/12\/2_23-1024x278.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-3705\"  sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div><\/figure>\n\n\n\n<p><strong>\u997c\u56fe VS \u5357\u4e01\u683c\u5c14\u73ab\u7470\u56fe\uff1a<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u76f8\u540c\u70b9\uff1a<\/strong><\/li>\n\n\n\n<li>\u90fd\u628a\u4e00\u4e2a\u603b\u4f53\u5206\u6210\u82e5\u5e72\u201c\u6247\u5f62\u201d\uff0c\u7528\u6765\u8868\u8fbe\u5404\u7c7b\u522b\u7684<strong>\u9891\u6570\/\u9891\u7387\/\u767e\u5206\u6bd4<\/strong>\u3002\u997c\u56fe\u91cc\u6bcf\u4e2a\u6247\u5f62\u9762\u79ef\u53cd\u6620\u9891\u7387\u6216\u767e\u5206\u6bd4\u3002\u73ab\u7470\u56fe\u540c\u6837\u662f\u5728\u5706\u5f62\u6247\u533a\u4e0a\u8868\u8fbe\u9891\u6570\u6216\u9891\u7387\u3002<\/li>\n\n\n\n<li>\u9002\u5408\u5c55\u793a\u201c\u6784\u6210\u7ed3\u6784\u201d\uff08\u8c01\u5360\u6bd4\u66f4\u5927\u3001\u8c01\u66f4\u5c0f\uff09\u3002<\/li>\n\n\n\n<li><strong>\u4e0d\u540c\u70b9\uff1a<\/strong><\/li>\n\n\n\n<li><strong>\u7f16\u7801\u65b9\u5f0f\u4e0d\u540c<\/strong><strong>\u997c\u56fe\u9760\u201c\u89d2\u5ea6\/\u9762\u79ef\u201d\uff0c\u73ab\u7470\u56fe\u9760\u201c\u534a\u5f84\uff08\u8fdb\u800c\u9762\u79ef\uff09\u201d\u3002<\/strong>\n<ul class=\"wp-block-list\">\n<li><strong>\u997c\u56fe<\/strong>\uff1a\u4ee5\u5706\u4e3a\u6574\u4f53\uff0c\u6309\u6bd4\u4f8b\u5207\u6210\u6247\u5f62\uff0c\u6247\u5f62\u7684\u201c\u5927\u5c0f\u201d\uff08\u672c\u8d28\u4e0a\u662f\u89d2\u5ea6\/\u9762\u79ef\uff09\u53cd\u6620\u6bd4\u4f8b<\/li>\n\n\n\n<li><strong>\u5357\u4e01\u683c\u5c14\u73ab\u7470\u56fe<\/strong>\uff1a\u4ee5\u201c\u6247\u5f62\u534a\u5f84\u201d\u8868\u793a\u9891\u6570\/\u9891\u7387\uff1b\u56e0\u4e3a<strong>\u9762\u79ef\u4e0e\u534a\u5f84\u5e73\u65b9\u6210\u6b63\u6bd4<\/strong>\uff0c\u6240\u4ee5\u5dee\u5f02\u4f1a\u88ab\u653e\u5927<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>\u89c6\u89c9\u6548\u679c\u4e0e\u9002\u7528\u573a\u666f\u4e0d\u540c<\/strong>\n<ul class=\"wp-block-list\">\n<li><strong>\u73ab\u7470\u56fe<\/strong>\uff1a\u66f4\u9002\u5408\u6bd4\u8f83\u6570\u503c\u63a5\u8fd1\u7684\u7c7b\u522b\uff1b\u5982\u679c\u5dee\u8ddd\u592a\u5927\uff0c\u5bb9\u6613\u5938\u5927\u5dee\u5f02\u3002\u53e6\u5916\u56e0\u4e3a\u5706\u5f62\u6709\u5468\u671f\u7279\u6027\uff0c\u5e38\u7528\u4e8e\u8868\u793a\u5468\u671f\u6027\u65f6\u95f4\u6570\u636e\uff08\u5982\u661f\u671f\/\u6708\uff09<\/li>\n\n\n\n<li><strong>\u997c\u56fe<\/strong>\uff1a\u5f53\u5404\u7c7b\u522b\u9891\u6570\u63a5\u8fd1\u65f6\u4e0d\u592a\u76f4\u89c2<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">2.4.2 \u5b9a\u91cf\u6570\u636e\u7684\u53ef\u89c6\u5316<\/h4>\n\n\n\n<h6 class=\"wp-block-heading\">\u76f4\u65b9\u56fe<\/h6>\n\n\n\n<p><strong>\u76f4\u65b9\u56fe (histogram)<\/strong>\uff1a\u6839\u636e\u9891\u6570\u5206\u5e03\u8868\u7ed8\u5236\uff0c\u5728\u5e73\u9762\u76f4\u89d2\u5750\u6807\u7cfb\u4e2d\u4ee5<strong>\u7ec4\u7aef\u70b9\u4e3a\u6a2a\u8f74\u3001\u9891\u6570\u4e3a\u7eb5\u8f74<\/strong>\uff0c\u6bcf\u4e2a<strong>\u77e9\u5f62\u7684\u9ad8\u5ea6\u8868\u793a\u8be5\u7ec4\u7684\u9891\u6570\u3001\u9891\u7387\u6216\u767e\u5206\u6bd4\u9891\u7387<\/strong><\/p>\n\n\n\n<p>\u76f4\u65b9\u56fe\u662f\u5b9a\u91cf\u6570\u636e\u9891\u6570\u5206\u5e03\u8868\u7684\u56fe\u5f62\u5316\u8868\u793a<\/p>\n\n\n\n<p><strong>\u76f4\u65b9\u56fe VS \u6761\u5f62\u56fe\uff1a<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u6761\u5f62\u56fe\u7528\u4e8e\u5b9a\u6027\u6570\u636e<\/strong>\uff0c\u5404\u77e9\u5f62\u8868\u793a\u4e0d\u540c\u6c34\u5e73\uff0c<strong>\u5f7c\u6b64\u79bb\u6563\u4e14\u5206\u9694\u6e05\u6670<\/strong><\/li>\n\n\n\n<li><strong>\u76f4\u65b9\u56fe\u7528\u4e8e\u5b9a\u91cf\u6570\u636e<\/strong>\uff0c\u56e0\u6570\u636e\u8fde\u7eed\uff0c\u5404\u77e9\u5f62\u76f8\u8fde\uff0c<strong>\u65e0\u660e\u663e\u5206\u5272<\/strong><\/li>\n\n\n\n<li><strong>\u6761\u5f62\u56fe<\/strong>\u6bcf\u4e00\u77e9\u5f62\u8868\u793a\u4e00\u4e2a\u7c7b\u522b\uff0c<strong>\u5176\u5bbd\u5ea6\u6ca1\u6709\u610f\u4e49<\/strong>\uff0c\u800c<strong>\u76f4\u65b9\u56fe\u7684\u5bbd\u5ea6\u8868\u793a\u7ec4\u8ddd<\/strong>\u3002<\/li>\n<\/ul>\n\n\n\n<p><em>\uff08\u4e0b\u56fe\u7b2c\u4e00\u884c\u4e09\u5f20\u56fe\u4e3a\u6761\u5f62\u56fe\uff0c\u7b2c\u4e8c\u884c\u4e3a\u76f4\u65b9\u56fe\uff09<\/em><\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-resized\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/tobykskgd.life\/wp-content\/uploads\/2025\/12\/2_24-1024x632.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"632\" data-original=\"https:\/\/tobykskgd.life\/wp-content\/uploads\/2025\/12\/2_24-1024x632.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-3706\" style=\"aspect-ratio:1.6207416340066325;width:697px;height:auto\"  sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div><\/figure>\n\n\n\n<h6 class=\"wp-block-heading\">\u7bb1\u7ebf\u56fe<\/h6>\n\n\n\n<p><strong>\u7bb1\u7ebf\u56fe(boxplot)<\/strong>\uff1a\u53c8\u79f0\u7bb1\u987b\u56fe\uff08box-whisker plot\uff09\uff0c\u57fa\u4e8e<strong>\u6700\u5c0f\u503c<\/strong>\u3001<strong>\u7b2c\u4e00\u56db\u5206\u4f4d\u6570\uff08\u4e0b\u56db\u5206\u4f4d\u6570\uff09<\/strong>\u3001<strong>\u4e2d\u4f4d\u6570<\/strong>\u3001<strong>\u7b2c\u4e09\u56db\u5206\u4f4d\u6570\uff08\u4e0a\u56db\u5206\u4f4d\u6570\uff09<\/strong>\u548c<strong>\u6700\u5927\u503c<\/strong>\u8fd9\u4e94\u4e2a\u7edf\u8ba1\u91cf\u7ed8\u5236<\/p>\n\n\n\n<p>\u7bb1\u7ebf\u56fe\u4e3b\u8981\u7528\u4e8e\u76f4\u89c2\u5c55\u793a<strong>\u5b9a\u91cf\u6570\u636e\u7684\u5206\u5e03\u7279\u5f81<\/strong>\uff0c\u5305\u62ec<strong>\u79bb\u6563\u7a0b\u5ea6\u3001\u5bf9\u79f0\u6027\u53ca\u5f02\u5e38\u503c<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u4e0a\u8fb9\u7f18\u6570 = ???