{"id":617,"date":"2021-09-02T16:44:56","date_gmt":"2021-09-02T08:44:56","guid":{"rendered":"https:\/\/aif.amtbbs.org\/?p=617"},"modified":"2021-09-02T16:44:56","modified_gmt":"2021-09-02T08:44:56","slug":"%e4%b8%81%e9%b9%8f%ef%bc%9a%e5%a4%9a%e8%a7%92%e5%ba%a6%e5%9b%9e%e9%a1%be%e5%9b%a0%e6%9e%9c%e6%8e%a8%e6%96%ad%e7%9a%84%e6%a8%a1%e5%9e%8b%e6%96%b9%e6%b3%95","status":"publish","type":"post","link":"https:\/\/aif.amtbbs.org\/index.php\/2021\/09\/02\/617\/","title":{"rendered":"\u4e01\u9e4f\uff1a\u591a\u89d2\u5ea6\u56de\u987e\u56e0\u679c\u63a8\u65ad\u7684\u6a21\u578b\u65b9\u6cd5"},"content":{"rendered":"<section data-mpa-powered-by=\"yiban.io\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-618\" src=\"https:\/\/aif.amtbbs.org\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-6.png\" width=\"1080\" height=\"564\" alt=\"\u56fe\u7247\" srcset=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-6.png 1080w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-6-300x157.png 300w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-6-1024x535.png 1024w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-6-768x401.png 768w\" sizes=\"auto, (max-width: 1080px) 100vw, 1080px\" \/><\/p>\n<section>\n<section>\n<section>\n<section>\n<section>\n<section>\n<section>\n<section>\n<section><\/section>\n<\/section>\n<section>\n<section><strong>\u5bfc\u8bed<\/strong><\/p>\n<\/section>\n<\/section>\n<section>\n<section><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<section>\n<section>\n<section><strong>\u63a8\u65ad\u56e0\u679c\u5173\u7cfb\uff0c\u662f\u4eba\u7c7b\u601d\u60f3\u53f2\u4e0e\u79d1\u5b66\u53f2\u4e0a\u7684\u91cd\u8981\u4e3b\u9898\u3002\u73b0\u4ee3\u56e0\u679c\u63a8\u65ad\u7684\u7814\u7a76\uff0c\u59cb\u4e8e\u7ea6\u5c14-\u8f9b\u666e\u68ee\u6096\u8bba\uff0c\u7ecf\u7531\u9c81\u5bbe\u56e0\u679c\u6a21\u578b\u3001\u968f\u673a\u8bd5\u9a8c\u7b49\u6539\u8fdb\uff0c\u5230\u6731\u529b\u4e9a\u00b7\u73c0\u5c14\u7684\u56e0\u679c\u9769\u547d\uff0c\u5982\u4eca\u56e0\u679c\u79d1\u5b66\u4e0e\u4eba\u5de5\u667a\u80fd\u7684\u7ed3\u5408\u6b63\u6380\u8d77\u70ed\u6f6e\u3002\u672c\u6587\u6574\u7406\u81ea\u4e01\u9e4f\u8001\u5e08\u76848\u7bc7\u77ed\u6587\uff0c\u4ece\u591a\u89d2\u5ea6\u56de\u987e\u4e86\u56e0\u679c\u63a8\u65ad\u7684\u5404\u79cd\u6a21\u578b\u65b9\u6cd5\u3002<\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<section>\n<section>\n<section>\n<section><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<section>\n<section><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-619\" src=\"https:\/\/aif.amtbbs.org\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-7.png\" width=\"1080\" height=\"79\" alt=\"\u56fe\u7247\" srcset=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-7.png 1080w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-7-300x22.png 300w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-7-1024x75.png 1024w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-7-768x56.png 768w\" sizes=\"auto, (max-width: 1080px) 100vw, 1080px\" \/><\/section>\n<\/section>\n<section>\u4e01\u9e4f\u00a0<strong>| \u4f5c\u8005<\/strong><\/p>\n<p>\u5411\u60a6\u00a0|\u00a0\u7f16\u8f91<\/p>\n<p>\u7edf\u8ba1\u4e4b\u90fd\u3001\u96c6\u667a\u4ff1\u4e50\u90e8\u00a0|\u00a0\u6765\u6e90<\/p>\n<\/section>\n<section><strong>\u76ee\u5f55<\/strong><\/p>\n<section><strong>1. \u56e0\u679c\u63a8\u65ad\u7b80\u4ecb\u4e4b\u4e00\uff1a\u4ece Yule-Simpson\u2019s Paradox \u8bb2\u8d77<\/strong><\/section>\n<section><strong>2. \u56e0\u679c\u63a8\u65ad\u7b80\u4ecb\u4e4b\u4e8c\uff1aRubin Causal Model (RCM) \u548c\u968f\u673a\u5316\u8bd5\u9a8c<\/strong><\/section>\n<section><strong>3. \u56e0\u679c\u63a8\u65ad\u7b80\u4ecb\u4e4b\u4e09\uff1aR. A. Fisher \u548c J. Neyman \u7684\u5206\u6b67<\/strong><\/section>\n<section><strong>4. \u56e0\u679c\u63a8\u65ad\u7b80\u4ecb\u4e4b\u56db\uff1a\u89c2\u5bdf\u6027\u7814\u7a76\uff0c\u53ef\u5ffd\u7565\u6027\u548c\u503e\u5411\u5f97\u5206<\/strong><\/section>\n<section><strong>5. \u56e0\u679c\u63a8\u65ad\u7b80\u4ecb\u4e4b\u4e94\uff1a\u56e0\u679c\u56fe (Causal Diagram)<\/strong><\/section>\n<section><strong>6. \u56e0\u679c\u63a8\u65ad\u7b80\u4ecb\u4e4b\u516d\uff1a\u5de5\u5177\u53d8\u91cf\uff08instrumental variable\uff09<\/strong><\/section>\n<section><strong>7. \u56e0\u679c\u63a8\u65ad\u7b80\u4ecb\u4e4b\u4e03\uff1aLord\u2019s Paradox<\/strong><\/section>\n<section><strong>8. \u56e0\u679c\u63a8\u65ad\u7b80\u4ecb\u4e4b\u516b\uff1a\u5438\u70df\u662f\u5426\u5bfc\u81f4\u80ba\u764c\uff1fFisher versus Cornfield<\/strong><\/section>\n<section>\n<section>\n<section>\n<section>\n<section><\/section>\n<section><\/section>\n<section>\n<section><\/section>\n<\/section>\n<\/section>\n<section><strong>1. \u56e0\u679c\u63a8\u65ad\u7b80\u4ecb\u4e4b\u4e00\uff1a<\/strong><\/p>\n<p><strong>\u4ece Yule-Simpson\u2019s Paradox \u8bb2\u8d77<\/strong><\/p>\n<\/section>\n<section>\n<section><\/section>\n<section><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<p>\u5728\u56fd\u5185\u7684\u65f6\u5019\uff0c\u5411\u522b\u4eba\u4ecb\u7ecd\u81ea\u5df1\u662f\u7814\u7a76\u56e0\u679c\u63a8\u65ad\uff08causal inference\uff09\u7684\uff0c\u591a\u534a\u7684\u53cd\u5e94\u662f\uff1a\u4ec0\u4e48\uff1f\u7edf\u8ba1\u8fd8\u80fd\u7814\u7a76\u56e0\u679c\uff1f\u8fd9\u786e\u5b9e\u662f\u4e00\u4e2a\u95ee\u9898\uff1a\u7edf\u8ba1\u7814\u7a76\u56e0\u679c\uff0c\u80fd\uff0c\u8fd8\u662f\u4e0d\u80fd\uff1f\u76f4\u63a5\u7ed9\u51fa\u56de\u7b54\uff0c\u6bd4\u8f83\u5192\u9669\uff1b\u5982\u679c\u6709\u53ef\u80fd\uff0c\u6211\u9700\u8981\u82b1\u4e00\u4e9b\u7bc7\u5e45\u6765\u9610\u8ff0\u8fd9\u4e2a\u95ee\u9898\u3002<\/p>\n<\/section>\n<p>\u76ee\u524d\u5e02\u9762\u4e0a\u80fd\u591f\u4e70\u5230\u7684\u76f8\u5173\u6559\u79d1\u4e66\u4ec5\u6709 2011 \u5e74\u56fe\u7075\u5956\u5f97\u4e3b Judea Pearl \u7684\u00a0<strong>Causality: Models, Reasoning, and Inference<\/strong>\u3002Harvard \u7684\u7edf\u8ba1\u5b66\u5bb6 Donald Rubin \u548c \u8ba1\u91cf\u7ecf\u6d4e\u5b66\u5bb6 Guido Imbens \u5408\u8457\u7684\u6559\u79d1\u4e66\u5386\u65f6\u591a\u5e74\u4ecd\u5c1a\u672a\u5b8c\u6210\uff1bHarvard \u7684\u6d41\u884c\u75c5\u5b66\u5bb6 James Robins \u548c\u4ed6\u7684\u540c\u4e8b\u4e5f\u5728\u5199\u4e00\u672c\u56e0\u679c\u63a8\u65ad\u7684\u6559\u79d1\u4e66\uff0c\u672c\u4e66\u76ee\u524d\u53ea\u5b8c\u6210\u4e86\u7b2c\u4e00\u90e8\u5206\uff0c\u8fd8\u672a\u51fa\u7248\u3002\u6211\u672c\u4eba\u5b66\u4e60\u56e0\u679c\u63a8\u65ad\u662f\u4ece Judea Pearl \u7684\u6559\u79d1\u4e66\u5165\u624b\u7684\uff0c\u4e0d\u8fc7\u8fd9\u672c\u4e66\u6666\u6da9\u96be\u61c2\uff0c\u5b9e\u5728\u4e0d\u9002\u5408\u4f5c\u4e3a\u5165\u95e8\u7684\u6559\u79d1\u4e66\u3002Donald Rubin \u5bf9 Judea Pearl \u63d0\u51fa\u7684\u56e0\u679c\u56fe\u6a21\u578b\uff08causal diagram\uff09\u975e\u5e38\u53cd\u5bf9\uff0c\u4ed6\u7684\u6559\u79d1\u4e66\u4e2d\u675c\u7edd\u4f7f\u7528\u56e0\u679c\u56fe\u6a21\u578b\u3002\u6211\u672c\u4eba\u867d\u7136\u8111\u4e2d\u4e60\u60ef\u7528\u56fe\u6a21\u578b\u8fdb\u884c\u601d\u8003\uff0c\u4f46\u662f\u8fd8\u662f\u66f4\u504f\u597d Donald Rubin \u7684\u98ce\u683c\uff0c\u56e0\u4e3a\u8fd9\u5bf9\u4e8e\u5165\u95e8\u8005\uff0c\u53ef\u80fd\u66f4\u5bb9\u6613\u3002\u4e0d\u8fc7\u8fd9\u4e00\u8282\uff0c\u5148\u4ece\u4e00\u4e2a\u4f8b\u5b50\u51fa\u53d1\uff0c\u4e0d\u5f15\u8fdb\u65b0\u7684\u7edf\u8ba1\u7b26\u53f7\u548c\u6982\u5ff5\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-620\" src=\"https:\/\/aif.amtbbs.org\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-15.jpg\" width=\"904\" height=\"1280\" alt=\"\u56fe\u7247\" srcset=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-15.jpg 904w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-15-212x300.jpg 212w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-15-723x1024.jpg 723w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-15-768x1087.jpg 768w\" sizes=\"auto, (max-width: 904px) 100vw, 904px\" \/><\/p>\n<p>\u5929\u624d\u7684\u9ad8\u65af\u5728\u7814\u7a76\u5929\u6587\u5b66\u65f6\uff0c\u9996\u6b21\u5f15\u8fdb\u4e86\u6700\u5927\u4f3c\u7136\u548c\u6700\u5c0f\u4e8c\u4e58\u7684\u601d\u60f3\uff0c\u5e76\u4e14\u5bfc\u51fa\u4e86\u6b63\u6001\u5206\u5e03\uff08\u6216\u79f0\u9ad8\u65af\u5206\u5e03\uff09\u3002\u5176\u4e2d\u6700\u5927\u4f3c\u7136\u6709\u4e9b\u4e89\u8bae\uff0c\u6bd4\u5982 Arthur Dempster \u6559\u6388\u8bf4\uff0c\u5176\u5b9e\u9ad8\u65af\u90a3\u91cc\u7684\u4f3c\u7136\uff0c\u6709\u8d1d\u53f6\u65af\u6216\u8005\u4fe1\u4ef0\u63a8\u65ad\uff08fiducial inference\uff09\u7684\u6210\u5206\u3002\u9ad8\u65af\u90a3\u91cc\u7684 \u201c\u7edf\u8ba1\u201d \u662f\u5173\u4e8e\u00a0<strong>\u201c\u8bef\u5dee\u201d \u7684\u7406\u8bba<\/strong>\uff0c\u56e0\u4e3a\u4ed6\u7814\u7a76\u7684\u5bf9\u8c61\u662f \u201c\u7269\u7406\u6a21\u578b\u201d \u52a0\u201c\u968f\u673a\u8bef\u5dee\u201d\u3002\u5927\u7ea6\u5728 100 \u591a\u5e74\u524d\uff0cFrancis Galton \u7814\u7a76\u4e86\u7236\u6bcd\u8eab\u9ad8\u548c\u5b50\u5973\u8eab\u9ad8\u7684 \u201c\u5173\u7cfb\u201d\uff0c\u63d0\u51fa\u4e86\u201c\uff08\u5411\u5747\u503c\uff09\u56de\u5f52\u201d \u7684\u6982\u5ff5\u3002\u4f17\u6240\u5468\u77e5\uff0c\u4ed6\u7528\u7684\u662f\u7ebf\u6027\u56de\u5f52\u6a21\u578b\u3002\u6b64\u65f6\u7684\u6a21\u578b\u4e0d\u518d\u662f\u4e25\u683c\u610f\u4e49\u7684\u201c\u7269\u7406\u6a21\u578b\u201d\uff0c\u800c\u662f\u201c\u7edf\u8ba1\u6a21\u578b\u201d \u2014 \u7528\u4e8e\u523b\u753b\u53d8\u91cf\u4e4b\u95f4\u7684\u5173\u7cfb\uff0c\u800c\u4e0d\u4e00\u5b9a\u662f\u7269\u7406\u673a\u5236\u3002\u4e4b\u540e\uff0cKarl Pearson \u63d0\u51fa\u4e86\u201c\u76f8\u5173\u7cfb\u6570\u201d\uff08correlation coefficient\uff09\u3002\u540e\u4e16\u7814\u7a76\u7684\u7edf\u8ba1\uff0c\u5927\u591a\u662f\u5173\u4e8e\u00a0<strong>\u201c\u76f8\u5173\u5173\u7cfb\u201d \u7684\u7406\u8bba<\/strong>\u3002\u4f46\u662f\u5173\u4e8e \u201c<strong>\u56e0\u679c\u5173\u7cfb<\/strong>\u201d \u7684\u7edf\u8ba1\u7406\u8bba\uff0c\u975e\u5e38\u7a00\u5c11\u3002\u636e Judea Pearl \u8bf4\uff0cKarl Pearson \u660e\u786e\u7684\u53cd\u5bf9\u7528\u7edf\u8ba1\u7814\u7a76\u56e0\u679c\u5173\u7cfb\uff1b\u6709\u610f\u601d\u7684\u662f\uff0c\u540e\u6765\u56e0\u679c\u63a8\u65ad\u4e3a\u6570\u4e0d\u591a\u7684\u91cd\u8981\u6587\u7ae0\uff08\u5982 Rosenbaum and Rubin 1983; Pearl 1995\uff09\u90fd\u53d1\u8868\u5728\u7531 Karl Pearson \u521b\u520a\u7684 Biometrika \u4e0a\u3002\u4e0b\u9762\u8bb2\u5230\u7684\u6096\u8bba\uff0c\u53ef\u4ee5\u8bf4\u662f\u56f0\u6270\u7edf\u8ba1\u7684\u6839\u672c\u95ee\u9898\uff0c\u6211\u5b66\u4e60\u56e0\u679c\u63a8\u65ad\u4fbf\u662f\u7531\u6b64\u5165\u95e8\u7684\u3002<\/p>\n<p>\u5728\u9ad8\u7ef4\u5217\u8054\u8868\u5206\u6790\u4e2d\uff0c \u6709\u4e00\u4e2a\u5f88\u6709\u540d\u7684\u4f8b\u5b50\uff0c\u53eb\u505a Yule-Simpson\u2019s Paradox\u3002\u6709\u6587\u732e\u79f0\uff0cKarl Pearson \u5f88\u65e9\u5c31\u53d1\u73b0\u4e86\u8fd9\u4e2a\u6096\u8bba \u2014\u2014\u4e5f\u8bb8\u8fd9\u6b63\u662f\u4ed6\u53cd\u5bf9\u7edf\u8ba1\u56e0\u679c\u63a8\u65ad\u7684\u539f\u56e0\u3002\u6b64\u6096\u8bba\u8868\u660e\uff0c\u5b58\u5728\u5982\u4e0b\u7684\u53ef\u80fd\u6027\uff1aX\u548cY\u5728\u8fb9\u7f18\u4e0a\u6b63\u76f8\u5173\uff1b\u4f46\u662f\u7ed9\u5b9a\u53e6\u5916\u4e00\u4e2a\u53d8\u91cfZ\u540e\uff0c\u5728Z\u7684\u6bcf\u4e00\u4e2a\u6c34\u5e73\u4e0a\uff0cX\u548cY\u90fd\u8d1f\u76f8\u5173\u3002Table 1 \u662f\u4e00\u4e2a\u6570\u503c\u7684\u4f8b\u5b50\uff0c\u53d6\u81eaPearl(2000)\u3002<\/p>\n<p><img decoding=\"async\" class=\"rich_pages img_loading\" src=\"data:image\/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVQImWNgYGBgAAAABQABh6FO1AAAAABJRU5ErkJggg==\" alt=\"\u56fe\u7247\" crossorigin=\"anonymous\" data-ratio=\"0.765625\" data-s=\"300,640\" data-type=\"png\" data-w=\"384\" data-src=\"https:\/\/mmbiz.qpic.cn\/mmbiz_png\/dMFkbmlFTgcicYzXUB08IUkOCOWf170AHS1hSAQz2dgicxTk8IDeMsZZ1vJOPXP5YFpR30xlcQibmRYP9Z7o7asSQ\/640?wx_fmt=png\" \/><\/p>\n<p>Table 1 \u4e2d\uff0c\u7b2c\u4e00\u4e2a\u8868\u662f\u6574\u4e2a\u4eba\u7fa4\u7684\u6570\u636e\uff1a\u63a5\u53d7\u5904\u7406\u548c\u5bf9\u7167\u7684\u4eba\u90fd\u662f 40 \u4eba\uff0c\u5904\u7406\u6709\u8f83\u9ad8\u7684\u5b58\u6d3b\u7387\uff0c\u56e0\u6b64\u5904\u7406\u5bf9\u6574\u4e2a\u4eba\u7fa4\u6709 \u201c\u6b63\u4f5c\u7528\u201d\u3002\u7b2c\u4e8c\u4e2a\u8868\u548c\u7b2c\u4e09\u4e2a\u8868\u662f\u5c06\u6574\u4e2a\u4eba\u7fa4\u7528\u6027\u522b\u5206\u5c42\u5f97\u5230\u7684\uff0c\u56e0\u4e3a\u7b2c\u4e00\u4e2a\u8868\u7684\u56db\u4e2a\u683c\u5b50\u6570\uff0c\u5206\u522b\u662f\u4e0b\u9762\u4e24\u4e2a\u8868\u5bf9\u5e94\u683c\u5b50\u6570\u7684\u548c\uff1a<br \/>\n<img decoding=\"async\" class=\"img_loading\" src=\"data:image\/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVQImWNgYGBgAAAABQABh6FO1AAAAABJRU5ErkJggg==\" alt=\"\u56fe\u7247\" crossorigin=\"anonymous\" data-ratio=\"0.08648648648648649\" data-type=\"png\" data-w=\"740\" data-src=\"https:\/\/mmbiz.qpic.cn\/mmbiz_png\/dMFkbmlFTgcicYzXUB08IUkOCOWf170AHzMDbWZXRGdJfmicHlolsfOkPcyIQhLibuibicy8KnggAGtnQZgcR2zYV8Q\/640?wx_fmt=png\" \/><br \/>\n\u5947\u602a\u7684\u662f\uff0c\u5904\u7406\u5bf9\u7537\u6027\u6709 \u201c\u8d1f\u4f5c\u7528\u201d\uff0c\u5bf9\u5973\u6027\u4e5f\u6709 \u201c\u8d1f\u4f5c\u7528\u201d\u3002\u4e00\u4e2a\u5904\u7406\u5bf9\u7537\u6027\u548c\u5973\u6027\u90fd\u6709 \u201c\u8d1f\u4f5c\u7528\u201d\uff0c\u4f46\u662f\u4ed6\u5bf9\u6574\u4e2a\u4eba\u7fa4\u5374\u6709 \u201c\u6b63\u4f5c\u7528\u201d\uff1a\u6096\u8bba\u4ea7\u751f\u4e86\uff01<\/p>\n<p>\u6709\u4eba\u53ef\u80fd\u4f1a\u8ba4\u4e3a\u8fd9\u79cd\u73b0\u8c61\u662f\u7531\u4e8e\u968f\u673a\u6027\u6216\u8005\u5c0f\u6837\u672c\u7684\u8bef\u5dee\u5bfc\u81f4\u7684\u3002\u4f46\u662f\u8fd9\u4e2a\u73b0\u8c61\u4e0e\u6837\u672c\u91cf\u65e0\u5173\uff0c\u4e0e\u7edf\u8ba1\u7684\u8bef\u5dee\u4e5f\u65e0\u5173\u3002\u6bd4\u5982\uff0c\u5c06\u4e0a\u9762\u7684\u6bcf\u4e2a\u683c\u5b50\u6570\u4e58\u4ee5\u4e00\u4e2a\u5de8\u5927\u7684\u6b63\u6570\uff0c\u4e0a\u9762\u7684\u6096\u8bba\u4f9d\u7136\u5b58\u5728\u3002<\/p>\n<p>\u7eaf\u6570\u5b66\u7684\u89d2\u5ea6\uff0c\u4e0a\u9762\u7684\u6096\u8bba\u53ef\u4ee5\u5199\u6210\u521d\u7b49\u6570\u5b66<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-621\" src=\"https:\/\/aif.amtbbs.org\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-16.jpg\" width=\"442\" height=\"74\" alt=\"\u56fe\u7247\" srcset=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-16.jpg 442w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-16-300x50.jpg 300w\" sizes=\"auto, (max-width: 442px) 100vw, 442px\" \/>\uff1b\u8fd9\u5e76\u65e0\u65b0\u5947\u4e4b\u5904\u3002\u4f46\u662f\u5728\u7edf\u8ba1\u4e0a\uff0c\u8fd9\u5177\u6709\u91cd\u8981\u7684\u610f\u4e49\u2014\u2014\u53d8\u91cf\u4e4b\u95f4\u7684\u76f8\u5173\u5173\u7cfb\u53ef\u4ee5\u5b8c\u5168\u7684\u88ab\u7b2c\u4e09\u4e2a\u53d8\u91cf \u201c\u626d\u66f2\u201d\u3002\u66f4\u4e25\u91cd\u7684\u95ee\u9898\u662f\uff0c\u6211\u4eec\u7684\u6536\u96c6\u7684\u6570\u636e\u53ef\u80fd\u5b58\u5728\u5c40\u9650\u6027\uff0c\u5ffd\u7565\u6f5c\u5728\u7684\u201c\u7b2c\u4e09\u4e2a\u53d8\u91cf\u201d \u53ef\u80fd\u6539\u53d8\u5df2\u6709\u7684\u7ed3\u8bba\uff0c\u800c\u6211\u4eec\u5e38\u5e38\u5374\u4e00\u65e0\u6240\u77e5\u3002\u9274\u4e8e Yule-Simpson \u6096\u8bba\u7684\u6f5c\u5728\u53ef\u80fd\uff0c\u4e0d\u5c11\u4eba\u8ba4\u4e3a\uff0c\u7edf\u8ba1\u4e0d\u53ef\u80fd\u7528\u6765\u7814\u7a76\u56e0\u679c\u5173\u7cfb\u3002<\/p>\n<p>\u4e0a\u9762\u7684\u4f8b\u5b50\u662f\u4eba\u5de5\u6784\u9020\u7684\uff0c\u5728\u73b0\u5b9e\u4e2d\uff0c\u4e5f\u5b58\u5728\u4e0d\u5c11\u7684\u5b9e\u4f8b\u6b63\u662f Yule-Simpson\u2019s Paradox\u3002\u6bd4\u5982\uff0cUC Berkeley \u7684\u8457\u540d\u7edf\u8ba1\u5b66\u5bb6 Peter Bickel \u6559\u6388 1975 \u5e74\u5728 Science \u4e0a\u53d1\u8868\u6587\u7ae0\uff0c\u62a5\u544a\u4e86 Berkeley \u7814\u7a76\u751f\u9662\u7537\u5973\u5f55\u53d6\u7387\u7684\u5dee\u5f02\u3002\u4ed6\u53d1\u73b0\uff0c\u603b\u4f53\u4e0a\uff0c\u7537\u6027\u7684\u5f55\u53d6\u7387\u9ad8\u4e8e\u5973\u6027\uff0c\u7136\u800c\u6309\u7167\u4e13\u4e1a\u5206\u5c42\u540e\uff0c\u5973\u6027\u7684\u5f55\u53d6\u7387\u5374\u9ad8\u4e8e\u7537\u6027\u00a0(Bickel \u7b49 1975)\u3002\u5728\u6d41\u884c\u75c5\u5b66\u7684\u6559\u79d1\u4e66\u00a0(\u5982 Rothman \u7b49 2008)\u00a0\u4e2d\uff0c\u90fd\u4f1a\u8bb2\u5230 \u201c\u6df7\u6742\u504f\u501a\u201d\uff08confounding bias\uff09\uff0c\u5176\u5b9e\u5c31\u662f Yule-Simpson\u2019s Paradox\uff0c\u4e66\u4e2d\u5217\u4e3e\u4e86\u5f88\u591a\u6d41\u884c\u75c5\u5b66\u7684\u5b9e\u9645\u4f8b\u5b50\u3002<\/p>\n<p>\u7531\u4e8e\u6709 Yule-Simpson\u2019s Paradox \u7684\u5b58\u5728\uff0c\u89c2\u5bdf\u6027\u7814\u7a76\u4e2d\u5f88\u96be\u5f97\u5230\u6709\u5173\u56e0\u679c\u7684\u7ed3\u8bba\uff0c\u9664\u975e\u52a0\u4e0a\u5f88\u5f3a\u7684\u5047\u5b9a\uff0c\u8fd9\u5728\u540e\u9762\u4f1a\u8c08\u5230\u3002\u6bd4\u5982\uff0c\u4e00\u4e2a\u5f88\u7ecf\u5178\u7684\u95ee\u9898\uff1a\u5438\u70df\u662f\u5426\u5bfc\u81f4\u80ba\u764c\uff1f\u7531\u4e8e\u6211\u4eec\u4e0d\u53ef\u80fd\u5bf9\u4eba\u7fa4\u662f\u5426\u5438\u70df\u505a\u968f\u673a\u5316\u8bd5\u9a8c\uff0c\u6211\u4eec\u5f97\u5230\u7684\u6570\u636e\u90fd\u662f\u89c2\u5bdf\u6027\u7684\u6570\u636e\uff1a\u5373\u5438\u70df\u548c\u80ba\u764c\u4e4b\u95f4\u7684\u76f8\u5173\u6027\u00a0\uff08\u6b63\u5982 Table 1 \u7684\u5408\u5e76\u8868\uff09\u3002\u6b64\u65f6\uff0c\u5373\u4f7f\u6211\u4eec\u5f97\u5230\u4e86\u5438\u70df\u4e0e\u80ba\u764c\u6b63\u76f8\u5173\uff0c\u4e5f\u4e0d\u80fd\u65ad\u8a00 \u201c\u5438\u70df\u5bfc\u81f4\u80ba\u764c\u201d\u3002\u8fd9\u662f\u56e0\u4e3a\u53ef\u80fd\u5b58\u5728\u4e00\u4e9b\u672a\u89c2\u6d4b\u7684\u56e0\u7d20\uff0c\u4ed6\u65e2\u5f71\u54cd\u4e2a\u4f53\u662f\u5426\u5438\u70df\uff0c\u540c\u65f6\u5f71\u54cd\u4e2a\u4f53\u662f\u5426\u5f97\u764c\u75c7\u3002\u6bd4\u5982\uff0c\u67d0\u4e9b\u57fa\u56e0\u53ef\u80fd\u4f7f\u5f97\u4eba\u66f4\u5bb9\u6613\u5438\u70df\uff0c\u540c\u65f6\u5bb9\u6613\u5f97\u80ba\u764c\uff1b\u5b58\u5728\u8fd9\u6837\u57fa\u56e0\u7684\u4eba\u4e0d\u5438\u70df\uff0c\u4e5f\u540c\u6837\u5f97\u80ba\u764c\u3002\u6b64\u65f6\uff0c\u5438\u70df\u548c\u80ba\u764c\u4e4b\u95f4\u76f8\u5173\uff0c\u5374\u6ca1\u6709\u56e0\u679c\u4f5c\u7528\u3002<\/p>\n<p>\u76f8\u53cd\u7684\uff0c\u6211\u4eec\u77e5\u9053\u653e\u5c04\u6027\u7269\u8d28\u5bf9\u4eba\u4f53\u7684\u5065\u5eb7\u6709\u5f88\u5927\u7684\u4f24\u5bb3\uff0c\u4f46\u662f\u94c0\u77ff\u7684\u5de5\u4eba\u5e73\u5747\u5bff\u547d\u5374\u4e0d\u6bd4\u5e38\u4eba\u77ed\uff1b\u8fd9\u662f\u6d41\u884c\u75c5\u5b66\u4e2d\u6709\u540d\u7684 \u201c\u5065\u5eb7\u5de5\u4eba\u6548\u5e94\u201d\uff08healthy worker effect\uff09\u3002\u8fd9\u6837\u4e00\u6765\uff0c\u4f3c\u4e4e\u662f\u8bf4\u94c0\u77ff\u5de5\u4f5c\u5bf9\u5065\u5eb7\u6ca1\u6709\u5f71\u54cd\u3002\u4f46\u662f\uff0c\u4e8b\u5b9e\u4e0a\uff0c\u94c0\u77ff\u7684\u5de5\u4eba\u901a\u5e38\u90fd\u662f\u8eab\u5f3a\u529b\u58ee\u7684\u4eba\uff0c\u4e0d\u5728\u94c0\u77ff\u5de5\u4f5c\u5bff\u547d\u4f1a\u66f4\u957f\u3002\u6b64\u65f6\uff0c\u5728\u94c0\u77ff\u5de5\u4f5c\u4e0e\u5426\u4e0e\u5bff\u547d\u4e0d\u76f8\u5173\uff0c\u4f46\u662f\u653e\u5c04\u6027\u7269\u8d28\u5bf9\u4eba\u7684\u5065\u5eb7\u662f\u6709\u56e0\u679c\u4f5c\u7528\u7684\u3002<\/p>\n<p>\u8fd9\u91cc\u4e3e\u4e86\u4e00\u4e2a\u6096\u8bba\uff0c\u4f46\u6ca1\u6709\u6df1\u5165\u7684\u9610\u91ca\u539f\u56e0\u3002\u9610\u91ca\u6e05\u695a\u8fd9\u4e2a\u95ee\u9898\u7684\u6839\u672c\u539f\u56e0\uff0c\u5176\u5b9e\u5c31\u8bb2\u6e05\u695a\u4e86\u4ec0\u4e48\u662f\u56e0\u679c\u63a8\u65ad\u3002\u8fd9\u5728\u540e\u9762\u4f1a\u8bb2\u5230\u3002\u4f5c\u4e3a\u7ed3\u675f\uff0c\u7559\u4e0b\u5982\u4e0b\u601d\u8003\u7684\u95ee\u9898\uff1a<\/p>\n<ol class=\"list-paddingleft-2\">\n<li>\n<section>Table 1 \u4e2d\uff0c\u5904\u7406\u7ec4\u548c\u5bf9\u7167\u7ec4\u4e2d\uff0c\u7537\u6027\u7684\u6bd4\u4f8b\u5206\u522b\u4e3a\u591a\u5c11\uff1f\u8fd9\u5bf9\u6096\u8bba\u7684\u4ea7\u751f\u6709\u4ec0\u4e48\u6837\u7684\u5f71\u54cd\uff1f\u53cd\u8fc7\u6765\u8003\u8651\u5904\u7406\u7684 \u201c\u5206\u914d\u673a\u5236\u201d\uff08assignment mechanism\uff09\uff0c\u8ba1\u7b97P(Treatment\u2223Male)\u548c P(Treatment\u2223Female)\u3002<\/section>\n<\/li>\n<li>\n<section>\u5047\u5982(X\uff0cY\uff0cZ)\u670d\u4ece\u4e09\u5143\u6b63\u6001\u5206\u5e03\uff0cX\u548cY\u6b63\u76f8\u5173\uff0cY\u548cZ\u6b63\u76f8\u5173\uff0c\u90a3\u4e48X\u548cZ\u662f\u5426\u6b63\u76f8\u5173\uff1f\uff08\u5317\u4eac\u5927\u5b66\u6982\u7387\u7edf\u8ba1\u7cfb 09 \u5e74\u300a\u5e94\u7528\u591a\u5143\u7edf\u8ba1\u5206\u6790\u300b\u671f\u672b\u7b2c\u4e00\u9898\uff09<\/section>\n<\/li>\n<li>\n<section>\u6d41\u884c\u75c5\u5b66\u7684\u6559\u79d1\u4e66\u5e38\u5e38\u4f1a\u8bb2\u5404\u79cd\u6096\u8bba\uff0c\u6bd4\u5982\u6df7\u6742\u504f\u501a\u00a0\uff08confounding bias\uff09\u548c\u5165\u9662\u7387\u504f\u501a\uff08Berkson\u2019s bias\uff09\u7b49\uff0c\u672c\u8d28\u4e0a\u662f\u5426\u4e0e\u56e0\u679c\u63a8\u65ad\u6709\u5173\uff1f<br \/>\n\u8ba1\u91cf\u7ecf\u6d4e\u5b66\u4e2d\u7684 \u201c\u5185\u751f\u6027\u201d\uff08endogeneity\uff09\u600e\u4e48\u5b9a\u4e49\uff1f\u5b83\u548c Yule-Simpson \u6096\u8bba\u6709\u4ec0\u4e48\u8054\u7cfb\uff1f<\/section>\n<\/li>\n<\/ol>\n<section><\/section>\n<section>\n<section>\n<section>\n<section>\n<section><\/section>\n<section><\/section>\n<section>\n<section><\/section>\n<\/section>\n<\/section>\n<section><strong>2. \u56e0\u679c\u63a8\u65ad\u7b80\u4ecb\u4e4b\u4e8c\uff1a<\/strong><\/p>\n<p><strong>Rubin Causal Model (RCM) \u548c\u968f\u673a\u5316\u8bd5\u9a8c<\/strong><\/p>\n<\/section>\n<section>\n<section><\/section>\n<section><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<p><img decoding=\"async\" class=\"rich_pages img_loading\" src=\"data:image\/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVQImWNgYGBgAAAABQABh6FO1AAAAABJRU5ErkJggg==\" alt=\"\u56fe\u7247\" crossorigin=\"anonymous\" data-ratio=\"1.102803738317757\" data-s=\"300,640\" data-type=\"jpeg\" data-w=\"214\" data-src=\"https:\/\/mmbiz.qpic.cn\/mmbiz_jpg\/dMFkbmlFTgdbjJeDmSYMMjibYicQvox1g8dvCy2icPKk60GtJBVWCFo0wzWmtCT3JibylhCU8tE6dT7HiacibRiaDzm2w\/640?wx_fmt=jpeg\" \/><\/p>\n<section>\u56e0\u679c\u63a8\u65ad\u7528\u7684\u6700\u591a\u7684\u6a21\u578b\u662f Rubin Causal Model\u00a0(RCM; Rubin 1978)\u00a0\u548c Causal Diagram\u00a0(Pearl 1995)\u3002Pearl\u00a0(2000)\u00a0\u4e2d\u4ecb\u7ecd\u4e86\u8fd9\u4e24\u4e2a\u6a21\u578b\u7684\u7b49\u4ef7\u6027\uff0c\u4f46\u662f\u5c31\u5e94\u7528\u6765\u770b\uff0cRCM \u66f4\u52a0\u7cbe\u786e\uff0c\u800c Causal Diagram \u66f4\u52a0\u76f4\u89c2\uff0c\u540e\u8005\u6df1\u53d7\u8ba1\u7b97\u673a\u4e13\u5bb6\u4eec\u7684\u63a8\u5d07\u3002\u8fd9\u90e8\u5206\u4e3b\u8981\u8bb2 RCM\u3002<\/p>\n<p>\u8bbe<img decoding=\"async\" class=\"rich_pages\" src=\"data:image\/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVQImWNgYGBgAAAABQABh6FO1AAAAABJRU5ErkJggg==\" alt=\"\u56fe\u7247\" crossorigin=\"anonymous\" data-ratio=\"1.0204081632653061\" data-s=\"300,640\" data-type=\"png\" data-w=\"49\" data-src=\"https:\/\/mmbiz.qpic.cn\/mmbiz_png\/dMFkbmlFTgdbjJeDmSYMMjibYicQvox1g8iatoq8ibDqibwWibQLk9RvxEfOjoyLy7tJSzeTwib89VZhgmoYVxia6MuhEQ\/640?wx_fmt=png\" \/>\u8868\u793a\u4e2a\u4f53 i\u63a5\u53d7\u5904\u7406\u4e0e\u5426\uff0c\u5904\u7406\u53d61\uff0c\u5bf9\u7167\u53d60\u00a0(\u8fd9\u90e8\u5206\u7684\u5904\u7406\u53d8\u91cf\u90fd\u8ba8\u8bba\u4e8c\u503c\u7684\uff0c\u591a\u503c\u7684\u53ef\u4ee5\u505a\u76f8\u5e94\u7684\u63a8\u5e7f)\uff1b<img decoding=\"async\" class=\"rich_pages\" src=\"data:image\/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVQImWNgYGBgAAAABQABh6FO1AAAAABJRU5ErkJggg==\" alt=\"\u56fe\u7247\" crossorigin=\"anonymous\" data-ratio=\"1.1555555555555554\" data-s=\"300,640\" data-type=\"png\" data-w=\"45\" data-src=\"https:\/\/mmbiz.qpic.cn\/mmbiz_png\/dMFkbmlFTgdbjJeDmSYMMjibYicQvox1g8GibiatIcGQHyHIcIcyYiaByXca4O77jbHVgkduwzVL0OiaibicrH4NVSkBJQ\/640?wx_fmt=png\" \/>\u8868\u793a\u4e2a\u4f53 i\u7684\u7ed3\u679c\u53d8\u91cf\u3002\u53e6\u5916\u8bb0\u00a0<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-622\" src=\"https:\/\/aif.amtbbs.org\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-8.png\" width=\"173\" height=\"61\" alt=\"\u56fe\u7247\" \/>\u00a0\u8868\u793a\u4e2a\u4f53 i\u63a5\u53d7\u5904\u7406\u6216\u8005\u5bf9\u7167\u7684\u6f5c\u5728\u7ed3\u679c\u00a0(potential outcome)\uff0c\u90a3\u4e48\u00a0<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-623\" src=\"https:\/\/aif.amtbbs.org\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-9.png\" width=\"166\" height=\"61\" alt=\"\u56fe\u7247\" \/>\u00a0\u00a0\u8868\u793a\u4e2a\u4f53 i \u63a5\u53d7\u6cbb\u7597\u7684\u4e2a\u4f53\u56e0\u679c\u4f5c\u7528\u3002\u4e0d\u5e78\u7684\u662f\uff0c\u6bcf\u4e2a\u4e2a\u4f53\u8981\u4e48\u63a5\u53d7\u5904\u7406\uff0c\u8981\u4e48\u63a5\u53d7\u5bf9\u7167\uff0c<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-624\" src=\"https:\/\/aif.amtbbs.org\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-10.png\" width=\"173\" height=\"61\" alt=\"\u56fe\u7247\" \/>\u00a0\u4e2d\u5fc5\u7136\u7f3a\u5931\u4e00\u534a\uff0c\u4e2a\u4f53\u7684\u56e0\u679c\u4f5c\u7528\u662f\u4e0d\u53ef\u8bc6\u522b\u7684\u3002\u89c2\u6d4b\u7684\u7ed3\u679c\u662f\u00a0<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-625\" src=\"https:\/\/aif.amtbbs.org\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-11.png\" width=\"337\" height=\"61\" alt=\"\u56fe\u7247\" srcset=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-11.png 337w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-11-300x54.png 300w\" sizes=\"auto, (max-width: 337px) 100vw, 337px\" \/>\u3002\u4f46\u662f\uff0c\u5728Z\u505a\u968f\u673a\u5316\u7684\u524d\u63d0\u4e0b\uff0c\u6211\u4eec\u53ef\u4ee5\u8bc6\u522b\u603b\u4f53\u7684\u5e73\u5747\u56e0\u679c\u4f5c\u7528\u00a0(Average Causal Effect; ACE\uff09\uff1a<\/p>\n<section><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-626\" src=\"https:\/\/aif.amtbbs.org\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-12.png\" width=\"498\" height=\"68\" alt=\"\u56fe\u7247\" srcset=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-12.png 498w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-12-300x41.png 300w\" sizes=\"auto, (max-width: 498px) 100vw, 498px\" \/><\/section>\n<section>\u8fd9\u662f\u56e0\u4e3a<\/section>\n<section><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-627\" src=\"https:\/\/aif.amtbbs.org\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-13.png\" width=\"847\" height=\"150\" alt=\"\u56fe\u7247\" srcset=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-13.png 847w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-13-300x53.png 300w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-13-768x136.png 