{?(?), ?3 + 1.5???}<\/strong><\/li>\n\n\n\n<li><strong>\u4e0b\u8fb9\u7f18\u6570 = ???{?(1), ?1 \u2212 1.5???}<\/strong><\/li>\n\n\n\n<li>?3 \u4e3a\u4e0a\u56db\u5206\u4f4d\u6570<\/li>\n\n\n\n<li>?1 \u4e3a\u4e0b\u56db\u5206\u4f4d\u6570<\/li>\n\n\n\n<li>??? \u4e3a\u56db\u5206\u4f4d\u8ddd\uff08\u4e0a\u4e0b\u56db\u5206\u4f4d\u6570\u4e4b\u5dee\uff1a??? = ?3 &#8211; ?1\uff09<\/li>\n\n\n\n<li>\u5927\u4e8e\u4e0a\u8fb9\u7f18\u6570\u6216\u5c0f\u4e8e\u4e0b\u8fb9\u7f18\u6570\u7684\u6570\u636e\u88ab\u89c6\u4e3a<strong>\u5f02\u5e38\u503c<\/strong><\/li>\n\n\n\n<li>\u5728\u5b9e\u9645\u64cd\u4f5c\u4e2d\uff0c\u53ef\u80fd\u6ca1\u6709\u5b9e\u9645\u6570\u636e\u843d\u5728\u4e0a\u8fb9\u7f18\u6570\u6216\u8005\u4e0b\u8fb9\u7f18\u6570\u4e0a<\/li>\n\n\n\n<li>\u4e00\u822c\u5c06\u4e0a\u8fb9\u7f18\u6570\u548c\u5176\u5bf9\u5e94\u7684\u987b\u7ebf\u753b\u5728\u4e0d\u8d85\u8fc7 <strong>?3+1.5???<\/strong> \u7684\u6700\u5927\u6570\u636e\u503c\u5904\uff1b\u628a\u4e0b\u8fb9\u7f18\u6570\u548c\u5176\u5bf9\u5e94\u7684\u987b\u7ebf\u753b\u5728\u4e0d\u5c0f\u4e8e <strong>?1\u22121.5???<\/strong> \u7684\u6700\u5c0f\u6570\u636e\u503c\u5904\u3002<\/li>\n\n\n\n<li>\u5176\u6838\u5fc3\u529f\u80fd\u662f\u89c2\u6d4b\u6570\u636e\u7684\u5206\u5e03\u7279\u5f81\uff0c\u5224\u65ad\u5206\u5e03\u7c7b\u578b\uff1a\u662f\u5426\u4e3a\u5bf9\u79f0\u5206\u5e03\uff08\u949f\u578b\uff09\u3001\u5de6\u504f\u5206\u5e03\u3001\u53f3\u504f\u5206\u5e03\u3001U\u578b\u5206\u5e03<\/li>\n\n\n\n<li>\u82e5<strong>\u6570\u636e\u5de6\u504f<\/strong>\uff0c\u5219<strong>\u5de6\u4fa7\u79bb\u6563\u7a0b\u5ea6\u66f4\u5927<\/strong>\uff0c<strong>\u7bb1\u4f53\u5de6\u534a\u90e8\u5206\u548c\u5de6\u987b\u6bd4\u53f3\u4fa7\u66f4\u5bbd<\/strong><\/li>\n\n\n\n<li>\u82e5\u6570\u636e\u5448<strong>\u5bf9\u79f0\u5206\u5e03<\/strong>\uff0c<strong>\u7bb1\u4f53\u5de6\u53f3\u5bbd\u5ea6\u53ca\u4e24\u4fa7\u987b\u7684\u957f\u5ea6\u5e94\u5927\u81f4\u76f8\u7b49<\/strong><\/li>\n\n\n\n<li>\u82e5<strong>\u6570\u636e\u53f3\u504f<\/strong>\uff0c\u5219<strong>\u53f3\u4fa7\u79bb\u6563\u7a0b\u5ea6\u66f4\u5927<\/strong>\uff0c<strong>\u7bb1\u4f53\u53f3\u534a\u90e8\u5206\u548c\u53f3\u987b\u6bd4\u5de6\u4fa7\u66f4\u5bbd<\/strong><\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-large\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/tobykskgd.life\/wp-content\/uploads\/2025\/12\/2_25-1024x508.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"508\" data-original=\"https:\/\/tobykskgd.life\/wp-content\/uploads\/2025\/12\/2_25-1024x508.