768w\" sizes=\"auto, (max-width: 847px) 100vw, 847px\" \/><\/section>\n<section>\u6700\u540e\u4e00\u4e2a\u7b49\u5f0f\u8868\u660e<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-628\" src=\"https:\/\/aif.amtbbs.org\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-14.png\" width=\"77\" height=\"61\" alt=\"\u56fe\u7247\" \/>\u53ef\u4ee5\u7531\u89c2\u6d4b\u7684\u6570\u636e\u4f30\u8ba1\u51fa\u6765\u3002\u5176\u4e2d\u7b2c\u4e00\u4e2a\u7b49\u5f0f\u7528\u5230\u4e86\u671f\u671b\u7b97\u5b50\u7684\u7ebf\u6027\u6027\uff08\u975e\u7ebf\u6027\u7684\u7b97\u5b50\u5bfc\u51fa\u7684\u56e0\u679c\u5ea6\u91cf\u5f88\u96be\u88ab\u8bc6\u522b\uff01)\uff1b\u7b2c\u4e8c\u4e2a\u5f0f\u5b50\u7528\u5230\u4e86\u968f\u673a\u5316\uff0c\u5373<\/section>\n<section><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-629\" src=\"https:\/\/aif.amtbbs.org\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-15.png\" width=\"255\" height=\"68\" alt=\"\u56fe\u7247\" \/><\/section>\n<section>\u5176\u4e2d\uff0c<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-630\" src=\"https:\/\/aif.amtbbs.org\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-16.png\" width=\"42\" height=\"37\" alt=\"\u56fe\u7247\" \/>\u8868\u793a\u72ec\u7acb\u6027\u3002\u7531\u6b64\u53ef\u89c1\uff0c\u968f\u673a\u5316\u8bd5\u9a8c\u5bf9\u4e8e\u5e73\u5747\u56e0\u679c\u4f5c\u7528\u7684\u8bc6\u522b\u8d77\u7740\u81f3\u5173\u91cd\u8981\u7684\u4f5c\u7528\u3002<\/section>\n<section>\u5f53Y\u662f\u4e8c\u503c\u7684\u65f6\u5019\uff0c\u5e73\u5747\u56e0\u679c\u4f5c\u7528\u662f\u6d41\u884c\u75c5\u5b66\u4e2d\u5e38\u7528\u7684\u201c\u98ce\u9669\u5dee\u201d\uff08risk difference; RD\uff09\uff1a<\/section>\n<section><img decoding=\"async\" class=\"rich_pages img_loading\" src=\"data:image\/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVQImWNgYGBgAAAABQABh6FO1AAAAABJRU5ErkJggg==\" alt=\"\u56fe\u7247\" crossorigin=\"anonymous\" data-ratio=\"0.12267657992565056\" data-s=\"300,640\" data-type=\"png\" data-w=\"807\" data-src=\"https:\/\/mmbiz.qpic.cn\/mmbiz_png\/dMFkbmlFTgdbjJeDmSYMMjibYicQvox1g87U1wUjZspK0aT2KGnvLCN4ckics2l0cnuNxT11kCQK5ybRqEI63cP8g\/640?wx_fmt=png\" \/><\/section>\n<section>\u5f53\u7136\uff0c\u6d41\u884c\u75c5\u5b66\u8fd8\u5e38\u7528\u201c\u98ce\u9669\u6bd4\u201d\uff08risk ratio; RR\uff09\uff1a<\/section>\n<section><img decoding=\"async\" class=\"rich_pages img_loading\" src=\"data:image\/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVQImWNgYGBgAAAABQABh6FO1AAAAABJRU5ErkJggg==\" alt=\"\u56fe\u7247\" crossorigin=\"anonymous\" data-ratio=\"0.3510436432637571\" data-s=\"300,640\" data-type=\"png\" data-w=\"527\" data-src=\"https:\/\/mmbiz.qpic.cn\/mmbiz_png\/dMFkbmlFTgdbjJeDmSYMMjibYicQvox1g8yn1SCeyicicNkCs9KoVHiayq8C2v9icCf6gnpO0VK3NiaaKOKawBzRIOxRw\/640?wx_fmt=png\" \/><\/section>\n<section>\u548c\u201c\u4f18\u52bf\u6bd4\u201d\uff08odds ratio;\u00a0OR\uff09\uff1a<\/section>\n<section><img decoding=\"async\" class=\"rich_pages img_loading\" src=\"data:image\/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVQImWNgYGBgAAAABQABh6FO1AAAAABJRU5ErkJggg==\" alt=\"\u56fe\u7247\" crossorigin=\"anonymous\" data-ratio=\"0.24434876210979548\" data-s=\"300,640\" data-type=\"png\" data-w=\"929\" data-src=\"https:\/\/mmbiz.qpic.cn\/mmbiz_png\/dMFkbmlFTgdbjJeDmSYMMjibYicQvox1g8q6YKBkaAOI2lYABYWJKrQib8kC0Tn81KPjSVdTEZveUJiaibicYTibWPLGw\/640?wx_fmt=png\" \/><\/section>\n<section>\u4e0a\u9762\u7684\u8bb0\u53f7\u90fd\u5e26\u7740\u201cC\u201d\uff0c\u662f\u4e3a\u4e86\u5f3a\u8c03\u201ccausal\u201d\u3002\u7ec6\u5fc3\u7684\u8bfb\u8005\u4f1a\u53d1\u73b0\uff0c\u5b9a\u4e49 CRR \u548c COR \u7684\u51fa\u53d1\u70b9\u548c ACE \u4e0d\u592a\u4e00\u6837\u3002ACE \u662f\u901a\u8fc7\u5bf9\u4e2a\u4f53\u56e0\u679c\u4f5c\u7528\u6c42\u671f\u671b\u5f97\u5230\u7684\uff0c\u4f46\u662f CRR \u548c COR \u662f\u76f4\u63a5\u5728\u603b\u4f53\u4e0a\u5b9a\u4e49\u7684\u3002\u8fd9\u70b9\u5fae\u5999\u7684\u533a\u522b\u8fd8\u5f15\u8d77\u4e86\u4e0d\u5c11\u4eba\u7684\u7814\u7a76\u5174\u8da3\u3002\u6bd4\u5982\uff0c\u7ecf\u6d4e\u5b66\u4e2d\u7684\u67d0\u4e9b\u95ee\u9898\uff0c\u53d7\u5230\u7ecf\u6d4e\u7406\u8bba\u7684\u542f\u793a\uff0c\u5904\u7406\u7684\u4f5c\u7528\u53ef\u80fd\u662f\u975e\u5e38\u6570\u7684\uff0c\u4ec5\u4ec5\u7814\u7a76\u5e73\u5747\u56e0\u679c\u4f5c\u7528\u4e0d\u80fd\u6ee1\u8db3\u5b9e\u9645\u95ee\u9898\u7684\u9700\u8981\u3002\u8fd9\u65f6\u5019\uff0c\u8ba1\u91cf\u7ecf\u6d4e\u5b66\u5bb6\u63d0\u51fa\u4e86\u201c\u5206\u4f4d\u6570\u5904\u7406\u4f5c\u7528\u201d\uff08quantile treatment effect: QTE\uff09\uff1a<\/section>\n<section><img decoding=\"async\" class=\"img_loading\" src=\"data:image\/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVQImWNgYGBgAAAABQABh6FO1AAAAABJRU5ErkJggg==\" alt=\"\u56fe\u7247\" crossorigin=\"anonymous\" data-ratio=\"0.1548974943052392\" data-type=\"png\" data-w=\"439\" data-src=\"https:\/\/mmbiz.qpic.cn\/mmbiz_png\/dMFkbmlFTgdbjJeDmSYMMjibYicQvox1g8vwYP7bkUlOPHI42yFeeiaNib6BJjUAS3noXvq1EeuZax3mRx23Fgn6oQ\/640?wx_fmt=png\" \/><\/section>\n<section>\u5728\u968f\u673a\u5316\u4e0b\uff0c\u8fd9\u4e2a\u91cf\u4e5f\u662f\u53ef\u4ee5\u8bc6\u522b\u7684\u3002\u4f46\u662f\uff0c\u5176\u5b9e\u8fd9\u4e2a\u91cf\u5e76\u4e0d\u80fd\u56de\u7b54\u5904\u7406\u4f5c\u7528\u5f02\u8d28\u6027\uff08heterogenous treatment effects\uff09\u7684\u95ee\u9898\uff0c\u56e0\u4e3a\u5904\u7406\u4f5c\u7528\u975e\u5e38\u6570\uff0c\u6700\u597d\u7528\u5982\u4e0b\u7684\u91cf\u523b\u753b\uff1a<\/section>\n<p><img decoding=\"async\" class=\"img_loading\" src=\"data:image\/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVQImWNgYGBgAAAABQABh6FO1AAAAABJRU5ErkJggg==\" alt=\"\u56fe\u7247\" crossorigin=\"anonymous\" data-ratio=\"0.16831683168316833\" data-type=\"png\" data-w=\"404\" data-src=\"https:\/\/mmbiz.qpic.cn\/mmbiz_png\/dMFkbmlFTgdbjJeDmSYMMjibYicQvox1g8uaU35kNiaaQt2mMAG7tzMqXaFWHnW4kpmcdQDt6QLm4pbbcpkfYYuYA\/640?wx_fmt=png\" \/><\/p>\n<section>\u8fd9\u4e2a\u91cf\u523b\u753b\u7684\u662f\u5904\u7406\u4f5c\u7528\u7684\u5206\u5e03\u3002\u4e0d\u5e78\u7684\u662f\uff0c\u4f30\u8ba1\u00a0<img decoding=\"async\" src=\"data:image\/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVQImWNgYGBgAAAABQABh6FO1AAAAABJRU5ErkJggg==\" alt=\"\u56fe\u7247\" crossorigin=\"anonymous\" data-ratio=\"0.8714285714285714\" data-type=\"png\" data-w=\"70\" data-src=\"https:\/\/mmbiz.qpic.cn\/mmbiz_png\/dMFkbmlFTgdbjJeDmSYMMjibYicQvox1g8xSDPmjyaOdaKKLhBTKUQYuMncHv642tOBYicwhFAEyvlbiblib1DdDR9A\/640?wx_fmt=png\" \/>\u00a0\u9700\u8981\u975e\u5e38\u5f3a\u7684\u5047\u5b9a\uff0c\u901a\u5e38\u4e0d\u5177\u6709\u53ef\u884c\u6027\u3002<\/section>\n<section>\n<section>\u4f5c\u4e3a\u7ed3\u675f\uff0c\u7559\u4e0b\u5982\u4e0b\u7684\u95ee\u9898\uff1a<\/section>\n<ol class=\"list-paddingleft-2\">\n<li>\n<section>\u201c\u53ef\u8bc6\u522b\u6027\u201d\uff08identifiability\uff09\u5728\u7edf\u8ba1\u4e2d\u662f\u600e\u4e48\u5b9a\u4e49\u7684\uff1f<\/section>\n<\/li>\n<li>\n<section>\u533b\u5b66\u7814\u7a76\u8005\u901a\u5e38\u8ba4\u4e3a\uff0c\u968f\u673a\u5bf9\u7167\u8bd5\u9a8c\uff08randomized controlled experiment\uff09\u662f\u7814\u7a76\u5904\u7406\u6709\u6548\u6027\u7684\u9ec4\u91d1\u6807\u51c6\uff0c\u539f\u56e0\u662f\u4ec0\u4e48\u5462\uff1f\u968f\u673a\u5316\u8bd5\u9a8c\u4e3a\u4ec0\u4e48\u80fd\u591f\u6d88\u9664 Yule-Simpson \u6096\u8bba\uff1f<\/section>\n<\/li>\n<li>\n<section><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-631\" src=\"https:\/\/aif.amtbbs.org\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-17.png\" width=\"112\" height=\"61\" alt=\"\u56fe\u7247\" \/>\u00a0\u5728\u968f\u673a\u5316\u4e0b\u662f\u53ef\u8bc6\u522b\u7684\u3002\u53e6\u5916\u4e00\u4e2a\u548c\u5b83\u201c\u5bf9\u5076\u201d\u7684\u91cf\u662f Ju and Geng (2010) \u63d0\u51fa\u7684\u5206\u5e03\u56e0\u679c\u4f5c\u7528\uff08distributional causal effect: DCE\uff09\uff1a<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-632\" src=\"https:\/\/aif.amtbbs.org\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-18.png\" width=\"476\" height=\"61\" alt=\"\u56fe\u7247\" srcset=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-18.png 476w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-18-300x38.png 300w\" sizes=\"auto, (max-width: 476px) 100vw, 476px\" \/>\u00a0\uff0c\u5728\u968f\u673a\u5316\u4e0b\u4e5f\u53ef\u4ee5\u8bc6\u522b\u3002<\/section>\n<\/li>\n<li>\n<section>\u5373\u4f7f\u5b8c\u5168\u968f\u673a\u5316\uff0c<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-633\" src=\"https:\/\/aif.amtbbs.org\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-19.png\" width=\"47\" height=\"61\" alt=\"\u56fe\u7247\" \/>\u00a0\u4e5f\u4e0d\u53ef\u8bc6\u522b\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u7ecf\u6d4e\u5b66\u5bb6\u63d0\u51fa\u7684\u5177\u6709\u201c\u7ecf\u6d4e\u5b66\u610f\u4e49\u201d\u7684\u91cf\uff0c\u5f88\u96be\u7528\u89c2\u6d4b\u6570\u636e\u6765\u4f30\u8ba1\u3002\u8fd9\u79cd\u73b0\u8c61\u5728\u5b9e\u9645\u4e2d\u5e38\u5e38\u53d1\u751f\uff1a\u5173\u5fc3\u5b9e\u9645\u95ee\u9898\u7684\u4eba\u5411\u7edf\u8ba1\u5b66\u5bb6\u7d22\u53d6\u7684\u592a\u591a\uff0c\u800c\u4ed6\u4eec\u63d0\u4f9b\u7684\u6570\u636e\u53c8\u5f88\u6709\u9650\u3002<\/section>\n<\/li>\n<\/ol>\n<section>\u5173\u4e8e RCM \u7684\u7248\u6743\uff0c\u9700\u8981\u505a\u4e00\u4e9b\u8bf4\u660e\u3002\u76ee\u524d\u53ef\u4ee5\u770b\u5230\u7684\u6587\u732e\uff0c\u6700\u65e9\u7684\u662f Jerzy Neyman \u4e8e 1923 \u5e74\u7528\u6ce2\u5170\u8bed\u5199\u7684\u535a\u58eb\u8bba\u6587\uff0c\u7b2c\u4e00\u4e2a\u5728\u8bd5\u9a8c\u8bbe\u8ba1\u4e2d\u63d0\u51fa\u4e86\u201c\u6f5c\u5728\u7ed3\u679c\u201d\uff08potential outcome\uff09\u7684\u6982\u5ff5\u3002\u540e\u6765 Donald Rubin \u5728\u89c2\u5bdf\u6027\u7814\u7a76\u4e2d\u91cd\u65b0\uff08\u72ec\u7acb\u5730\uff09\u63d0\u51fa\u4e86\u8fd9\u4e2a\u6982\u5ff5\uff0c\u5e76\u8fdb\u884c\u4e86\u5e7f\u6cdb\u7684\u7814\u7a76\u3002Donald Rubin \u65e9\u671f\u7684\u6587\u7ae0\u5e76\u6ca1\u6709\u5f15\u7528 Jerzy Neyman \u7684\u6587\u7ae0\uff0cJerzy Neyman \u7684\u6587\u7ae0\u4e5f\u4e0d\u4e3a\u4eba\u6240\u77e5\u3002\u4e00\u76f4\u5230 1990 \u5e74\uff0cD. M. Dabrowska \u548c T. P. Speed \u5c06 Jerzy Neyman \u7684\u6587\u7ae0\u7ffb\u8bd1\u6210\u82f1\u6587\u53d1\u8868\u5728 Statistical Science \u4e0a\uff0c\u5927\u5bb6\u624d\u77e5\u9053 Jerzy Neyman \u65e9\u671f\u7684\u91cd\u8981\u8d21\u732e\u3002\u4eca\u5929\u7684\u6587\u732e\u4e2d\uff0c\u6709\u4eba\u79f0 Neyman-Rubin Model\uff0c\u5176\u5b9e\u5c31\u662f\u6f5c\u5728\u7ed3\u679c\u6a21\u578b\u3002\u8ba1\u91cf\u7ecf\u6d4e\u5b66\u5bb6\uff0c\u5982 James Heckman \u79f0\uff0c\u7ecf\u6d4e\u5b66\u4e2d\u7684 Roy Model \u662f\u6f5c\u5728\u7ed3\u679c\u6a21\u578b\u7684\u66f4\u65e9\u63d0\u51fa\u8005\u3002\u5728 Donald Rubin 2004 \u5e74\u7684 Fisher Lecture \u4e2d\uff0c\u4ed6\u975e\u5e38\u4e0d\u6ee1\u5730\u6279\u8bc4\u8ba1\u91cf\u7ecf\u6d4e\u5b66\u5bb6\uff0c\u56e0\u4e3a Roy \u6700\u65e9\u7684\u8bba\u6587\u4e2d\uff0c\u5168\u6587\u6ca1\u6709\u4e00\u4e2a\u6570\u5b66\u7b26\u53f7\uff0c\u786e\u5b9e\u6ca1\u6709\u660e\u786e\u7684\u63d0\u51fa\u8fd9\u4e2a\u6a21\u578b\u3002\u8be6\u60c5\u8bf7\u89c1\uff0cDonald Rubin \u7684 Fisher Lecture\uff0c\u53d1\u8868\u5728 2005 \u5e74\u7684 Journal of the American Statistical Association \u4e0a\u3002\u7814\u7a76 Causal Diagram \u7684\u5b66\u8005\uff0c\u5927\u591a\u6bd4\u8f83\u8ba4\u53ef Donald Rubin \u7684\u8d21\u732e\u3002\u4f46\u662f Donald Rubin \u5374\u662f Causal Diagram \u7684\u575a\u5b9a\u53cd\u5bf9\u8005\uff0c\u4ed6\u8ba4\u4e3a Causal Diagram \u5177\u6709\u8bef\u5bfc\u6027\uff0c\u4e14\u6ca1\u6709\u4ed6\u7684\u6a21\u578b\u6e05\u695a\u3002\u4ed6\u4e0eJames Heckman\u00a0\uff08\u8bfa\u8d1d\u5c14\u7ecf\u6d4e\u5b66\u5956\uff09\uff0c Judea Pearl\u00a0\uff08\u56fe\u7075\u5956\uff09\u00a0\u548c James Robins \u4e4b\u95f4\u7684\u6fc0\u70c8\u4e89\u8bba\uff0c\u6210\u4e3a\u4e86\u5e7f\u4e3a\u6d41\u4f20\u7684\u8da3\u95fb\u3002<\/section>\n<section><\/section>\n<\/section>\n<\/section>\n<section>\n<section>\n<section>\n<section>\n<section><\/section>\n<section><\/section>\n<section>\n<section><\/section>\n<\/section>\n<\/section>\n<section><strong>3. \u56e0\u679c\u63a8\u65ad\u7b80\u4ecb\u4e4b\u4e09\uff1a<\/strong><\/p>\n<p><strong>R. A. Fisher \u548c J. Neyman \u7684\u5206\u6b67<\/strong><\/p>\n<\/section>\n<section>\n<section><\/section>\n<section><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<p><img decoding=\"async\" class=\"rich_pages img_loading\" src=\"data:image\/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVQImWNgYGBgAAAABQABh6FO1AAAAABJRU5ErkJggg==\" alt=\"\u56fe\u7247\" crossorigin=\"anonymous\" data-ratio=\"1.4234875444839858\" data-s=\"300,640\" data-type=\"jpeg\" data-w=\"562\" data-src=\"https:\/\/mmbiz.qpic.cn\/mmbiz_jpg\/dMFkbmlFTgewYynhibDukpcVJiaNiaY0sr3x3A15u5klzP14ZNBJ3FxglwlqNj96TuklbN176KJex2brUTFrmAQzQ\/640?wx_fmt=jpeg\" \/><\/p>\n<section>R.A.Fisher<\/section>\n<p>\u8fd9\u90e8\u5206\u8c08\u5230\u7684\u95ee\u9898\u975e\u5e38\u5fae\u5999\uff1a\u5b8c\u5168\u968f\u673a\u5316\u8bd5\u9a8c\u4e0b\u7684 Fisher randomization test \u548c Neyman repeated sampling procedure\u3002\u7b80\u5355\u5730\u8bf4\uff0c\u524d\u8005\u662f\u968f\u673a\u5316\u68c0\u9a8c\uff0c\u6216\u8005\u5982\u5f88\u591a\u6559\u79d1\u4e66\u8bb2\u7684Fisher \u7cbe\u786e\u68c0\u9a8c\u00a0\uff08Fisher exact test\uff09\uff1b\u540e\u8005\u662f Neyman \u63d0\u51fa\u7684\u7f6e\u4fe1\u533a\u95f4\u00a0\uff08confidence interval\uff09\u7406\u8bba\u3002<\/p>\n<p>\u6211\u521d\u5b66\u56e0\u679c\u63a8\u65ad\u7684\u65f6\u5019\uff0c\u5e76\u6ca1\u6709\u7ec6\u81f4\u7684\u8ffd\u6c42\u8fd9\u4e9b\u5fae\u5999\u7684\u533a\u522b\uff0c\u89c9\u5f97\u4e86\u89e3\u5230\u7b80\u4ecb\u4e4b\u4e8c\u7684\u5c42\u6b21\u5c31\u591f\u4e86\u3002\u4e0d\u8fc7\u5728 Guido Imbens \u548c Donald Rubin \u6240\u5199\u7684\u56e0\u679c\u63a8\u65ad\u6559\u79d1\u4e66\uff08\u8fd8\u672a\u51fa\u7248\uff09\u4e2d\uff0c\u8fd9\u4e24\u70b9\u5185\u5bb9\u653e\u5728\u4e86\u5168\u4e66\u7684\u5f00\u7aef\uff0c\u4f5c\u4e3a\u56e0\u679c\u63a8\u65ad\u7684\u5f15\u5b50\u3002\u5728\u5176\u4ed6\u7684\u6559\u79d1\u4e66\u4e2d\uff0c\u662f\u770b\u4e0d\u5230\u8fd9\u6837\u7684\u8bb2\u6cd5\u7684\u3002\u5e73\u65e5\u91cc\u5e38\u5e38\u542c\u5230 Donald Rubin \u8001\u7237\u5b50\u5bf9 Fisher randomization test \u7684\u63a8\u5d07\uff0c\u6211\u6e10\u6e10\u5730\u4e5f\u88ab\u4ed6\u6d17\u8111\u4e86\u3002<\/p>\n<p>Fisher \u7684\u968f\u673a\u5316\u68c0\u9a8c\uff0c\u9488\u5bf9\u7684\u662f\u5982\u4e0b\u7684\u96f6\u5047\u8bbe\uff0c\u53c8\u88ab\u79f0\u4e3a sharp null\uff1a\u00a0<img decoding=\"async\" class=\"img_loading\" src=\"data:image\/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVQImWNgYGBgAAAABQABh6FO1AAAAABJRU5ErkJggg==\" alt=\"\u56fe\u7247\" crossorigin=\"anonymous\" data-ratio=\"0.13654618473895583\" data-type=\"png\" data-w=\"498\" data-src=\"https:\/\/mmbiz.qpic.cn\/mmbiz_png\/dMFkbmlFTgewYynhibDukpcVJiaNiaY0sr3g1dP6wjArDpiarPwW0Js1Oc7bibyrwRibjmnOYibfic1Sfvwhz0wicGlOkBw\/640?wx_fmt=png\" \/>\u5766\u767d\u5730\u8bf4\uff0c\u8fd9\u4e2a\u96f6\u5047\u8bbe\u662f\u6211\u89c1\u8fc7\u7684\u6700\u5947\u602a\u7684\u96f6\u5047\u8bbe\uff0c\u6ca1\u6709\u4e4b\u4e00\u3002\u73b0\u884c\u7684\u7edf\u8ba1\u6559\u79d1\u4e66\u4e2d\uff0c\u8bb2\u5230\u5047\u8bbe\u68c0\u9a8c\uff0c\u96f6\u5047\u8bbe\u90fd\u662f\u9488\u5bf9\u67d0\u4e9b\u53c2\u6570\u7684\uff0c\u800c Fisher \u7684 sharp null \u770b\u8d77\u6765\u5374\u50cf\u662f\u9488\u5bf9\u968f\u673a\u53d8\u91cf\u7684\u3002\u8fd9\u91cc\u9700\u8981\u8bb2\u660e\u767d\u7684\u662f\uff0c\u5f53\u6211\u4eec\u5173\u5fc3<strong>\u6709\u9650\u6837\u672c \uff08finite sample\uff09<\/strong>\u7684\u56e0\u679c\u4f5c\u7528\u65f6\uff0c\u6bcf\u4e2a\u4e2a\u4f53\u7684\u6f5c\u5728\u7ed3\u679c\u00a0<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-634\" src=\"https:\/\/aif.amtbbs.org\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-20.png\" width=\"173\" height=\"61\" alt=\"\u56fe\u7247\" \/>\u00a0\u90fd\u662f\u56fa\u5b9a\u7684\uff0c\u89c2\u6d4b\u53d8\u91cf<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-635\" src=\"https:\/\/aif.amtbbs.org\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-17.jpg\" width=\"395\" height=\"38\" alt=\"\u56fe\u7247\" srcset=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-17.jpg 395w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-17-300x29.jpg 300w\" sizes=\"auto, (max-width: 395px) 100vw, 395px\" \/>\u7684\u968f\u673a\u6027\u4ec5\u4ec5\u7531\u4e8e\u201c\u968f\u673a\u5316\u201d\u00a0\u672c\u8eab\u5bfc\u81f4\u7684\u3002\u7406\u89e3\u6e05\u695a\u8fd9\u70b9\uff0c\u624d\u80fd\u7406\u89e3 Fisher randomization test \u548c\u540e\u9762\u7684 Neyman repeated sampling procedure\u3002\u5982\u679c\u8bfb\u8005\u5bf9\u4e8e\u8fd9\u79cd\u6709\u9650\u6837\u672c\u7684\u601d\u8003\u65b9\u5f0f\u4e0d\u4e60\u60ef\uff0c\u53ef\u4ee5\u5148\u9605\u8bfb\u4e00\u4e0b\u7ecf\u5178\u7684\u62bd\u6837\u8c03\u67e5\u6559\u79d1\u4e66\uff0c\u90a3\u91cc\u51e0\u4e4e\u5168\u662f\u6709\u9650\u6837\u672c\u7684\u7406\u8bba\uff0c\u6240\u6709\u7684\u968f\u673a\u6027\u90fd\u6765\u81ea\u4e8e\u968f\u673a\u91c7\u6837\u7684\u8fc7\u7a0b\u3002<\/p>\n<p>\u5982\u679c\u8ba4\u4e3a\u6f5c\u5728\u7ed3\u679c\u662f\u56fa\u5b9a\u7684\u6570\uff0c\u90a3\u4e48 Fisher sharp null \u5c31\u548c\u73b0\u884c\u7684\u5047\u8bbe\u68c0\u9a8c\u7406\u8bba\u4e0d\u76f8\u6096\u3002\u8fd9\u4e2a null \u4e4b\u6240\u4ee5\u201csharp\u201d\u7684\u539f\u56e0\u662f\uff0c\u5728\u8fd9\u4e2a\u96f6\u5047\u8bbe\u4e0b\uff0c\u6240\u6709\u4e2a\u4f53\u7684\u6f5c\u5728\u7ed3\u679c\u90fd\u56fa\u5b9a\u4e86\uff0c\u4e2a\u4f53\u7684\u56e0\u679c\u4f5c\u7528\u4e3a\u96f6\uff0c\u552f\u4e00\u7684\u968f\u673a\u6027\u6765\u81ea\u4e8e\u968f\u673a\u5316\u7684\u201c\u7269\u7406\u201d\u7279\u6027\u3002\u5b9a\u4e49\u5904\u7406\u5206\u914d\u673a\u5236\u7684\u5411\u91cf\u4e3a<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-636\" src=\"https:\/\/aif.amtbbs.org\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-21.png\" width=\"285\" height=\"71\" alt=\"\u56fe\u7247\" \/>\u7ed3\u679c\u5411\u91cf\u4e3a<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-637\" src=\"https:\/\/aif.amtbbs.org\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-22.png\" width=\"278\" height=\"71\" alt=\"\u56fe\u7247\" \/><\/p>\n<p>\u6b64\u65f6\u6709\u9650\u6837\u672c\u4e0b\u7684<strong>\u968f\u673a\u5316\u5206\u914d\u673a\u5236<\/strong>\u5982\u4e0b\u5b9a\u4e49\uff1a<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-638\" src=\"https:\/\/aif.amtbbs.org\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-23.png\" width=\"373\" height=\"99\" alt=\"\u56fe\u7247\" srcset=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-23.png 373w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-23-300x80.png 300w\" sizes=\"auto, (max-width: 373px) 100vw, 373px\" \/><\/p>\n<p>\u5176\u4e2d\uff0c\u00a0<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-639\" src=\"https:\/\/aif.amtbbs.org\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-24.png\" width=\"138\" height=\"61\" alt=\"\u56fe\u7247\" \/>\u00a0\u4e3a\u5904\u7406\u7ec4\u4e2d\u7684\u603b\u6570\u3002\u8fd9\u91cc\u7684\u201c\u6761\u4ef6\u671f\u671b\u201d\u5e76\u4e0d\u662f\u8bf4 \u00a0<img decoding=\"async\" src=\"https:\/\/mmbiz.qpic.cn\/mmbiz_jpg\/dMFkbmlFTgewYynhibDukpcVJiaNiaY0sr3vhDNIXf4wSxS4G7xiaIxq9zQhyZ3155Z6LsCbhREQCwJibpNGAyHUicgQ\/640?wx_fmt=jpeg&amp;tp=webp&amp;wxfrom=5&amp;wx_lazy=1&amp;wx_co=1\" alt=\"\u56fe\u7247\" crossorigin=\"anonymous\" data-croporisrc=\"https:\/\/mmbiz.qlogo.cn\/mmbiz_png\/dMFkbmlFTgewYynhibDukpcVJiaNiaY0sr3jmJufRxT0HRwJwibW85iaEjEicCsVaHE7QNdMDZzNHIA6c2mial7icIYicqg\/0?wx_fmt=png\" data-cropx1=\"0\" data-cropx2=\"29.059233449477354\" data-cropy1=\"56.66550522648083\" data-cropy2=\"108.97212543554005\" data-ratio=\"1.793103448275862\" data-type=\"jpeg\" data-w=\"29\" data-src=\"https:\/\/mmbiz.qpic.cn\/mmbiz_jpg\/dMFkbmlFTgewYynhibDukpcVJiaNiaY0sr3vhDNIXf4wSxS4G7xiaIxq9zQhyZ3155Z6LsCbhREQCwJibpNGAyHUicgQ\/640?wx_fmt=jpeg\" data-fail=\"0\" \/>\u00a0\u662f\u968f\u673a\u53d8\u91cf\uff0c\u800c\u662f\u5f3a\u8c03\u5904\u7406\u7684\u5206\u914d\u673a\u5236\u4e0d\u4f9d\u8d56\u4e8e\u6f5c\u5728\u7ed3\u679c\u3002\u6bd4\u5982\uff0c\u6211\u4eec\u9009\u62e9\u7edf\u8ba1\u91cf<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-640\" src=\"https:\/\/aif.amtbbs.org\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-25.png\" width=\"733\" height=\"95\" alt=\"\u56fe\u7247\" srcset=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-25.png 733w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-25-300x39.png 300w\" sizes=\"auto, (max-width: 733px) 100vw, 733px\" \/><\/p>\n<p>\u6765\u68c0\u9a8c\u96f6\u5047\u8bbe\uff0c\u95ee\u9898\u5728\u4e8e\u8fd9\u4e2a\u7edf\u8ba1\u91cf\u7684\u5206\u5e03\u4e0d\u6613\u6c42\u51fa\u3002\u4f46\u662f\uff0c\u6211\u4eec\u53c8\u77e5\u9053\uff0c\u8fd9\u4e2a\u7edf\u8ba1\u91cf\u7684\u5206\u5e03\u5b8c\u5168\u6765\u81ea\u968f\u673a\u5316\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u53ef\u4ee5\u7528\u5982\u4e0b\u7684\u201c\u968f\u673a\u5316\u201d\u65b9\u6cd5\u00a0\uff08Monte Carlo \u65b9\u6cd5\u6a21\u62df\u7edf\u8ba1\u91cf\u7684\u5206\u5e03\uff09\uff1a\u5c06\u5904\u7406\u5206\u914d\u673a\u5236\u7684\u5411\u91cf\u00a0\u00a0\u8fdb\u884c\u968f\u673a\u7f6e\u6362\u5f97\u5230<img decoding=\"async\" src=\"data:image\/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVQImWNgYGBgAAAABQABh6FO1AAAAABJRU5ErkJggg==\" alt=\"\u56fe\u7247\" crossorigin=\"anonymous\" data-ratio=\"0.25311203319502074\" data-type=\"png\" data-w=\"241\" data-src=\"https:\/\/mmbiz.qpic.cn\/mmbiz_png\/dMFkbmlFTgewYynhibDukpcVJiaNiaY0sr3ZX2iclbdhoM0mx2AUcCeoB64p5n5M7aqwvfDzRttdq0WTAqibmqUzLibA\/640?wx_fmt=png\" \/>\uff0c\u8ba1\u7b97\u6b64\u65f6\u7684\u68c0\u9a8c\u7edf\u8ba1\u91cf\u00a0<img decoding=\"async\" class=\"img_loading\" src=\"data:image\/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVQImWNgYGBgAAAABQABh6FO1AAAAABJRU5ErkJggg==\" alt=\"\u56fe\u7247\" crossorigin=\"anonymous\" data-ratio=\"0.3096446700507614\" data-type=\"png\" data-w=\"197\" data-src=\"https:\/\/mmbiz.qpic.cn\/mmbiz_png\/dMFkbmlFTgewYynhibDukpcVJiaNiaY0sr3icM4jfOofXEaeF7GvIAveyMULTNTP9oJ1oWrwibAiavkosvw3lAlaXLjQ\/640?wx_fmt=png\" \/>\uff1b\u5982\u6b64\u91cd\u590d\u591a\u6b21n\u4e0d\u5927\u65f6\uff0c\u53ef\u4ee5\u7a77\u5c3d\u6240\u6709\u7684\u7f6e\u6362\uff0c\u4fbf\u53ef\u4ee5\u6a21\u62df\u51fa\u7edf\u8ba1\u91cf\u5728\u96f6\u5047\u8bbe\u4e0b\u7684\u5206\u5e03\uff0c\u8ba1\u7b97\u51fa p \u503c\u3002<\/p>\n<p>\u6709\u4eba\u8bf4\uff0cFisher randomization test \u5df2\u7ecf\u8574\u542b\u4e86 bootstrap \u7684\u601d\u60f3\uff0c\u4f3c\u4e4e\u4e5f\u6709\u4e00\u5b9a\u7684\u9053\u7406\u3002\u4e0d\u8fc7\uff0c\u8fd9\u91cc\u968f\u673a\u5316\u7684\u65b9\u6cd5\u662f\u9488\u5bf9\u4e00\u4e2a\u7279\u4f8b\u63d0\u51fa\u6765\u7684\u3002<\/p>\n<p><img decoding=\"async\" class=\"rich_pages img_loading\" src=\"data:image\/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVQImWNgYGBgAAAABQABh6FO1AAAAABJRU5ErkJggg==\" alt=\"\u56fe\u7247\" crossorigin=\"anonymous\" data-ratio=\"1.3157894736842106\" data-s=\"300,640\" data-type=\"jpeg\" data-w=\"380\" data-src=\"https:\/\/mmbiz.qpic.cn\/mmbiz_jpg\/dMFkbmlFTgewYynhibDukpcVJiaNiaY0sr3haWJfVoCu1OrQrEC8cg3AAYY09kPghuzBXUfp4MvCAmOEsusibKdbkQ\/640?wx_fmt=jpeg\" \/><\/p>\n<section>J. Neyman<\/section>\n<p>\u4e0b\u9762\u8981\u4ecb\u7ecd\u7684 Neyman \u7684\u65b9\u6cd5\uff0c\u5176\u5b9e\u65e9\u4e8e Fisher \u7684\u65b9\u6cd5\u3002\u8fd9\u79cd\u65b9\u6cd5\u5728 Neyman 1923 \u5e74\u7684\u535a\u58eb\u8bba\u6587\u4e2d\uff0c\u6b63\u5f0f\u63d0\u51fa\u4e86\u3002\u8fd9\u79cd\u65b9\u6cd5\u5047\u5b9an\u4e2a\u4e2a\u4f53\u4e2d\u6709m\u4e2a\u968f\u673a\u7684\u63a5\u53d7\u5904\u7406\uff0c\u76ee\u7684\u662f\u4f30\u8ba1\uff08\u6709\u9650\uff09\u603b\u4f53\u7684\u5e73\u5747\u56e0\u679c\u4f5c\u7528\uff1a<\/p>\n<p><img decoding=\"async\" class=\"rich_pages img_loading\" src=\"data:image\/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVQImWNgYGBgAAAABQABh6FO1AAAAABJRU5ErkJggg==\" alt=\"\u56fe\u7247\" crossorigin=\"anonymous\" data-ratio=\"0.257372654155496\" data-s=\"300,640\" data-type=\"png\" data-w=\"373\" data-src=\"https:\/\/mmbiz.qpic.cn\/mmbiz_png\/dMFkbmlFTgewYynhibDukpcVJiaNiaY0sr3l4YKzicdKboa96Ckw5x8XvRQXZ6Ye1EoIOoRb3TQ1hCHiagXn7UoN1Yg\/640?wx_fmt=png\" \/><\/p>\n<p>\u4e00\u4e2a\u663e\u7136\u7684\u65e0\u504f\u4f30\u8ba1\u91cf\u662f<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-641\" src=\"https:\/\/aif.amtbbs.org\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-26.png\" width=\"692\" height=\"93\" alt=\"\u56fe\u7247\" srcset=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-26.png 692w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-26-300x40.png 300w\" sizes=\"auto, (max-width: 692px) 100vw, 692px\" \/><\/p>\n<p>\u4f46\u662f\uff0c\u901a\u5e38\u7684\u65b9\u5dee\u4f30\u8ba1\u91cf\uff0c<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-642\" src=\"https:\/\/aif.amtbbs.org\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-27.png\" width=\"1030\" height=\"85\" alt=\"\u56fe\u7247\" srcset=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-27.png 1030w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-27-300x25.png 300w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-27-1024x85.png 1024w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-27-768x63.png 768w\" sizes=\"auto, (max-width: 1030px) 100vw, 1030px\" \/><\/p>\n<p>\u9ad8\u4f30\u4e86\u65b9\u5dee\uff0c\u6784\u9020\u51fa\u6765\u7684\u7f6e\u4fe1\u533a\u95f4\u5728 Neyman \u2013 Pearson \u610f\u4e49\u4e0b\u592a\u201c\u4fdd\u5b88\u201d\u3002\u53ef\u4ee5\u8bc1\u660e\uff0c\u5728\u4e2a\u4f53\u5904\u7406\u4f5c\u7528\u662f\u5e38\u6570\u7684\u5047\u5b9a\u4e0b\uff0c\u4e0a\u9762\u7684\u65b9\u5dee\u4f30\u8ba1\u662f\u65e0\u504f\u7684\u3002<\/p>\n<p>\u901a\u5e38\u7684\u6559\u79d1\u4e66\u8bb2\u5047\u8bbe\u68c0\u9a8c\uff0c\u90fd\u662f\u4ece\u6b63\u6001\u5747\u503c\u7684\u68c0\u9a8c\u5f00\u59cb\u3002Neyman \u7684\u65b9\u6cd5\u7ed9\u51fa\u4e86\u00a0\u7684\u70b9\u4f30\u8ba1\u548c\u533a\u95f4\u4f30\u8ba1\uff0c\u4e5f\u53ef\u4ee5\u7528\u6765\u68c0\u9a8c\u5982\u4e0b\u7684\u96f6\u5047\u8bbe\uff1a<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-643\" src=\"https:\/\/aif.amtbbs.org\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-28.png\" width=\"173\" height=\"68\" alt=\"\u56fe\u7247\" \/><\/p>\n<p>\u5b9e\u9645\u4e2d\uff0c\u5230\u5e95\u662f Fisher \u548c\u96f6\u5047\u8bbe\u5408\u7406\u8fd8\u662f Neyman \u7684\u96f6\u5047\u8bbe\u5408\u7406\uff0c\u53d6\u51b3\u4e8e\u5177\u4f53\u7684\u95ee\u9898\u3002\u6bd4\u5982\uff0c\u6211\u4eec\u60f3\u7814\u7a76\u67d0\u9879\u653f\u7b56\u5bf9\u4e8e\u4e2d\u56fd\u4e09\u5341\u591a\u4e2a\u7701\u7684\u5f71\u54cd\uff0c\u8fd9\u662f\u4e00\u4e2a\u6709\u9650\u6837\u672c\u7684\u95ee\u9898\uff0c\u56e0\u4e3a\u6211\u4eec\u5f88\u96be\u60f3\u8c61\u4e2d\u56fd\u7684\u7701\u662f\u6765\u81ea\u67d0\u4e2a\u201c\u8d85\u603b\u4f53\u201d\u3002\u4f46\u662f\u793e\u4f1a\u79d1\u5b66\u4e2d\u7684\u5f88\u591a\u95ee\u9898\uff0c\u6211\u4eec\u4e0d\u5149\u9700\u8981\u56de\u7b54\u5904\u7406\u6216\u8005\u653f\u7b56\u5bf9\u4e8e\u89c2\u6d4b\u5230\u7684\u6709\u9650\u6837\u672c\u7684\u4f5c\u7528\uff0c\u6211\u4eec\u66f4\u5173\u5fc3\u8fd9\u79cd\u5904\u7406\u6216\u8005\u653f\u7b56\u5bf9\u4e8e\u4e00\u4e2a\u66f4\u5927\u603b\u4f53\u7684\u5f71\u54cd\u3002\u524d\u8005\uff0cFisher \u7684\u96f6\u5047\u8bbe\u66f4\u5408\u9002\uff0c\u540e\u8005 Neyman \u7684\u96f6\u5047\u8bbe\u66f4\u5408\u9002\u3002<\/p>\n<p>\u5173\u4e8e\u8fd9\u4e24\u79cd\u89d2\u5ea6\u7684\u4e89\u8bba\uff0c\u53ef\u4ee5\u4e0a\u8ff0\u5230 Fisher \u548c Neyman \u4e24\u4eba\u30021935 \u5e74\uff0cNeyman \u5411\u82f1\u56fd\u7687\u5bb6\u7edf\u8ba1\u5b66\u4f1a\u63d0\u4ea4\u4e86\u4e00\u7bc7\u8bba\u6587\u201cStatistical problems in agricultural experimentation\u201d\uff0cFisher \u548c Neyman \u5728\u8ba8\u8bba\u6587\u7ae0\u65f6\u53d1\u751f\u4e86\u6fc0\u70c8\u7684\u4e89\u6267\u3002\u4e0d\u8fc7\uff0c\u4ece\u4eca\u5929\u7684\u7edf\u8ba1\u6559\u80b2\u6765\u770b\uff0cNeyman \u4f3c\u4e4e\u5360\u4e86\u4e0a\u98ce\u3002<\/p>\n<p>\u7528\u4e0b\u9762\u7684\u95ee\u9898\u7ed3\u675f\uff1a<\/p>\n<ol class=\"list-paddingleft-2\">\n<li>\n<section>\u5728 sharp null\u4e0b\uff0cNeyman \u65b9\u6cd5\u4e0b\u6784\u9020\u7684 T \u7edf\u8ba1\u91cf\uff0c\u662f\u5426\u548c Fisher randomization test \u6784\u9020\u7684\u7edf\u8ba1\u91cf\u76f8\u540c\uff1f\u5206\u5e03\u662f\u5426\u76f8\u540c\uff1f<\/section>\n<\/li>\n<li>\n<section>Fisher randomization test \u4e2d\u7684\u7edf\u8ba1\u91cf\u53ef\u4ee5\u6709\u5176\u4ed6\u9009\u62e9\uff0c\u6bd4\u5982 Wilcoxon \u79e9\u548c\u7edf\u8ba1\u91cf\u7b49\uff0c\u63a8\u65ad\u7684\u65b9\u6cd5\u7c7b\u4f3c\u3002<\/section>\n<\/li>\n<li>\n<section>\u5f53Y\u662f\u4e8c\u503c\u53d8\u91cf\u65f6\uff0c\u4e0a\u9762 Fisher \u7684\u65b9\u6cd5\u5c31\u662f\u6559\u79d1\u4e66\u4e2d\u7684 Fisher exact test\u3002\u5728\u6ca1\u6709\u5b66\u4e60 potential outcome \u8fd9\u5957\u8bed\u8a00\u4e4b\u524d\uff0c\u7406\u89e3 Fisher exact test \u662f\u6709\u4e9b\u56f0\u96be\u7684\u3002<\/section>\n<\/li>\n<li>\n<section>\u8bc1\u660e<\/section>\n<section><img decoding=\"async\" class=\"rich_pages\" src=\"data:image\/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVQImWNgYGBgAAAABQABh6FO1AAAAABJRU5ErkJggg==\" alt=\"\u56fe\u7247\" crossorigin=\"anonymous\" data-ratio=\"0.14006514657980457\" data-s=\"300,640\" data-type=\"png\" data-w=\"307\" data-src=\"https:\/\/mmbiz.qpic.cn\/mmbiz_png\/dMFkbmlFTgewYynhibDukpcVJiaNiaY0sr3s6CdHqKY89INyfyCUqPw2xbnQymXnInDUt27ickO9SdxibbQ9lbfBMOg\/640?wx_fmt=png\" \/>\u3002<\/section>\n<\/li>\n<li>\n<section>\u5047\u5b9an\u4e2a\u4e2a\u4f53\u662f\u4e00\u4e2a\u8d85\u603b\u4f53\uff08super-population\uff09\u7684\u968f\u673a\u6837\u672c\uff0c\u8d85\u603b\u4f53\u7684\u5e73\u5747\u56e0\u679c\u4f5c\u7528\u5b9a\u4e49\u4e3a<\/section>\n<section><img decoding=\"async\" class=\"rich_pages\" src=\"data:image\/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVQImWNgYGBgAAAABQABh6FO1AAAAABJRU5ErkJggg==\" alt=\"\u56fe\u7247\" crossorigin=\"anonymous\" data-ratio=\"0.12883435582822086\" data-s=\"300,640\" data-type=\"png\" data-w=\"326\" data-src=\"https:\/\/mmbiz.qpic.cn\/mmbiz_png\/dMFkbmlFTgewYynhibDukpcVJiaNiaY0sr3MR0NskMbb0MUEJ46SpTBXbP9cTBYtaKnibheAcODYkICUeukSFbQNrQ\/640?wx_fmt=png\" \/><\/section>\n<section>\u90a3\u4e48 Neyman \u7684\u65b9\u6cd5\u5f97\u5230\u4f30\u8ba1\u91cf\u662f\u8d85\u603b\u4f53\u5e73\u5747\u56e0\u679c\u4f5c\u7528\u7684\u65e0\u504f\u4f30\u8ba1\uff0c\u4e14\u65b9\u5dee\u7684\u8868\u8fbe\u5f0f\u662f\u7cbe\u786e\u7684\uff1b\u800c sharp null \u5728\u8d85\u603b\u4f53\u7684\u60c5\u5f62\u4e0b\u4e0d\u592a\u9002\u5408\u3002<\/section>\n<\/li>\n<\/ol>\n<section>\n<section>\n<section>\n<section>\n<section><\/section>\n<section><\/section>\n<section>\n<section><\/section>\n<\/section>\n<\/section>\n<section><strong>4. \u56e0\u679c\u63a8\u65ad\u7b80\u4ecb\u4e4b\u56db\uff1a<\/strong><\/p>\n<p><strong>\u89c2\u5bdf\u6027\u7814\u7a76\uff0c\u53ef\u5ffd\u7565\u6027\u548c\u503e\u5411\u5f97\u5206<\/strong><\/p>\n<\/section>\n<section>\n<section><\/section>\n<section><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<p>\u8fd9\u8282\u91c7\u7528\u548c\u524d\u9762\u76f8\u540c\u7684\u8bb0\u53f7\u3002Z\u8868\u793a\u5904\u7406\u53d8\u91cf\uff081\u662f\u5904\u7406\uff0c0\u662f\u5bf9\u7167\uff09\uff0cY\u8868\u793a\u7ed3\u679c\uff0cX\u8868\u793a\u5904\u7406\u524d\u7684\u534f\u53d8\u91cf\u3002\u5728\u5b8c\u5168\u968f\u673a\u5316\u8bd5\u9a8c\u4e2d\uff0c\u53ef\u5ffd\u7565\u6027\u00a0<img decoding=\"async\" class=\"img_loading\" src=\"data:image\/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVQImWNgYGBgAAAABQABh6FO1AAAAABJRU5ErkJggg==\" alt=\"\u56fe\u7247\" crossorigin=\"anonymous\" data-ratio=\"0.2890995260663507\" data-type=\"png\" data-w=\"211\" data-src=\"https:\/\/mmbiz.qpic.cn\/mmbiz_png\/dMFkbmlFTgfca7gzSraagYubH91TuuJj3dqn7lXM4qo8SCldcfpMohSzpcbAURGCnwlQnm1iak0KbyUhSBKINfw\/640?wx_fmt=png\" \/>\u6210\u7acb\uff0c\u8fd9\u4fdd\u8bc1\u4e86\u5e73\u5747\u56e0\u679c\u4f5c\u7528<\/p>\n<p><img decoding=\"async\" src=\"data:image\/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVQImWNgYGBgAAAABQABh6FO1AAAAABJRU5ErkJggg==\" alt=\"\u56fe\u7247\" crossorigin=\"anonymous\" data-croporisrc=\"https:\/\/mmbiz.qlogo.cn\/mmbiz_png\/dMFkbmlFTgfca7gzSraagYubH91TuuJjUApC4Lrn3KavULwibVSz4U11CibboSic5dFFAEPx5pk5kzN0VkWHJ6FAg\/0?wx_fmt=png\" data-cropx1=\"0\" data-cropx2=\"789\" data-cropy1=\"53.23702422145328\" data-cropy2=\"107.83910034602076\" data-ratio=\"0.0697084917617237\" data-type=\"jpeg\" data-w=\"789\" data-src=\"https:\/\/mmbiz.qpic.cn\/mmbiz_jpg\/dMFkbmlFTgfca7gzSraagYubH91TuuJjEr9honBZQ48iaPmxve5J8Bv8fCbh1YWVbjVFYoJb1N6pMIrwlJhQCkg\/640?wx_fmt=jpeg\" \/><\/p>\n<p>\u53ef\u4ee5\u8868\u793a\u6210\u89c2\u6d4b\u6570\u636e\u7684\u51fd\u6570\uff0c\u56e0\u6b64\u53ef\u4ee5\u8bc6\u522b\u3002\u5728\u67d0\u4e9b\u8bd5\u9a8c\u4e2d\uff0c\u6211\u4eec\u201c\u5148\u9a8c\u7684\u201d\u77e5\u9053\u67d0\u4e9b\u53d8\u91cf\u4e0e\u7ed3\u679c\u5f3a\u76f8\u5173\uff0c\u56e0\u6b64\u8981\u5728\u8bd5\u9a8c\u4e2d\u63a7\u5236\u4ed6\u4eec\uff0c\u4ee5\u51cf\u5c11\u8bd5\u9a8c\u7684\u65b9\u5dee\u3002\u5728\u4e00\u822c\u7684\u6709\u533a\u7ec4\uff08blocking\uff09\u7684\u968f\u673a\u5316\u8bd5\u9a8c\u4e2d\uff0c\u66f4\u4e00\u822c\u7684\u53ef\u5ffd\u7565\u6027\u00a0<img decoding=\"async\" src=\"data:image\/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVQImWNgYGBgAAAABQABh6FO1AAAAABJRU5ErkJggg==\" alt=\"\u56fe\u7247\" crossorigin=\"anonymous\" data-ratio=\"0.25102880658436216\" data-type=\"png\" data-w=\"243\" data-src=\"https:\/\/mmbiz.qpic.cn\/mmbiz_png\/dMFkbmlFTgfca7gzSraagYubH91TuuJjlUiaHwK4SAV6qBDoYIYhAV12oXRu4TVUXRVnyt1pPQk9sM0czKpXI2g\/640?wx_fmt=png\" \/>\u00a0\u6210\u7acb\uff0c\u56e0\u4e3a\u53ea\u6709\u5728\u7ed9\u5b9a\u534f\u53d8\u91cfX\u540e\uff0c\u5904\u7406\u7684\u5206\u914d\u673a\u5236\u624d\u662f\u5b8c\u5168\u968f\u673a\u5316\u7684\u3002\u6bd4\u5982\uff0c\u7537\u6027\u548c\u5973\u6027\u4e2d\uff0c\u63a5\u53d7\u5904\u7406\u7684\u6bd4\u4f8b\u4e0d\u540c\uff0c\u4f46\u662f\u8fd9\u4e2a\u6bd4\u4f8b\u662f\u4e8b\u5148\u7ed9\u5b9a\u7684\u3002<\/p>\n<p>\u5728\u4f20\u7edf\u7684\u519c\u4e1a\u548c\u5de5\u4e1a\u8bd5\u9a8c\u4e2d\uff0c\u7531\u4e8e\u968f\u673a\u5316\uff0c\u53ef\u5ffd\u7565\u6027\u4e00\u822c\u662f\u80fd\u591f\u5f97\u5230\u4fdd\u8bc1\u7684\uff1b\u56e0\u6b64\u5728\u8fd9\u4e9b\u9886\u57df\u8c08\u8bba\u56e0\u679c\u63a8\u65ad\u662f\u6ca1\u6709\u592a\u5927\u95ee\u9898\u7684\u3002Jerzy Neyman \u6700\u65e9\u7684\u535a\u58eb\u8bba\u6587\uff0c\u5c31\u7814\u7a76\u7684\u662f\u519c\u4e1a\u8bd5\u9a8c\u3002\u4f46\u662f\uff0c\u8fd9\u7bc7\u5199\u4e8e 1923 \u5e74\u7684\u91cd\u8981\u7edf\u8ba1\u5b66\u6587\u7ae0\uff0c\u8fdf\u8fdf\u6ca1\u6709\u5f97\u5230\u7edf\u8ba1\u5b66\u754c\u7684\u91cd\u89c6\uff0c\u4e5f\u6ca1\u6709\u4eba\u5c06\u76f8\u5173\u65b9\u6cd5\u7528\u5230\u793e\u4f1a\u79d1\u5b66\u7684\u7814\u7a76\u4e2d\u30021970 \u5e74\u4ee3\uff0cDonald Rubin \u8bbf\u95ee UC Berkeley \u7edf\u8ba1\u7cfb\uff0c\u5df2\u9000\u4f11\u7684 Jerzy Neyman \u66fe\u95ee\u8d77\uff1a\u4e3a\u4ec0\u4e48\u6ca1\u6709\u4eba\u5c06\u6f5c\u5728\u7ed3\u679c\u7684\u8bb0\u53f7\u7528\u5230\u8bd5\u9a8c\u8bbe\u8ba1\u4e4b\u5916\uff1f\u6b63\u5982 Jerzy Neyman \u672c\u4eba\u6240\u8bf4 \u201cwithout randomization an experiment has little value irrespective of the subsequent treatment\uff08\u6ca1\u6709\u968f\u673a\u5316\u7684\u8bd5\u9a8c\u4ef7\u503c\u5f88\u5c0f\uff09\u201d\uff0c\u4eba\u4eec\u5bf9\u4e8e\u89c2\u5bdf\u6027\u7814\u7a76\u4e2d\u7684\u56e0\u679c\u63a8\u65ad\u603b\u662f\u62b1\u7740\u5f3a\u70c8\u7684\u6000\u7591\u6001\u5ea6\u3002\u6211\u4eec\u7ecf\u5e38\u542c\u5230\u8fd9\u6837\u7684\u58f0\u97f3\uff1a\u7edf\u8ba1\u5c31\u4e0d\u662f\u7528\u6765\u7814\u7a76\u56e0\u679c\u5173\u7cfb\u7684\uff01<\/p>\n<section><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-644\" src=\"https:\/\/aif.amtbbs.org\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-18.jpg\" width=\"688\" height=\"310\" alt=\"\u56fe\u7247\" srcset=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-18.jpg 688w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-18-300x135.jpg 300w\" sizes=\"auto, (max-width: 688px) 100vw, 688px\" \/><\/section>\n<p>\u5728\u7b2c\u4e00\u8bb2 Yule-Simpson \u6096\u8bba\u7684\u8bc4\u8bba\u4e2d\uff0c\u6709\u4eba\u63d0\u5230\u4e86\u54f2\u5b66\uff08\u53f2\uff09\u4e0a\u7684\u4f11\u8c1f\u95ee\u9898\uff08\u6211\u7684\u8f6c\u8ff0\uff09\uff1a\u4eba\u7c7b\u662f\u5426\u80fd\u4ece\u6709\u9650\u7684\u7ecf\u9a8c\u4e2d\u5f97\u5230\u56e0\u679c\u5f8b\uff1f\u8fd9\u7684\u786e\u662f\u4e00\u4e2a\u95ee\u9898\uff0c\u8fd9\u4e2a\u95ee\u9898\u6700\u540e\u4fc3\u4f7f\u5fb7\u56fd\u54f2\u5b66\u5bb6\u5eb7\u5fb7\u4e3a\u8c03\u548c\u82f1\u56fd\u7ecf\u9a8c\u6d3e\uff08\u4f11\u8c1f\uff09\u548c\u5927\u9646\u7406\u6027\u6d3e\uff08\u83b1\u5e03\u5c3c\u5179-\u6c83\u5c14\u592b\uff09\u800c\u5199\u4e86\u5de8\u8457\u300a\u7eaf\u7cb9\u7406\u6027\u6279\u5224\u300b\u3002\u5176\u5b9e\uff0c\u5982\u679c\u4e00\u4e2a\u4eba\u662f\u7edd\u5bf9\u7684\u6000\u7591\u8bba\u8005\uff08\u5982\u4f11\u8c1f\uff09\uff0c\u4ed6\u53ef\u80fd\u6000\u7591\u4e00\u5207\uff0c\u751a\u81f3\u5305\u62ec\u56e0\u679c\u5f8b\uff0c\u6240\u4ee5\uff0c\u5eb7\u5fb7\u7684\u7406\u8bba\u4e5f\u4e0d\u80fd\u5b8c\u5168\u201c\u89e3\u51b3\u201d\u4f11\u8c1f\u95ee\u9898\u3002\u6000\u7591\u8bba\u8005\u662f\u65e0\u6cd5\u53cd\u9a73\u7684\uff0c\u4ed6\u4eec\u7684\u95ee\u9898\u4e5f\u662f\u65e0\u6cd5\u56de\u7b54\u7684\u3002\u4ed6\u4eec\u5b58\u5728\u7684\u4ef7\u503c\u662f\u4e3a\u73b0\u884c\u4e00\u5207\u7406\u8bba\u8d77\u5230\u8b66\u793a\u4f5c\u7528\u3002\u4e00\u822c\u6765\u8bf4\uff0c\u7edf\u8ba1\u5b66\u5bb6\u4e0d\u4f1a\u4ece\u8fc7\u5ea6\u54f2\u5b66\u7684\u89d2\u5ea6\u8c08\u8bba\u95ee\u9898\u3002\u4ece\u524d\u9762\u7684\u8bf4\u660e\u4e2d\u53ef\u4ee5\u770b\u51fa\uff0c\u7edf\u8ba1\u4e2d\u6240\u8c13\u7684\u201c\u56e0\u679c\u201d\u662f<strong>\u201c\u67d0\u79cd\u201d\u610f\u4e49\u7684\u201c\u56e0\u679c\u201d<\/strong>\uff0c\u5373\u7edf\u8ba1\u5b66\u53ea\u8ba8\u8bba<strong>\u201c\u539f\u56e0\u7684\u7ed3\u679c\u201d<\/strong>\uff0c\u800c\u4e0d\u8ba8\u8bba<strong>\u201c\u7ed3\u679c\u7684\u539f\u56e0\u201d<\/strong>\u3002\u524d\u8005\u662f\u53ef\u4ee5\u7528\u6570\u636e\u8bc1\u660e\u6216\u8005\u8bc1\u4f2a\u7684\uff1b\u540e\u8005\u662f\u5c5e\u4e8e\u79d1\u5b66\u7814\u7a76\u6240\u63a2\u7d22\u7684\u3002\u7528\u79d1\u5b66\u54f2\u5b66\u5bb6\u5361\u5c14\u00b7\u6ce2\u666e\u7684\u8bdd\u6765\u8bf4\uff0c\u79d1\u5b66\u77e5\u8bc6\u7684\u79ef\u7d2f\u662f\u201c\u731c\u60f3\u4e0e\u53cd\u9a73\u201d\u7684\u8fc7\u7a0b\uff1a\u201c\u731c\u60f3\u201d\u7ed3\u679c\u7684\u539f\u56e0\uff0c\u518d\u201c\u8bc1\u4f2a\u201d\u539f\u56e0\u7684\u7ed3\u679c\uff1b\u5982\u6b64\u5faa\u73af\u5373\u79d1\u5b66\u3002<\/p>\n<p>\u4e0b\u9762\u8c08\u5230\u7684\u662f\uff0c<strong>\u5728\u4ec0\u4e48\u6837\u7684\u6761\u4ef6\u4e0b<\/strong>\uff0c\u89c2\u5bdf\u6027\u7814\u7a76\u4e5f\u53ef\u4ee5\u63a8\u65ad\u56e0\u679c\u3002\u8fd9\u662f\u4e00\u5207\u793e\u4f1a\u79d1\u5b66\u6240\u5173\u5fc3\u7684\u95ee\u9898\u3002\u7b54\u6848\u662f\uff1a\u53ef\u5ffd\u7565\u6027\uff0c\u5373\u00a0<img decoding=\"async\" src=\"data:image\/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVQImWNgYGBgAAAABQABh6FO1AAAAABJRU5ErkJggg==\" alt=\"\u56fe\u7247\" crossorigin=\"anonymous\" data-croporisrc=\"https:\/\/mmbiz.qlogo.cn\/mmbiz_png\/dMFkbmlFTgfca7gzSraagYubH91TuuJjO57bHAcBcWqPO4mFBed3lEhkhD83MtAVj2FKzDFGFtOuFE3tnzd4kQ\/0?wx_fmt=png\" data-cropx1=\"0\" data-cropx2=\"236.70934256055364\" data-cropy1=\"51.40657439446367\" data-cropy2=\"106.39965397923875\" data-ratio=\"0.2330508474576271\" data-type=\"jpeg\" data-w=\"236\" data-src=\"https:\/\/mmbiz.qpic.cn\/mmbiz_jpg\/dMFkbmlFTgfca7gzSraagYubH91TuuJj0bBthgc91VDXy9ibpoprHsjrJ1yYmibv3iawhmkbupjb9paiaovRTxjK2A\/640?wx_fmt=jpeg\" \/>\u3002\u5728\u53ef\u5ffd\u7565\u6027\u4e0b\uff0cACE\u53ef\u4ee5\u8bc6\u522b\uff0c\u56e0\u4e3a<\/p>\n<p><img