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-3707\"  sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div><\/figure>\n\n\n\n<p><strong>\u5bf9\u4e8e\u53f3\u504f\u5206\u5e03\u7684\u6570\u636e\uff0c\u5e38\u901a\u8fc7\u53d6\u5bf9\u6570\u6765\u51cf\u5f31\u504f\u6001\u6027<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-resized\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/tobykskgd.life\/wp-content\/uploads\/2025\/12\/2_26-1024x352.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"352\" data-original=\"https:\/\/tobykskgd.life\/wp-content\/uploads\/2025\/12\/2_26-1024x352.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-3708\" style=\"aspect-ratio:2.9053177691309986;width:758px;height:auto\"  sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div><\/figure>\n\n\n\n<p>\u53ef\u4ee5\u628a\u591a\u7ec4\u6570\u636e\u753b\u6210\u4e00\u4e2a\u7bb1\u7ebf\u56fe<\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-resized\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/tobykskgd.life\/wp-content\/uploads\/2025\/12\/2_27-1024x585.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"585\" data-original=\"https:\/\/tobykskgd.life\/wp-content\/uploads\/2025\/12\/2_27-1024x585.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-3709\" style=\"aspect-ratio:1.7490321111364153;width:619px;height:auto\"  sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\">2.4.3 \u53d8\u91cf\u5173\u7cfb\u7684\u53ef\u89c6\u5316<\/h4>\n\n\n\n<h5 class=\"wp-block-heading\">2.4.3.1 \u4e24\u4e2a\u5b9a\u6027\u53d8\u91cf<\/h5>\n\n\n\n<p>\u5bf9\u4e8e<strong>\u4e24\u4e2a\u5b9a\u6027\u53d8\u91cf\u7684\u5173\u7cfb<\/strong>\uff0c\u53ef\u4f7f\u7528<strong>\u590d\u5408\u6761\u5f62\u56fe\uff08side-by-side bar chart\uff09<\/strong>\u3001<strong>\u5806\u53e0\u6761\u5f62\u56fe\uff08stacked bar chart\uff09<\/strong>\u6216<strong>\u5357\u4e01\u683c\u5c14\u73ab\u7470\u56fe<\/strong>\u3002<\/p>\n\n\n\n<p><em>\uff08\u5de6\uff1a\u5806\u53e0\u6761\u5f62\u56fe\uff1b\u53f3\uff1a\u5357\u4e01\u683c\u5c14\u73ab\u7470\u56fe\uff09<\/em><\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/tobykskgd.life\/wp-content\/uploads\/2025\/12\/2_28-1024x350.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"350\" data-original=\"https:\/\/tobykskgd.life\/wp-content\/uploads\/2025\/12\/2_28-1024x350.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-3710\"  sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div><\/figure>\n\n\n\n<h5 class=\"wp-block-heading\">2.4.3.2 \u5b9a\u91cf\u53d8\u91cf\u95f4<\/h5>\n\n\n\n<h6 class=\"wp-block-heading\">\u6563\u70b9\u56fe<\/h6>\n\n\n\n<p><strong>\u6563\u70b9\u56fe\uff08scatter