decoding=\"async\" class=\"rich_pages img_loading\" src=\"data:image\/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVQImWNgYGBgAAAABQABh6FO1AAAAABJRU5ErkJggg==\" alt=\"\u56fe\u7247\" crossorigin=\"anonymous\" data-ratio=\"0.24489795918367346\" data-s=\"300,640\" data-type=\"png\" data-w=\"833\" data-src=\"https:\/\/mmbiz.qpic.cn\/mmbiz_png\/dMFkbmlFTgfca7gzSraagYubH91TuuJj5dmUWDGINH5MOM2vfrkxfdUfXUnWhub3n6rntjv2icnYRHWXYw25oIw\/640?wx_fmt=png\" \/><\/p>\n<p>\u4ece\u4e0a\u9762\u7684\u516c\u5f0f\u6765\u770b\uff0c\u4f3c\u4e4e\u6211\u4eec\u7684\u4efb\u52a1\u662f\u4f30\u8ba1\u4e24\u4e2a\u6761\u4ef6\u77e9E{Y|X, Z=z}(z=0,1). \u8fd9\u5c31\u662f\u4e00\u4e2a\u56de\u5f52\u95ee\u9898\u3002\u4e0d\u9519\uff0c\u8fd9\u4e5f\u662f\u4e3a\u4ec0\u4e48\u901a\u5e38\u7684\u56de\u5f52\u6a21\u578b\u88ab\u8d4b\u4e88\u201c\u56e0\u679c\u201d\u542b\u4e49\u7684\u539f\u56e0\u3002\u5982\u679c\u6211\u4eec\u5047\u5b9a\u53ef\u5ffd\u7565\u6027\u548c\u7ebf\u6027\u6a21\u578b\u00a0<img decoding=\"async\" class=\"img_loading\" src=\"data:image\/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVQImWNgYGBgAAAABQABh6FO1AAAAABJRU5ErkJggg==\" alt=\"\u56fe\u7247\" crossorigin=\"anonymous\" data-ratio=\"0.15099009900990099\" data-type=\"png\" data-w=\"404\" data-src=\"https:\/\/mmbiz.qpic.cn\/mmbiz_png\/dMFkbmlFTgfca7gzSraagYubH91TuuJjP6SZMZHMrRzBbYT4zd6BHPhLKrtMNQRhFWQrholfzCJaRTqKn8jzrw\/640?wx_fmt=png\" \/>\u00a0\u6210\u7acb\uff0c\u90a3\u4e48<img decoding=\"async\" src=\"data:image\/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVQImWNgYGBgAAAABQABh6FO1AAAAABJRU5ErkJggg==\" alt=\"\u56fe\u7247\" crossorigin=\"anonymous\" data-ratio=\"1.605263157894737\" data-type=\"png\" data-w=\"38\" data-src=\"https:\/\/mmbiz.qpic.cn\/mmbiz_png\/dMFkbmlFTgfca7gzSraagYubH91TuuJjWvxicsLBUECGNVic1rOJfaLCHpXpgzCIHeDDKzSkdPZfVftEE0TV1l7Q\/640?wx_fmt=png\" \/>\u00a0\u5c31\u8868\u793a\u5e73\u5747\u56e0\u679c\u4f5c\u7528\u3002\u7ebf\u6027\u6a21\u578b\u6bd4\u8f83\u5bb9\u6613\u5b9e\u73b0\uff0c\u5b9e\u9645\u4e2d\u4eba\u4eec\u6bd4\u8f83\u503e\u5411\u8fd9\u79cd\u65b9\u6cd5\u3002\u4f46\u662f\u4ed6\u7684\u95ee\u9898\u662f\uff1a\uff081\uff09\u5047\u5b9a\u4e2a\u4f53\u56e0\u679c\u4f5c\u7528\u662f\u5e38\u6570\uff1b\uff082\uff09\u5bf9\u4e8e\u5904\u7406\u548c\u5bf9\u7167\u7ec4\u4e4b\u95f4\u7684\u4e0d\u5e73\u8861\uff08unbalance\uff09\u6ca1\u6709\u5f88\u597d\u7684\u68c0\u6d4b\uff0c\u5e38\u5e38\u5728\u5bf9\u89c2\u6d4b\u6570\u636e\u5916\u63a8\uff08extrapolation\uff09\u3002<\/p>\n<p>\u4e0a\u9762\u7684\u7b2c\u4e8c\u6761\uff0c\u662f\u7ebf\u6027\u56de\u5f52\u6700\u4e3b\u8981\u7684\u7f3a\u9677\u3002\u5728 Donald Rubin \u65e9\u671f\u56e0\u679c\u63a8\u65ad\u7684\u6587\u732e\u4e2d\uff0c\u63a8\u5d07\u7684\u65b9\u6cd5\u662f\u201c\u5339\u914d\u201d\uff08matching\uff09\u3002\u4e00\u822c\u6765\u8bf4\uff0c\u6211\u4eec\u6709\u4e00\u4e9b\u4e2a\u4f53\u63a5\u53d7\u5904\u7406\uff0c\u53e6\u5916\u66f4\u591a\u7684\u4e2a\u4f53\u63a5\u53d7\u5bf9\u7167\uff1b\u7b80\u5355\u7684\u60f3\u6cd5\u5c31\u662f\u4ece\u5bf9\u7167\u7ec4\u4e2d\u627e\u5230\u548c\u5904\u7406\u7ec4\u4e2d\u6bd4\u8f83\u201c\u63a5\u8fd1\u201d\u7684\u4e2a\u4f53\u8fdb\u884c\u5339\u914d\uff0c\u8fd9\u6837\u5f97\u51fa\u7684\u4f5c\u7528\uff0c\u53ef\u4ee5\u8fd1\u4f3c\u5e73\u5747\u56e0\u679c\u4f5c\u7528\u3002\u201c\u63a5\u8fd1\u201d\u7684\u6807\u51c6\u662f\u57fa\u4e8e\u89c2\u6d4b\u534f\u53d8\u91cf\u7684\uff0c\u6bd4\u5982\uff0c\u5982\u679c\u67d0\u9879\u7814\u7a76\uff0c\u6027\u522b\u662f\u552f\u4e00\u91cd\u8981\u7684\u6df7\u6742\u56e0\u7d20\uff0c\u6211\u4eec\u5c31\u5c06\u5904\u7406\u7ec4\u4e2d\u7684\u7537\u6027\u548c\u5bf9\u7167\u7ec4\u4e2d\u7684\u7537\u6027\u8fdb\u884c\u5339\u914d\u3002\u4f46\u662f\uff0c\u5982\u679c\u89c2\u6d4b\u534f\u53d8\u91cf\u7684\u7ef4\u6570\u8f83\u9ad8\uff0c\u5339\u914d\u5c31\u5f88\u96be\u5b9e\u73b0\u4e86\u3002\u73b0\u6709\u7684\u6e10\u8fd1\u7406\u8bba\u8868\u660e\uff0c\u5339\u914d\u65b9\u6cd5\u7684\u6536\u655b\u901f\u5ea6\u968f\u7740\u534f\u53d8\u91cf\u7ef4\u6570\u7684\u589e\u9ad8\u800c\u7ebf\u6027\u7684\u8870\u51cf\u3002<\/p>\n<p>\u540e\u6765 Paul Rosenbaum \u5230 Harvard \u7edf\u8ba1\u7cfb\u8bfb Ph.D.\uff0c\u5728 Donald Rubin \u7684\u8bfe\u4e0a\u95ee\u5230\u4e86\u8fd9\u4e2a\u95ee\u9898\u3002\u8fd9\u5c31\u4fc3\u4f7f\u4e24\u4eba\u5408\u4f5c\u5199\u4e86\u4e00\u7bc7\u975e\u5e38\u6709\u540d\u7684\u6587\u7ae0\uff0c\u4e8e 1983 \u5e74\u53d1\u8868\u5728 Biometrika \u4e0a\uff1a\u201cThe central role of the propensity score in observational studies for causal effects\u201d\u3002\u503e\u5411\u5f97\u5206\u5b9a\u4e49\u4e3a\u00a0<img decoding=\"async\" src=\"data:image\/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVQImWNgYGBgAAAABQABh6FO1AAAAABJRU5ErkJggg==\" alt=\"\u56fe\u7247\" crossorigin=\"anonymous\" data-ratio=\"0.21708185053380782\" data-type=\"png\" data-w=\"281\" data-src=\"https:\/\/mmbiz.qpic.cn\/mmbiz_png\/dMFkbmlFTgfca7gzSraagYubH91TuuJjITUdyfloxiaupVRprN03kTxjqrP7BLrbTOOBdhjuOyUewdEpgrWLjgQ\/640?wx_fmt=png\" \/>\u00a0\u5bb9\u6613\u9a8c\u8bc1\uff0c\u5728\u53ef\u5ffd\u7565\u6027\u4e0b\uff0c\u5b83\u6ee1\u8db3\u6027\u8d28\u00a0<img decoding=\"async\" src=\"data:image\/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVQImWNgYGBgAAAABQABh6FO1AAAAABJRU5ErkJggg==\" alt=\"\u56fe\u7247\" crossorigin=\"anonymous\" data-ratio=\"0.41496598639455784\" data-type=\"png\" data-w=\"147\" data-src=\"https:\/\/mmbiz.qpic.cn\/mmbiz_png\/dMFkbmlFTgfca7gzSraagYubH91TuuJjkesx8u9UcNmFE5A58Y29rds7WW8lqJsNFXdsev8XT8S2RKLscicMYbA\/640?wx_fmt=png\" \/>\u00a0\uff08\u5728\u6570\u636e\u964d\u7ef4\u7684\u6587\u732e\u4e2d\uff0c\u79f0\u4e4b\u4e3a\u201c\u5145\u5206\u964d\u7ef4\u201d\uff0csufficient dimension reduction\uff09\u00a0\u548c\u00a0<img decoding=\"async\" src=\"data:image\/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVQImWNgYGBgAAAABQABh6FO1AAAAABJRU5ErkJggg==\" alt=\"\u56fe\u7247\" crossorigin=\"anonymous\" data-ratio=\"0.21942446043165467\" data-type=\"png\" data-w=\"278\" data-src=\"https:\/\/mmbiz.qpic.cn\/mmbiz_png\/dMFkbmlFTgfca7gzSraagYubH91TuuJjkRHU9Uib4vcWb3cqQEicULuPpsp4KB7QTaYaTOVzBlicJrLCojRiayRib4w\/640?wx_fmt=png\" \/>\uff08\u7ed9\u5b9a\u503e\u5411\u5f97\u5206\u4e0b\u7684\u53ef\u5ffd\u7565\u6027\uff09\u3002\u6839\u636e\u524d\u9762\u7684\u63a8\u5bfc\uff0c\u663e\u7136\u6709 ACE=E[E(Y|e(X), Z=1)]-E[E(Y|e(X),Z=0)] \u3002\u6b64\u65f6\uff0c\u503e\u5411\u5f97\u5206\u662f\u4e00\u7ef4\u7684\uff0c\u6211\u4eec\u53ef\u4ee5\u6839\u636e\u5b83\u5206\u5c42\u00a0\uff08Rosenbaum \u548c Rubin \u5efa\u8bae\u5206\u6210 5 \u5c42\uff09\uff0c\u5f97\u5230\u5e73\u5747\u56e0\u679c\u4f5c\u7528\u7684\u4f30\u8ba1\u3002\u8fde\u7eed\u7248\u672c\u7684\u5206\u5c42\uff0c\u5c31\u662f\u4e0b\u9762\u7684\u52a0\u6743\u4f30\u8ba1\uff1a<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-645\" src=\"https:\/\/aif.amtbbs.org\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-29.png\" width=\"925\" height=\"92\" alt=\"\u56fe\u7247\" srcset=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-29.png 925w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-29-300x30.png 300w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-29-768x76.png 768w\" sizes=\"auto, (max-width: 925px) 100vw, 925px\" \/><\/p>\n<p>\u4e0d\u8fc7\uff0c\u4e0d\u7ba1\u662f\u5206\u5c42\u8fd8\u662f\u52a0\u6743\uff0c\u7b2c\u4e00\u6b65\u6211\u4eec\u90fd\u9700\u8981\u5bf9\u503e\u5411\u5f97\u5206\u8fdb\u884c\u4f30\u8ba1\uff0c\u901a\u5e38\u7684\u5efa\u8bae\u662f Logistic \u56de\u5f52\u3002\u751a\u81f3\u6709\u6587\u732e\u8bc1\u660e\u7684\u4e0b\u9762\u7684\u201c\u79bb\u5947\u201d\u7ed3\u8bba\uff1a\u4f7f\u7528\u4f30\u8ba1\u7684\u503e\u5411\u5f97\u5206\u5f97\u5230\u5e73\u5747\u56e0\u679c\u4f5c\u7528\u7684\u4f30\u8ba1\u91cf\u7684\u6e10\u8fd1\u65b9\u5dee\u6bd4\u4f7f\u7528\u771f\u5b9e\u7684\u503e\u5411\u5f97\u5206\u5f97\u5230\u7684\u5c0f\u3002<\/p>\n<p>\u719f\u6089\u4f20\u7edf\u56de\u5f52\u5206\u6790\u7684\u4eba\u4f1a\u611f\u5230\u5947\u602a\uff0c\u76f4\u63a5\u5c06 Y\u5bf9 Z\u548c X\u505a\u56de\u5f52\u7684\u65b9\u6cd5\u7b80\u5355\u76f4\u63a5\uff0c\u4e3a\u4f55\u8981\u63a8\u8350\u503e\u5411\u5f97\u5206\u7684\u65b9\u6cd5\u5462\uff1f\u786e\u5b9e\uff0c\u8bfb\u8fc7 Rosenbaum \u548c Rubin \u539f\u59cb\u8bba\u6587\u7684\u4eba\uff0c\u4e00\u822c\u4f1a\u89c9\u5f97\uff0c\u8fd9\u7bc7\u6587\u7ae0\u5f88\u6709\u610f\u601d\uff0c\u4f46\u662f\u53c8\u89c9\u5f97\u7ebf\u6027\u56de\u5f52\uff08\u6216\u8005 logistic \u56de\u5f52\uff09\u8db3\u77e3\uff0c\u4f55\u5fc5\u8fd9\u4e48\u590d\u6742\uff1f\u5728\u56e0\u679c\u63a8\u65ad\u4e2d\uff0c\u6211\u4eec\u5e94\u8be5\u66f4\u52a0\u5173\u5fc3\u5904\u7406\u673a\u5236\uff0c\u4e5f\u5c31\u662f\u503e\u5411\u5f97\u5206\u3002\u6309\u7167 Don Rubin \u7684\u8bf4\u6cd5\uff0c\u6211\u4eec\u5e94\u8be5\u6839\u636e\u503e\u5411\u5f97\u5206\u6765\u201c\u8bbe\u8ba1\u201d\u89c2\u5bdf\u6027\u7814\u7a76\uff1b\u6309\u7167\u503e\u5411\u5f97\u5206\u5c06\u4eba\u7fa4\u8fdb\u884c\u5339\u914d\uff0c\u5f62\u6210\u4e00\u4e2a\u8fd1\u4f3c\u7684\u201c\u968f\u673a\u5316\u8bd5\u9a8c\u201d\u3002\u800c\u8fd9\u4e2a\u8bbe\u8ba1\u7684\u8fc7\u7a0b\uff0c\u4e0d\u80fd\u4f9d\u8d56\u4e8e\u7ed3\u679c\u53d8\u91cf\uff1b\u751a\u81f3\u5728\u8bbe\u8ba1\u7684\u9636\u6bb5\uff0c\u6211\u4eec\u8981\u5047\u88c5\u6ca1\u6709\u89c2\u5bdf\u5230\u7ed3\u679c\u53d8\u91cf\u3002\u5426\u5219\uff0c\u5c06\u4f1a\u51fa\u73b0\u5982\u4e0b\u7684\u602a\u73b0\u8c61\uff1a\u793e\u4f1a\u79d1\u5b66\u7684\u7814\u7a76\u8005\u4e0d\u65ad\u5730\u5c1d\u8bd5\u52a0\u5165\u6216\u8005\u5254\u9664\u67d0\u4e9b\u56de\u5f52\u53d8\u91cf\uff0c\u76f4\u5230\u56de\u5f52\u7684\u7ed3\u679c\u7b26\u5408\u81ea\u5df1\u7684\u201c\u6545\u4e8b\u201d\u4e3a\u6b62\u3002\u8fd9\u79cd\u73b0\u8c61\u5728\u793e\u4f1a\u79d1\u5b66\u4e2d\u5b9e\u5728\u592a\u666e\u904d\u4e86\uff01\u7ed3\u679c\u7684\u56de\u5f52\u6a21\u578b\u56fa\u7136\u91cd\u8981\uff0c\u4f46\u662f\u5982\u679c\u5728 Y\u6a21\u578b\u4e0a\u505a\u6587\u7ae0\uff0c\u5f88\u591a\u5177\u6709\u201c\u6b3a\u9a97\u6027\u201d\u7684\u6709\u504f\u7ed3\u679c\u5c31\u4f1a\u51fa\u73b0\u5728\u6587\u732e\u4e2d\u3002\u8fd9\u5bfc\u81f4\u5927\u591a\u6570\u7684\u7814\u7a76\u4e2d\uff0c\u56e0\u679c\u6027\u5e76\u4e0d\u53ef\u9760\u3002<\/p>\n<p>\u8bb2\u5230\u8fd9\u91cc\uff0c\u6211\u4eec\u6709\u5fc5\u8981\u56de\u5230\u6700\u5f00\u59cb\u7684 Yule-Simpson\u2019s Paradox\u3002\u7528Z\u8868\u793a\u5904\u7406\uff081\u8868\u793a\u5904\u7406\uff0c0\u8868\u793a\u5bf9\u7167\uff09\uff0cY\u8868\u793a\u5b58\u6d3b\u4e0e\u5426\uff081\u662f\u8868\u793a\u5b58\u6d3b\uff0c0\u8868\u793a\u6b7b\u4ea1\uff09\uff0cX\u8868\u793a\u6027\u522b\uff081\u8868\u793a\u7537\u6027\uff0c0\u8868\u793a\u5973\u6027\uff09\u3002\u76ee\u524d\u6211\u4eec\u6709\u5904\u7406\u201c\u56e0\u679c\u4f5c\u7528\u201d\u7684\u4e24\u4e2a\u4f30\u8ba1\u91cf\uff1a\u4e00\u4e2a\u4e0d\u7528\u6027\u522b\u8fdb\u884c\u52a0\u6743\u8c03\u6574<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-646\" src=\"https:\/\/aif.amtbbs.org\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-30.png\" width=\"996\" height=\"116\" alt=\"\u56fe\u7247\" srcset=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-30.png 996w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-30-300x35.png 300w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-30-768x89.png 768w\" sizes=\"auto, (max-width: 996px) 100vw, 996px\" \/><\/p>\n<p>\u53e6\u4e00\u4e2a\u7528\u6027\u522b\u8fdb\u884c\u52a0\u6743\u8c03\u6574\uff08\u7531\u4e8e\u6b64\u65f6\u534f\u53d8\u91cf\u662f\u4e00\u7ef4\u7684\uff0c\u503e\u5411\u5f97\u5206\u548c\u534f\u53d8\u91cf\u672c\u8eab\u5b58\u5728\u4e00\u4e00\u5bf9\u5e94\uff0c\u7528\u503e\u5411\u5f97\u5206\u8c03\u6574\u7ed3\u679c\u76f8\u540c\uff0c\u89c1\u4e0b\u9762\u95ee\u9898 1\uff09<\/p>\n<p><img decoding=\"async\" class=\"rich_pages img_loading\" src=\"data:image\/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVQImWNgYGBgAAAABQABh6FO1AAAAABJRU5ErkJggg==\" alt=\"\u56fe\u7247\" crossorigin=\"anonymous\" data-ratio=\"0.26582278481012656\" data-s=\"300,640\" data-type=\"png\" data-w=\"1027\" data-src=\"https:\/\/mmbiz.qpic.cn\/mmbiz_png\/dMFkbmlFTgfca7gzSraagYubH91TuuJjI4p4Nxhr5SiaickgOiaLNziaqXU5WuDM3icNekic0NUpgt73TweQ1puggttA\/640?wx_fmt=png\" \/><\/p>\n<p>\u5176\u4e2d\uff0c\u8868\u793a\u76f8\u5e94\u7684\u77e9\u4f30\u8ba1\u3002\u662f\u5426\u6839\u636e\u6027\u522b\u8fdb\u884c\u8c03\u6574\uff0c\u5bf9\u7ed3\u679c\u6709\u672c\u8d28\u7684\u5f71\u54cd\u3002\u5f53\u00a0<img decoding=\"async\" src=\"data:image\/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVQImWNgYGBgAAAABQABh6FO1AAAAABJRU5ErkJggg==\" alt=\"\u56fe\u7247\" crossorigin=\"anonymous\" data-ratio=\"0.2890995260663507\" data-type=\"png\" data-w=\"211\" data-src=\"https:\/\/mmbiz.qpic.cn\/mmbiz_png\/dMFkbmlFTgfca7gzSraagYubH91TuuJj3dqn7lXM4qo8SCldcfpMohSzpcbAURGCnwlQnm1iak0KbyUhSBKINfw\/640?wx_fmt=png\" \/>\u00a0\u65f6\uff0c \u7b2c\u4e00\u4e2a\u4f30\u8ba1\u91cf\u662f\u56e0\u679c\u4f5c\u7528\u7684\u76f8\u5408\u4f30\u8ba1\uff1b\u5f53<img