plot\uff09<\/strong>\u662f\u523b\u753b<strong>\u4e24\u4e2a\u5b9a\u91cf\u53d8\u91cf\u5173\u7cfb<\/strong>\u7684\u5e38\u7528\u56fe\u5f62\u3002<\/p>\n\n\n\n<p>\u5b83\u4ee5\u4e24\u7ec4\u6570\u636e\u751f\u6210\u4e00\u7cfb\u5217\u5750\u6807\u70b9\uff0c\u901a\u8fc7<strong>\u89c2\u5bdf\u70b9\u7684\u5206\u5e03<\/strong>\u6765<strong>\u5224\u65ad\u53d8\u91cf\u95f4\u662f\u5426\u5b58\u5728\u5173\u8054<\/strong>\u6216\u603b\u7ed3\u5206\u5e03\u6a21\u5f0f\u3002<\/p>\n\n\n\n<p>\u7814\u7a76\u4e24\u4e2a\u5b9a\u91cf\u53d8\u91cf\u5173\u7cfb\u65f6\uff0c\u53ef\u5f15\u5165<strong>\u5b9a\u6027\u53d8\u91cf<\/strong>\u8fdb\u884c\u5206\u7ec4\u6bd4\u8f83<em>\uff08\u53f3\uff09<\/em><\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/tobykskgd.life\/wp-content\/uploads\/2025\/12\/2_29-1024x387.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"387\" data-original=\"https:\/\/tobykskgd.life\/wp-content\/uploads\/2025\/12\/2_29-1024x387.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-3711\"  sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/div><\/figure>\n\n\n\n<p>\u5bf9\u4e8e\u591a\u4e2a\u5b9a\u91cf\u53d8\u91cf\uff0c\u53ef\u5728 R \u4e2d\u7528 cor \u51fd\u6570\u8ba1\u7b97\u4e24\u4e24\u76f8\u5173\u7cfb\u6570\uff0c\u5e76\u7528 ggpairs \u51fd\u6570\u7ed8\u5236<strong>\u6563\u70b9\u56fe\u77e9\u9635<\/strong>\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/tobykskgd.life\/wp-content\/uploads\/2025\/12\/2_30.png'><img class=\"lazyload lazyload-style-1\" src=\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\"  loading=\"lazy\" decoding=\"async\" width=\"815\" height=\"548\" data-original=\"https:\/\/tobykskgd.life\/wp-content\/uploads\/2025\/12\/2_30.png\" src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAANSURBVBhXYzh8+PB\/AAffA0nNPuCLAAAAAElFTkSuQmCC\" alt=\"\" class=\"wp-image-3712\" style=\"aspect-ratio:1.4872863693205502;width:446px;height:auto\"  sizes=\"auto, (max-width: 815px) 100vw, 815px\" \/><\/div><\/figure>\n\n\n\n<h5 class=\"wp-block-heading\">2.4.3.3 \u5b9a\u6027\u4e0e\u5b9a\u91cf\u53d8\u91cf\u95f4<\/h5>\n\n\n\n<p>\u5728\u7814\u7a76\u5b9a\u6027\u4e0e\u5b9a\u91cf\u53d8\u91cf\u7684\u5173\u7cfb\u65f6\uff0c\u5e38\u901a\u8fc7<strong>\u5bf9\u5b9a\u6027\u53d8\u91cf\u5206\u7ec4<\/strong>\uff0c\u7ed8\u5236\u5b9a\u91cf\u53d8\u91cf\u7684\u56fe\u5f62\u8fdb\u884c\u6bd4\u8f83\uff0c\u5982<strong>\u5206\u7ec4\u76f4\u65b9\u56fe\u3001\u5206\u7ec4\u7bb1\u7ebf\u56fe\u548c\u5206\u7ec4\u5bc6\u5ea6\u56fe<\/strong>\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u4f8b\u5982\uff1a\u6027\u522b\uff08\u7537\/\u5973\uff09\u4e3a\u5b9a\u6027\u53d8\u91cf\uff0c\u800c\u5e73\u5747\u5bff\u547d\u3001\u4eba\u5747\u56fd\u6c11\u603b\u6536\u5165\u4e3a\u5b9a\u91cf\u53d8\u91cf<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-large\"><div class='fancybox-wrapper lazyload-container-unload' data-fancybox='post-images' href='https:\/\/tobykskgd.life\/wp-content\/uploads\/2025\/12\/2_31-1024x349.png'><img class=\"lazyload lazyload-style-1\" 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