decoding=\"async\" src=\"data:image\/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVQImWNgYGBgAAAABQABh6FO1AAAAABJRU5ErkJggg==\" alt=\"\u56fe\u7247\" crossorigin=\"anonymous\" data-ratio=\"0.25102880658436216\" data-type=\"png\" data-w=\"243\" data-src=\"https:\/\/mmbiz.qpic.cn\/mmbiz_png\/dMFkbmlFTgfca7gzSraagYubH91TuuJjlUiaHwK4SAV6qBDoYIYhAV12oXRu4TVUXRVnyt1pPQk9sM0czKpXI2g\/640?wx_fmt=png\" \/>\u00a0\u65f6\uff0c\u7b2c\u4e8c\u4e2a\u4f30\u8ba1\u91cf\u662f\u56e0\u679c\u4f5c\u7528\u7684\u76f8\u5408\u4f30\u8ba1\u3002\u6839\u636e\u5b9e\u9645\u95ee\u9898\u7684\u80cc\u666f\uff0c\u6211\u4eec\u5e94\u8be5\u9009\u62e9\u54ea\u4e2a\u4f30\u8ba1\u91cf\u5462\uff1f\u5230\u6b64\u4e3a\u6b62\uff0c\u56de\u7b54\u8fd9\u4e2a\u95ee\u9898\u6709\u4e9b\u4f3c\u662f\u800c\u975e\uff08\u9009\u62e9\u8c03\u6574\u7684\u4f30\u8ba1\u91cf\uff1f\uff09\uff0c\u66f4\u8fdb\u4e00\u6b65\u7684\u56de\u7b54\uff0c\u8bf7\u542c\u4e0b\u56de\u5206\u89e3\uff1a\u56e0\u679c\u56fe\uff08causal diagram\uff09\u3002<\/p>\n<p>\u4f5c\u4e3a\u7ed3\u675f\uff0c\u7559\u4e0b\u5982\u4e0b\u7684\u95ee\u9898\uff1a<\/p>\n<ol class=\"list-paddingleft-2\">\n<li>\n<section>\u5982\u679cX\u662f\u4e8c\u503c\u7684\u53d8\u91cf\uff08\u5982\u6027\u522b\uff09\uff0c\u90a3\u4e48\u5339\u914d\u6216\u8005\u503e\u5411\u7684\u5206\u90fd\u5bfc\u81f4\u5982\u4e0b\u7684\u4f30\u8ba1\u91cf:<img decoding=\"async\" class=\"rich_pages\" src=\"data:image\/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVQImWNgYGBgAAAABQABh6FO1AAAAABJRU5ErkJggg==\" alt=\"\u56fe\u7247\" crossorigin=\"anonymous\" data-ratio=\"0.068\" data-s=\"300,640\" data-type=\"png\" data-w=\"1000\" data-src=\"https:\/\/mmbiz.qpic.cn\/mmbiz_png\/dMFkbmlFTgfca7gzSraagYubH91TuuJjftUHWhr19HMl62OU0qicib8JT9iactyTceGMsgPzLHBBZTEOl6I35xl8A\/640?wx_fmt=png\" \/><\/section>\n<section>\u8fd9\u4e2a\u516c\u5f0f\u5728\u6d41\u884c\u75c5\u5b66\u4e2d\u975e\u5e38\u57fa\u672c\uff0c\u5373\u6839\u636e\u6df7\u6742\u53d8\u91cf\u8fdb\u884c\u5206\u5c42\u8c03\u6574\u3002\u5728\u540e\u9762\u7684\u4ecb\u7ecd\u4e2d\u5c06\u8bb2\u5230\uff0c\u8fd9\u4e2a\u516c\u5f0f\u88ab Judea Pearl \u79f0\u4e3a\u201c\u540e\u95e8\u51c6\u5219\u201d\uff08backdoor criterion\uff09\u3002<\/section>\n<\/li>\n<li>\n<section>\u503e\u5411\u5f97\u5206\u7684\u52a0\u6743\u5f62\u5f0f\uff0c<\/section>\n<section><img decoding=\"async\" class=\"rich_pages img_loading\" src=\"data:image\/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVQImWNgYGBgAAAABQABh6FO1AAAAABJRU5ErkJggg==\" alt=\"\u56fe\u7247\" crossorigin=\"anonymous\" data-ratio=\"0.09938650306748466\" data-s=\"300,640\" data-type=\"png\" data-w=\"815\" data-src=\"https:\/\/mmbiz.qpic.cn\/mmbiz_png\/dMFkbmlFTgfca7gzSraagYubH91TuuJjmvpaf1H21AYpReanTZCaya2nCToZjTfllTCPrTQcF7l78tTJ5lk2cw\/640?wx_fmt=png\" \/><\/section>\n<section>\u672c\u8d28\u4e0a\u662f\u62bd\u6837\u8c03\u67e5\u4e2d\u7684 Horvitz-Thompson \u4f30\u8ba1\u3002\u5728\u6d41\u884c\u75c5\u5b66\u7684\u6587\u732e\u4e2d\uff0c\u8fd9\u6837\u7684\u4f30\u8ba1\u91cf\u5e38\u88ab\u79f0\u4e3a\u201c\u9006\u6982\u52a0\u6743\u4f30\u8ba1\u91cf\u201d\uff08inverse probability weighting estimator; IPWE\uff09\u3002<\/section>\n<\/li>\n<li>\n<section>\u76f4\u89c2\u4e0a\uff0c\u4e3a\u4ec0\u4e48\u4f30\u8ba1\u7684\u503e\u5411\u5f97\u5206\u4f1a\u66f4\u597d\uff1f\u60f3\u60f3\u504f\u5dee\u548c\u65b9\u5dee\u7684\u6743\u8861\uff08bias-variance tradeoff\uff09\u3002<\/section>\n<\/li>\n<\/ol>\n<section>\u5173\u4e8e\u201c\u53ef\u5ffd\u7565\u6027\u201d\uff08ignorability\uff09\uff0c\u9700\u8981\u505a\u4e00\u4e9b\u8bf4\u660e\u3002\u5728\u4e2d\u6587\u7ffb\u8bd1\u7684\u8ba1\u91cf\u7ecf\u6d4e\u5b66\u6559\u79d1\u4e66\u4e2d\uff0c\u8fd9\u4e2a\u672f\u8bed\u7ffb\u8bd1\u5b58\u5728\u9519\u8bef\uff0c\u6bd4\u5982 Wooldridge \u7684 Econometric Analysis of Cross Section and Panel Data \u7684\u4e2d\u8bd1\u672c\u4e2d\uff0c\u201c\u53ef\u5ffd\u7565\u6027\u201d\u88ab\u7ffb\u8bd1\u6210\u201c\u4e0d\u53ef\u77e5\u201d\u3002\u5b50\u66f0\uff1a\u201c\u540d\u4e0d\u6b63\uff0c\u5219\u8a00\u4e0d\u987a\uff1b\u8a00\u4e0d\u987a\uff0c\u5219\u4e8b\u4e0d\u6210\u3002\u201d\u5728 Rubin\u00a0(1978)\u00a0\u4e2d\uff0c\u201c\u53ef\u5ffd\u7565\u6027\u201d\u8fd9\u4e2a\u6982\u5ff5\u662f\u5728\u8d1d\u53f6\u65af\u63a8\u65ad\u7684\u6846\u67b6\u4e0b\u63d0\u51fa\u6765\u7684\uff1a\u5f53\u5904\u7406\u7684\u5206\u914d\u673a\u5236\u6ee1\u8db3\u8fd9\u6837\u7684\u6761\u4ef6\u65f6\uff0c\u5728\u540e\u9a8c\u7684\u63a8\u65ad\u4e2d\uff0c\u53ef\u5c06\u5206\u914d\u673a\u5236\u201c\u5ffd\u7565\u201d\u6389\u3002\u5728\u4f20\u7edf\u7684\u8d1d\u53f6\u65af\u770b\u6765\uff0c\u6240\u6709\u7684\u63a8\u65ad\u90fd\u662f\u6761\u4ef6\u5728\u89c2\u6d4b\u6570\u636e\u4e0a\u7684\uff0c\u90a3\u4e48\u4e3a\u4ec0\u4e48\u5904\u7406\u7684\u5206\u914d\u673a\u5236\u4f1a\u5f71\u54cd\u8d1d\u53f6\u65af\u540e\u9a8c\u63a8\u65ad\u5462\uff1fDonald Rubin \u8bf4\uff0c\u5f53\u65f6\u8fde Leonard Jimmie Savage \u548c Dennis Victor Lindley \u90fd\u5728\u6b64\u56f0\u60d1\u4e0d\u89e3\uff0c\u4ed6 1978 \u5e74\u7684\u6587\u7ae0\uff0c\u539f\u610f\u5c31\u662f\u4e3a\u4e86\u89e3\u91ca\u4e3a\u4ec0\u4e48\u968f\u673a\u5316\u4f1a\u5f71\u54cd\u8d1d\u53f6\u65af\u63a8\u65ad\u3002<\/section>\n<section>\u201c\u53ef\u5ffd\u7565\u6027\u201d \u8fd9\u4e2a\u540d\u5b57\u6700\u65e9\u662f\u5728\u7f3a\u5931\u6570\u636e\u7684\u6587\u732e\u4e2d\u63d0\u51fa\u6765\u7684\u3002\u5f53\u7f3a\u5931\u673a\u5236\u662f\u968f\u673a\u7f3a\u5931\uff08missing at random\uff1aMAR\uff09\u4e14\u6a21\u578b\u7684\u53c2\u6570\u4e0e\u7f3a\u5931\u673a\u5236\u7684\u53c2\u6570\u4e0d\u540c\u65f6\uff0c\u7f3a\u5931\u673a\u5236\u201c\u53ef\u5ffd\u7565\u201d\uff08ignorable\uff09\u3002\u201c\u53ef\u5ffd\u7565\u201d\u662f\u6307\uff0c\u7f3a\u5931\u673a\u5236\u4e0d\u8fdb\u5165\u57fa\u4e8e\u89c2\u6d4b\u6570\u636e\u7684\u4f3c\u7136\u6216\u8005\u8d1d\u53f6\u65af\u540e\u9a8c\u5206\u5e03\u3002<\/section>\n<section><\/section>\n<section>\n<section>\n<section>\n<section>\n<section><\/section>\n<section><\/section>\n<section>\n<section><\/section>\n<\/section>\n<\/section>\n<section><strong>5. \u56e0\u679c\u63a8\u65ad\u7b80\u4ecb\u4e4b\u4e94\uff1a<\/strong><\/p>\n<p><strong>\u56e0\u679c\u56fe (Causal Diagram)<\/strong><\/p>\n<\/section>\n<section>\n<section><\/section>\n<section><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-647\" src=\"https:\/\/aif.amtbbs.org\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-19.jpg\" width=\"469\" height=\"717\" alt=\"\u56fe\u7247\" srcset=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-19.jpg 469w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-19-196x300.jpg 196w\" sizes=\"auto, (max-width: 469px) 100vw, 469px\" \/><\/p>\n<section data-tool=\"mdnice\u7f16\u8f91\u5668\" data-website=\"https:\/\/www.mdnice.com\">\u8fd9\u90e8\u5206\u4ecb\u7ecd\u00a0Judea Pearl\u00a0\u4e8e 1995 \u5e74\u53d1\u8868\u5728 Biometrika \u4e0a\u7684\u5de5\u4f5c \u201cCausal diagrams for empirical research\u201d\uff0c\u8fd9\u7bc7\u6587\u7ae0\u662f Biometrika \u521b\u520a\u4e00\u767e\u591a\u5e74\u6765\u5c11\u6709\u7684\u8ba8\u8bba\u6587\u7ae0\uff0cSir David Cox\uff0cGuido Imbens, Donald Rubin \u548c James Robins \u7b49\u4eba\u90fd\u5bf9\u6587\u7ae0\u4f5c\u4e86\u8ba8\u8bba\u3002\u7531\u4e8e Judea Pearl \u6700\u8fd1\u521a\u83b7\u5f97\u4e86\u56fe\u7075\u5956\uff0c\u6211\u60f3\u4ed6\u7684\u5de5\u4f5c\u4f1a\u5f15\u8d77\u66f4\u591a\u7684\u5173\u6ce8\uff08\u4e8b\u5b9e\u4e0a\u8ba1\u7b97\u673a\u754c\u65e9\u5c31\u5df2\u7ecf\u8fc7\u5ea6\u7684\u5173\u6ce8\u4e86\uff09\u3002<\/p>\n<h1 data-tool=\"mdnice\u7f16\u8f91\u5668\">\u4e00\u3001 \u6709\u5411\u65e0\u73af\u56fe\u548c do \u7b97\u5b50<\/h1>\n<section>\u4e3a\u4e86\u907f\u514d\u8fc7\u591a\u56fe\u8bba\u7684\u672f\u8bed\uff0c\u8fd9\u91cc\u4ec5\u4ec5\u9700\u8981\u77e5\u9053\u6709\u5411\u56fe\u4e2d\u201c\u7236\u4eb2\u201d\u548c\u201c\u540e\u4ee3\u201d\u7684\u6982\u5ff5\uff1a\u6709\u5411\u7bad\u5934\u4e0a\u6e38\u7684\u53d8\u91cf\u662f\u201c\u7236\u4eb2\u201d\uff0c\u4e0b\u6e38\u7684\u53d8\u91cf\u662f\u201c\u540e\u4ee3\u201d\u3002\u5728\u4e00\u4e2a\u6709\u5411\u65e0\u73af\u56fe\uff08Directed Acyclic Graph\uff1bDAG\uff09\u4e2d\uff0c\u8bb0\u6240\u6709\u7684\u8282\u70b9\u96c6\u5408\u4e3a\u00a0\u3002\u8fd9\u91cc\u7528\u00a0\u00a0\u8868\u793a\u8fde\u7eed\u53d8\u91cf\u7684\u5bc6\u5ea6\u51fd\u6570\u548c\u79bb\u6563\u53d8\u91cf\u7684\u6982\u7387\u51fd\u6570\u3002\u6709\u4e24\u79cd\u89c2\u70b9\u770b\u5f85\u4e00\u4e2a DAG\uff1a\u4e00\u662f\u5c06\u5176\u770b\u6210\u8868\u793a\u6761\u4ef6\u72ec\u7acb\u6027\u7684\u6a21\u578b\uff1b\u4e8c\u662f\u5c06\u5176\u770b\u6210\u4e00\u4e2a\u6570\u636e\u751f\u6210\u673a\u5236\u3002\u5f53\u7136\uff0c\u672c\u8d28\u4e0a\u8fd9\u4e24\u79cd\u89c2\u70b9\u662f\u4e00\u6837\u7684\u3002\u5728\u7b2c\u4e00\u79cd\u89c2\u70b9\u4e0b\uff0c\u7ed9\u5b9a DAG \u4e2d\u67d0\u4e2a\u8282\u70b9\u7684\u201c\u7236\u4eb2\u201d\u8282\u70b9\uff0c\u5b83\u4e0e\u5176\u6240\u6709\u7684\u975e\u201c\u540e\u4ee3\u201d\u90fd\u72ec\u7acb\u3002\u6839\u636e\u5168\u6982\u516c\u5f0f\u548c\u6761\u4ef6\u72ec\u7acb\u6027\uff0cDAG \u4e2d\u53d8\u91cf\u7684\u8054\u5408\u5206\u5e03\u53ef\u4ee5\u6709\u5982\u4e0b\u7684\u9012\u5f52\u5206\u89e3\uff1a<\/section>\n<section><\/section>\n<section>\u5176\u4e2d\u8868\u793a\u7684\u201c\u7236\u4eb2\u201d\u96c6\u5408\uff0c\u5373\u6240\u6709\u6307\u5411\u7684\u8282\u70b9\u96c6\u5408\u3002<\/section>\n<section><img decoding=\"async\" class=\"rich_pages img_loading\" src=\"data:image\/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVQImWNgYGBgAAAABQABh6FO1AAAAABJRU5ErkJggg==\" alt=\"\u56fe\u7247\" crossorigin=\"anonymous\" data-ratio=\"0.8195121951219512\" data-s=\"300,640\" data-type=\"png\" data-w=\"205\" data-src=\"https:\/\/mmbiz.qpic.cn\/mmbiz_png\/dMFkbmlFTgd6FibE9qxxMQiaxziacZqCQgMMBNKlG2InqQynrKIRkicicXMQ6BiaibCoLD9XIkZs8vkQCeMW9ZaWxUmTw\/640?wx_fmt=png\" \/><\/section>\n<section>Figure 1: An Example of Causal Diagram<\/section>\n<section><strong>\u4f8b\u5b50\uff1a<\/strong>\u5728 Figure\u00a01 \u4e2d\uff0c\u8054\u5408\u5206\u5e03\u53ef\u4ee5\u5206\u89e3\u6210\u4e3a<\/section>\n<section>\u5982\u679c\u5c06 DAG \u770b\u6210\u4e00\u4e2a\u6570\u636e\u751f\u6210\u673a\u5236\uff0c\u90a3\u4e48\u5b83\u548c\u4e0b\u9762\u7684\u975e\u53c2\u6570\u7ed3\u6784\u65b9\u7a0b\u6a21\u578b\u662f\u7b49\u4ef7\u7684\uff1a<\/section>\n<section>\u6ce8\u610f\uff0c\u8fd9\u4e2a\u8054\u7acb\u65b9\u7a0b\u7ec4\u662f\u201c\u4e09\u89d2\u7684\u201d\uff08triangular\uff09\u6216\u8005\u201c\u9012\u5f52\u7684\u201d\uff08recursive\uff09\uff0c\u56e0\u4e3a DAG \u4e2d\u6ca1\u6709\u73af\uff0c\u65b9\u7a0b\u7ec4\u4e2d\u4e5f\u5c31\u6ca1\u6709\u53cd\u9988\u3002\u8ba1\u91cf\u7ecf\u6d4e\u5b66\u4e2d\u7684\u8054\u7acb\u65b9\u7a0b\u7ec4\u6a21\u578b\u00a0\uff08simultaneous equation model: SEM\uff09\uff0c\u5e76\u4e0d\u5728\u8fd9\u4e2a\u8ba8\u8bba\u7684\u6846\u67b6\u4e0b\u3002DAG \u7528\u4e8e\u63cf\u8ff0\u6570\u636e\u7684\u751f\u6210\u673a\u5236\uff0c\u800c\u4e0d\u5e38\u7528\u4e8e\u63cf\u8ff0\u7cfb\u7edf\u5747\u8861\u65f6\u7684\u72b6\u6001\uff1b\u540e\u8005\u4e3b\u8981\u662f SEM \u7684\u76ee\u7684\u3002\u8fd9\u6837\u63cf\u8ff0\u53d8\u91cf\u8054\u5408\u5206\u5e03\u6216\u8005\u6570\u636e\u751f\u6210\u673a\u5236\u7684\u6a21\u578b\uff0c\u88ab\u79f0\u4e3a\u201c\u56fe\u6a21\u578b\u201d\u6216\u8005\u201c\u8d1d\u53f6\u65af\u7f51\u7edc\u201d\uff08Bayesian network\uff09\u3002<\/section>\n<section>\u663e\u7136\uff0c\u4e00\u4e2a\u6709\u5411\u65e0\u73af\u56fe\u552f\u4e00\u5730\u51b3\u5b9a\u4e86\u4e00\u4e2a\u8054\u5408\u5206\u5e03\uff1b\u53cd\u8fc7\u6765\uff0c\u4e00\u4e2a\u8054\u5408\u5206\u5e03\u4e0d\u80fd\u552f\u4e00\u5730\u51b3\u5b9a\u6709\u5411\u65e0\u73af\u56fe\u3002\u53cd\u8fc7\u6765\u7684\u7ed3\u8bba\u4e0d\u6210\u7acb\uff0c\u5bf9\u6211\u4eec\u7684\u5b9e\u8df5\u6709\u5f88\u91cd\u8981\u7684\u610f\u4e49\uff0c\u6bd4\u5982 Figure 2 \u4e2d\u7684\u4e24\u4e2a\u6709\u5411\u65e0\u73af\u56fe\uff0c\u539f\u56e0\u548c\u7ed3\u679c\u4e0d\u540c\uff0c\u56fe\u7684\u7ed3\u6784\u4e5f\u4e0d\u540c\uff1b\u4f46\u662f\uff0c\u6211\u4eec\u89c2\u6d4b\u5230\u7684\u8054\u5408\u5206\u5e03\u53ef\u4ee5\u6709\u4e24\u79cd\u5206\u89e3\u548c\u56e0\u6b64\uff0c\u6211\u4eec\u4ece\u89c2\u6d4b\u53d8\u91cf\u7684\u8054\u5408\u5206\u5e03\uff0c\u5f88\u96be\u786e\u5b9a\u201c\u539f\u56e0\u201d\u548c\u201c\u7ed3\u679c\u201d\u3002\u5728\u4e0b\u4e00\u8282\u56fe\u6a21\u578b\u7ed3\u6784\u7684\u5b66\u4e60\u4e2d\uff0c\u6211\u4eec\u4f1a\u770b\u5230\uff0c\u53ea\u6709\u5728\u4e00\u4e9b\u5047\u5b9a\u548c\u7279\u6b8a\u60c5\u5f62\u4e0b\uff0c\u6211\u4eec\u53ef\u4ee5\u4ece\u89c2\u6d4b\u6570\u636e\u786e\u5b9a\u201c\u539f\u56e0\u201d\u548c\u201c\u7ed3\u679c\u201d\u3002<\/section>\n<section>\u7528\u4e00\u4e2a DAG \u8fde\u8868\u793a\u53d8\u91cf\u4e4b\u95f4\u7684\u5173\u7cfb\uff0c\u5e76\u4e0d\u662f\u6700\u8fd1\u624d\u6709\u7684\u3002\u56fe\u6a21\u578b\u4e5f\u5e76\u4e0d\u662f Judea Pearl \u53d1\u660e\u7684\u3002\u4f46\u662f\uff0c\u65e9\u671f\u5c06\u56fe\u6a21\u578b\u4f5c\u4e3a\u56e0\u679c\u63a8\u65ad\u7684\u5de5\u5177\uff0c\u6210\u679c\u5e76\u4e0d\u6df1\u523b\uff0c\u5927\u5bb6\u4e5f\u4e0d\u592a\u6e05\u695a\u4ec5\u4ec5\u51ed\u4e00\u4e2a\u56fe\uff0c\u600e\u4e48\u80fd\u8bb2\u6e05\u695a\u56e0\u679c\u5173\u7cfb\u3002\u6559\u80b2\u3001\u5fc3\u7406\u548c\u793e\u4f1a\u5b66\u4e2d\u5e38\u7528\u7684\u7ed3\u6784\u65b9\u7a0b\u6a21\u578b\uff08structural equation model: SEM\uff09\uff0c\u5c31\u662f\u65e9\u671f\u7684\u5c1d\u8bd5\uff1b\u751a\u81f3\u53ef\u4ee5\u8bf4 SEM \u662f\u56e0\u679c\u56fe\u7684\u5148\u9a71\u3002\uff08\u6ce8\u610f\uff0c\u8fd9\u91cc\u51fa\u73b0\u7684\u4e24\u4e2a SEM \u8868\u793a\u4e0d\u540c\u7684\u6a21\u578b\uff01\uff09<\/section>\n<section>DAG \u4e2d\u7684\u7bad\u5934\uff0c\u4f3c\u4e4e\u8868\u793a\u4e86\u67d0\u79cd\u201c\u56e0\u679c\u5173\u7cfb\u201d\u3002\u4f46\u662f\uff0c\u8981\u5728 DAG \u4e0a\u5f15\u5165\u201c\u56e0\u679c\u201d\u7684\u6982\u5ff5\uff0c\u5219\u9700\u8981\u5f15\u8fdb\u00a0<strong>do \u7b97\u5b50<\/strong>\uff0cdo \u7684\u610f\u601d\u53ef\u4ee5\u7406\u89e3\u6210\u201c\u5e72\u9884\u201d\u00a0\uff08intervention\uff09\u3002\u6ca1\u6709\u201c\u5e72\u9884\u201d\u7684\u6982\u5ff5\uff0c\u5f88\u591a\u65f6\u5019\u6ca1\u6709\u529e\u6cd5\u8c08\u56e0\u679c\u5173\u7cfb\u3002\u5728 DAG \u4e2d\u00a0\uff08\u4e5f\u53ef\u4ee5\u8bb0\u505a\u00a0\uff09\uff0c\u8868\u793a\u5982\u4e0b\u7684\u64cd\u4f5c\uff1a\u5c06\u00a0\u00a0\u4e2d\u6307\u5411\u00a0\u00a0\u7684\u6709\u5411\u8fb9\u5168\u90e8\u5207\u65ad\uff0c\u4e14\u5c06\u00a0\u00a0\u7684\u53d6\u503c\u56fa\u5b9a\u4e3a\u5e38\u6570\u00a0. \u5982\u6b64\u64cd\u4f5c\uff0c\u5f97\u5230\u7684\u65b0\u00a0\u00a0\u7684\u8054\u5408\u5206\u5e03\u53ef\u4ee5\u8bb0\u505a\u00a0\u00a0\u53ef\u4ee5\u8bc1\u660e\uff0c\u5e72\u9884\u540e\u7684\u8054\u5408\u5206\u5e03\u4e3a<\/section>\n<section><\/section>\n<section>\u8bf7\u6ce8\u610f\uff0c\u00a0\u548c\u00a0\u00a0\u5728\u7edd\u5927\u591a\u6570\u60c5\u51b5\u4e0b\u662f\u4e0d\u540c\u7684\u3002<\/section>\n<section><strong>\u4f8b\u5b50<\/strong>\uff1a\u8003\u8651\u5982\u4e0b\u7684\u4e24\u4e2a DAG\uff1a<\/section>\n<section><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-648\" src=\"https:\/\/aif.amtbbs.org\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-31.png\" width=\"513\" height=\"89\" alt=\"\u56fe\u7247\" srcset=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-31.png 513w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-31-300x52.png 300w\" sizes=\"auto, (max-width: 513px) 100vw, 513px\" \/><\/section>\n<section>\u5728 Figure 2 (1) \u4e2d\uff0c\u6709\u3002\u7531\u4e8e\u662f\u7684\u201c\u539f\u56e0\u201d\uff0c\u201c\u6761\u4ef6\u201d\u548c\u201c\u5e72\u9884\u201d\uff0c\u5bf9\u5e94\u7684\u7684\u5206\u5e03\u76f8\u540c\u3002\u4f46\u662f\u5728 Figure 2 (2) \u4e2d\uff0c\u6709. \u7531\u4e8e\u662f\u7684\u201c\u7ed3\u679c\u201d\uff0c\u201c\u6761\u4ef6\u201d\uff08\u6216\u8005\u201c\u7ed9\u5b9a\u201d\uff09\u201c\u7ed3\u679c\u201d\uff0c\u201c\u539f\u56e0\u201d\u7684\u5206\u5e03\u4e0d\u518d\u7b49\u4e8e\u4ed6\u7684\u8fb9\u7f18\u5206\u5e03\uff0c\u4f46\u662f\u4eba\u4e3a\u7684\u201c\u5e72\u9884\u201d\u201c\u7ed3\u679c\u201d\uff0c\u5e76\u4e0d\u5f71\u54cd\u201c\u539f\u56e0\u201d\u7684\u5206\u5e03\u3002<\/section>\n<section>\u6839\u636e do \u7b97\u5b50\uff0c\u4fbf\u53ef\u4ee5\u5b9a\u4e49\u56e0\u679c\u4f5c\u7528\u3002\u6bd4\u5982\u4e8c\u503c\u7684\u53d8\u91cf\u00a0\u00a0\u5bf9\u4e8e\u00a0\u00a0\u7684\u5e73\u5747\u56e0\u679c\u4f5c\u7528\u5b9a\u4e49\u4e3a<\/section>\n<section><\/section>\n<section>\u4e0a\u9762 do \u7b97\u5b50\u4e0b\u7684\u671f\u671b\uff0c\u5206\u522b\u5bf9\u5e94 do \u7b97\u5b50\u4e0b\u7684\u5206\u5e03\u3002\u8fd9\u6837\u5728 do \u7b97\u5b50\u4e0b\u5b9a\u4e49\u7684\u56e0\u679c\u6a21\u578b\uff0c\u88ab\u5df2\u6545\u8ba1\u91cf\u7ecf\u6d4e\u5b66\u5bb6 Halbert White \u79f0\u4e3a Pearl Causal Model (PCM; White and Chalak 2009)\u3002Pearl \u5728\u5176\u4e66\u4e2d\u5199\u5230\uff1a<\/section>\n<blockquote data-tool=\"mdnice\u7f16\u8f91\u5668\">\n<section>\u201cI must take the opportunity to acknowledge four colleagues who saw clarity shining through the do(x) operator before it gained popularity: Steffen Lauritzen, David Freedman, James Robins and Philip David. Phil showed special\u00a0courage in pringting my paper in Biometrika, the journal founded by causality\u2019s worst adversary \u2013 Karl Pearson.\u201d (Pearl, 2000)<\/section>\n<\/blockquote>\n<section>\u5728\u4e66\u4e2d Pearl \u8bba\u8ff0\u4e86 RCM \u548c PCM \u7684\u7b49\u4ef7\u6027\uff0c\u5373<\/section>\n<section><img decoding=\"async\" class=\"rich_pages\" src=\"data:image\/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVQImWNgYGBgAAAABQABh6FO1AAAAABJRU5ErkJggg==\" alt=\"\u56fe\u7247\" crossorigin=\"anonymous\" data-ratio=\"0.13948497854077252\" data-s=\"300,640\" data-type=\"png\" data-w=\"466\" data-src=\"https:\/\/mmbiz.qpic.cn\/mmbiz_png\/dMFkbmlFTgd6FibE9qxxMQiaxziacZqCQgMU5ia5Ny9QYqjHiawiahE7oWqIBHC7Z0ZAXl2BMrxUAtIxkemxNtnOIwmQ\/640?wx_fmt=png\" \/><\/section>\n<section>\u5176\u4e2d\uff0c\u8868\u793a\u6f5c\u5728\u7ed3\u679c\u3002\u8981\u60f3\u8bf4\u660e\u4e24\u4e2a\u6a21\u578b\u7684\u7b49\u4ef7\u6027\uff0c\u53ef\u4ee5\u5c06\u6f5c\u5728\u7ed3\u679c\u5d4c\u5957\u5728 DAG \u6240\u5bf9\u5e94\u7684\u6570\u636e\u751f\u6210\u673a\u5236\u4e4b\u4e2d\uff0c\u6240\u6709\u7684\u6f5c\u5728\u7ed3\u679c\u90fd\u7531\u8fd9\u4e2a\u975e\u53c2\u6570\u7ed3\u6784\u65b9\u7a0b\u6a21\u578b\u4ea7\u751f\uff1a<\/section>\n<section><\/section>\n<section>\u5176\u4e2d\uff0c\u8868\u793a\u9664\u53bb\u7684\u7236\u4eb2\u8282\u70b9\u3002\u4e0a\u9762\u7684\u65b9\u7a0b\u8868\u793a\uff1a\u5c06\u7684\u503c\u5f3a\u5236\u5728\u65f6\uff0cDAG \u7cfb\u7edf\u6240\u4ea7\u751f\u7684\u503c\u3002\u8fd9\u4e2a\u610f\u4e49\u4e0b\uff0cdo \u7b97\u5b50\u5bfc\u51fa\u7684\u7ed3\u679c\uff0c\u5c31\u662f\u201c\u6f5c\u5728\u7ed3\u679c\u201d\u3002<\/section>\n<h1 data-tool=\"mdnice\u7f16\u8f91\u5668\">\u4e8c\u3001 d\u5206\u79bb\uff0c\u524d\u95e8\u51c6\u5219\u548c\u540e\u95e8\u51c6\u5219<\/h1>\n<section>\u5728\u4e0a\u9762\u7684\u53d9\u8ff0\u4e2d\uff0c\u5982\u679c\u6574\u4e2a DAG \u7684\u7ed3\u6784\u5df2\u77e5\u4e14\u6240\u6709\u7684\u53d8\u91cf\u90fd\u53ef\u89c2\u6d4b\uff0c\u90a3\u4e48\u6211\u4eec\u53ef\u4ee5\u6839\u636e\u4e0a\u9762 do \u7b97\u5b50\u7684\u516c\u5f0f\u7b97\u51fa\u4efb\u610f\u53d8\u91cf\u4e4b\u95f4\u7684\u56e0\u679c\u4f5c\u7528\u3002\u4f46\u662f\uff0c\u5728\u7edd\u5927\u591a\u6570\u7684\u5b9e\u9645\u95ee\u9898\u4e2d\uff0c\u6211\u4eec\u65e2\u4e0d\u77e5\u9053\u6574\u4e2a DAG \u7684\u7ed3\u6784\uff0c\u4e5f\u4e0d\u80fd\u5c06\u6240\u6709\u7684\u53d8\u91cf\u89c2\u6d4b\u5230\u3002\u56e0\u6b64\uff0c\u4ec5\u4ec5\u6709\u4e0a\u9762\u7684\u516c\u5f0f\u662f\u4e0d\u591f\u7684\u3002<\/section>\n<section>\u4e0b\u9762\uff0c\u6211\u5c06\u4ecb\u7ecd Judea Pearl \u63d0\u51fa\u7684\u201c\u540e\u95e8\u51c6\u5219\u201d\uff08backdoor criterion\uff09\u548c\u201c\u524d\u95e8\u51c6\u5219\u201d\uff08frontdoor criterion\uff09\u3002\u8fd9\u4e24\u4e2a\u51c6\u5219\u7684\u610f\u4e49\u5728\u4e8e\uff1a\uff081\uff09\u67d0\u4e9b\u7814\u7a76\u4e2d\uff0c\u5373\u4f7f DAG \u4e2d\u7684\u67d0\u4e9b\u53d8\u91cf\u4e0d\u53ef\u89c2\u6d4b\uff0c\u6211\u4eec\u4f9d\u7136\u53ef\u4ee5\u4ece\u89c2\u6d4b\u6570\u636e\u4e2d\u4f30\u8ba1\u51fa\u67d0\u4e9b\u56e0\u679c\u4f5c\u7528\uff1b\uff082\uff09\u8fd9\u4e24\u4e2a\u51c6\u5219\u6709\u52a9\u4e8e\u6211\u4eec\u9274\u522b\u201c\u6df7\u6742\u53d8\u91cf\u201d\u548c\u8bbe\u8ba1\u89c2\u5bdf\u6027\u7814\u7a76\u3002<\/section>\n<section>\u4e0b\u9762\u7684\u8ba8\u8bba\u4e2d\uff0c\u201c<strong>\u53ef\u8bc6\u522b\u6027<\/strong>\u201d\u8fd9\u4e2a\u6982\u5ff5\u5c06\u88ab\u9891\u7e41\u7684\u4f7f\u7528\u3002\u56e0\u679c\u63a8\u65ad\u4e2d\u7684\u8bc6\u522b\u6027\uff0c\u548c\u4f20\u7edf\u7edf\u8ba1\u4e2d\u7684\u8bc6\u522b\u6027\u5b9a\u4e49\u662f\u4e00\u81f4\u7684\u3002\u7edf\u8ba1\u4e2d\uff0c\u5982\u679c\u4e24\u4e2a\u4e0d\u540c\u7684\u6a21\u578b\u53c2\u6570\uff0c\u5bf9\u5e94\u4e0d\u540c\u7684\u89c2\u6d4b\u6570\u636e\u7684\u5206\u5e03\uff0c\u90a3\u4e48\u6211\u4eec\u79f0\u6a21\u578b\u7684\u53c2\u6570\u53ef\u4ee5\u8bc6\u522b\u3002\u8fd9\u91cc\uff0c\u5982\u679c\u56e0\u679c\u4f5c\u7528\u53ef\u4ee5\u7528\u89c2\u6d4b\u6570\u636e\u7684\u5206\u5e03\u552f\u4e00\u7684\u8868\u793a\uff0c\u90a3\u4e48\u6211\u4eec\u79f0\u56e0\u679c\u4f5c\u7528\u662f<strong>\u53ef\u4ee5\u8bc6\u522b<\/strong>\u7684\u3002<\/section>\n<section>\u524d\u95e8\u51c6\u5219\u548c\u540e\u95e8\u51c6\u5219\uff0c\u90fd\u6d89\u53ca\u4e86 d \u5206\u79bb\uff08d-seperation\uff09\u7684\u6982\u5ff5\u3002<\/section>\n<section>\u5b9a\u4e49\uff08<strong>d \u5206\u79bb<\/strong>\uff09: \u8bbe\u00a0\uff0c\uff0c\u00a0\u662f DAG \u4e2d\u4e0d\u76f8\u4ea4\u7684\u8282\u70b9\u96c6\u5408\uff0c\u00a0\u4e3a\u4e00\u6761\u8fde\u63a5\u00a0\u00a0\u4e2d\u67d0\u8282\u70b9\u5230\u00a0\u00a0\u4e2d\u67d0\u8282\u70b9\u7684\u8def\u5f84\u00a0\uff08\u4e0d\u7ba1\u65b9\u5411\uff09\u3002\u5982\u679c\u8def\u5f84\u00a0\u00a0\u4e0a\u67d0\u8282\u70b9\u6ee1\u8db3\u5982\u4e0b\u7684\u6761\u4ef6\uff1a<\/section>\n<ol class=\"list-paddingleft-2\" data-tool=\"mdnice\u7f16\u8f91\u5668\">\n<li>\n<section>\u5728\u8def\u5f84\u00a0\u00a0\u4e0a\uff0c\u00a0\u70b9\u5904\u4e3a\u00a0\u00a0\u7ed3\u6784\u00a0\uff08\u6216\u79f0\u51b2\u649e\u70b9\uff0ccollider\uff09\uff0c\u4e14\u00a0\u00a0\u53ca\u5176\u540e\u4ee3\u4e0d\u5728\u00a0\u00a0\u4e2d\uff1b<\/section>\n<\/li>\n<li>\n<section>\u5728\u8def\u5f84\u00a0\u00a0\u4e0a\uff0c\u00a0\u70b9\u5904\u4e0d\u662f\u00a0\u00a0\u7ed3\u6784\uff0c\u4e14\u00a0\u00a0\u5728\u00a0\u00a0\u4e2d,<\/section>\n<\/li>\n<\/ol>\n<section>\u90a3\u4e48\u79f0\u00a0\u00a0\u963b\u65ad (block) \u4e86\u8def\u5f84\u00a0\u3002\u8fdb\u4e00\u6b65\uff0c\u5982\u679c\u00a0\u00a0\u963b\u65ad\u4e86\u00a0\u5230\u00a0\u00a0\u7684\u6240\u6709\u8def\u5f84\uff0c\u90a3\u4e48\u79f0\u00a0\u00a0d \u5206\u79bb\u00a0\u00a0\u548c\u00a0\uff0c\u8bb0\u4e3a\u00a0\u3002<\/section>\n<section>\u4e0b\u9762\u4ecb\u7ecd Pearl\u00a0(1995)\u00a0\u7684\u4e3b\u8981\u5de5\u4f5c\uff1a<strong>\u540e\u95e8\u51c6\u5219\u548c\u524d\u95e8\u51c6\u5219<\/strong>\u3002<\/section>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-649\" src=\"https:\/\/aif.amtbbs.org\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-32.png\" width=\"393\" height=\"500\" alt=\"\u56fe\u7247\" srcset=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-32.png 393w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-32-236x300.png 236w\" sizes=\"auto, (max-width: 393px) 100vw, 393px\" \/><\/p>\n<section><strong>\u540e\u95e8\u51c6\u5219\uff1a<\/strong>\u5728 DAG \u4e2d\uff0c\u5982\u679c\u5982\u4e0b\u6761\u4ef6\u6ee1\u8db3\uff1a<\/section>\n<ol class=\"list-paddingleft-2\" data-tool=\"mdnice\u7f16\u8f91\u5668\">\n<li>\n<section>\u00a0\u4e2d\u8282\u70b9\u4e0d\u80fd\u662f\u00a0\u00a0\u7684\u540e\u4ee3\uff1b<\/section>\n<\/li>\n<li>\n<section>\u00a0\u963b\u65ad\u4e86\u4e4b\u95f4\u6240\u6709\u6307\u5411\u00a0\u00a0\u7684\u8def\u5f84\uff08\u8fd9\u6837\u7684\u8def\u5f84\u53ef\u4ee5\u79f0\u4e3a\u540e\u95e8\u8def\u5f84\uff09\uff1b<\/section>\n<\/li>\n<\/ol>\n<section>\u5219\u79f0\u53d8\u91cf\u7684\u96c6\u5408\u76f8\u5bf9\u4e8e\u53d8\u91cf\u7684\u6709\u5e8f\u5bf9\u6ee1\u8db3\u540e\u95e8\u51c6\u5219\u3002\u8fdb\u4e00\u6b65\uff0c\u82e5\u76f8\u5bf9\u4e8e\u53d8\u91cf\u7684\u6709\u5e8f\u5bf9\u6ee1\u8db3\u540e\u95e8\u51c6\u5219\uff0c\u5176\u4e2d\u00a0\u00a0\u548c\u00a0\u662f\u548c\u4e2d\u7684\u4efb\u610f\u8282\u70b9\uff1b\u90a3\u4e48\u79f0\u53d8\u91cf\u7684\u96c6\u5408\u76f8\u5bf9\u4e8e\u8282\u70b9\u96c6\u5408\u7684\u6709\u5e8f\u5bf9\u6ee1\u8db3\u540e\u95e8\u51c6\u5219\u3002<\/section>\n<section>Pearl\u00a0(1995)\u00a0\u8bc1\u660e\uff0c\u82e5\u5b58\u5728\u4e00\u4e2a\u53d8\u91cf\u96c6\u5408\u76f8\u5bf9\u4e8e\u6ee1\u8db3\u540e\u95e8\u51c6\u5219\uff0c\u90a3\u4e48\u5230\u7684\u56e0\u679c\u4f5c\u7528\u662f\u53ef\u4ee5\u8bc6\u522b\u7684\uff0c\u4e14<\/section>\n<section><\/section>\n<section>\u4e3a\u4e86\u7406\u89e3\u56e0\u679c\u56fe\u7684\u6982\u5ff5\uff0c\u4e0b\u9762\u7684\u7b80\u77ed\u8bc1\u660e\u662f\u5f88\u6709\u5fc5\u8981\u7684\u3002<\/section>\n<section><strong>\u8bc1\u660e\uff1a<\/strong>\u5728 Figure 3 (a) \u4e2d\uff0c<\/section>\n<section><\/section>\n<section>\u4ece\u4e0a\u9762\u53ef\u4ee5\u770b\u51fa\uff0c\u4e0a\u9762\u7684\u540e\u95e8\u51c6\u5219\u548c\u53ef\u5ffd\u7565\u6027\u5047\u5b9a\u4e0b ACE \u7684\u8bc6\u522b\u516c\u5f0f\u4e00\u6837\uff1a\u90fd\u662f\u7528\u00a0\u00a0\u505a\u8c03\u6574\u00a0(adjustment)\uff0c\u5148\u5206\u5c42\u518d\u52a0\u6743\u6c42\u548c\u3002\u8fd9\u6761\u7ed3\u8bba\u5728 Rosenbaum and Rubin\u00a0(1983)\u00a0\u4e4b\u540e\u63d0\u51fa\uff0c\u4e14\u6d41\u884c\u75c5\u5b66\u5bb6\u4e5f\u90fd\u7528\u8fd9\u6837\u7684\u8c03\u6574\u65b9\u6cd5\u63a7\u5236\u6df7\u6742\u56e0\u7d20\uff0c\u56e0\u6b64\u5bf9\u5f88\u591a\u7edf\u8ba1\u5b66\u5bb6\u548c\u6d41\u884c\u75c5\u5b66\u5bb6\u6765\u8bf4\u5e76\u4e0d\u65b0\u5947\u3002\u6bd4\u8f83\u65b0\u9896\u7684\u7ed3\u8bba\u662f\u4e0b\u9762\u7684\u524d\u95e8\u51c6\u5219\u3002<\/section>\n<section><strong>\u524d\u95e8\u51c6\u5219\uff1a<\/strong>\u5728 DAG \u4e2d\uff0c\u79f0\u8282\u70b9\u7684\u96c6\u5408\u00a0\u00a0\u76f8\u5bf9\u4e8e\u6709\u5e8f\u5bf9\u00a0\u00a0\u6ee1\u8db3\u524d\u95e8\u51c6\u5219\uff0c\u5982\u679c<\/section>\n<ol class=\"list-paddingleft-2\" data-tool=\"mdnice\u7f16\u8f91\u5668\">\n<li>\n<section>\u00a0\u5207\u65ad\u4e86\u6240\u6709\u00a0\u00a0\u5230\u00a0\u00a0\u7684\u76f4\u63a5\u8def\u5f84\uff1b<\/section>\n<\/li>\n<li>\n<section>\u00a0\u5230\u00a0\u00a0\u6ca1\u6709\u540e\u95e8\u8def\u5f84\uff1b<\/section>\n<\/li>\n<li>\n<section>\u6240\u6709\u00a0\u00a0\u5230\u00a0\u00a0\u7684\u540e\u95e8\u8def\u5f84\u90fd\u88ab\u00a0\u00a0\u963b\u65ad\u3002<\/section>\n<\/li>\n<\/ol>\n<section>\u6b64\u65f6\uff0c\u5982\u679c\uff0c\u5219\u5230\u7684\u56e0\u679c\u4f5c\u7528\u53ef\u8bc6\u522b\uff0c\u4e3a<\/section>\n<section><\/section>\n<section><strong>\u8bc1\u660e\uff1a<\/strong>Figure 3 (b) \u4e2d\u8574\u542b\u4e86\u6761\u4ef6\u72ec\u7acb\u6027\uff0c\u5c06\u5728\u63a8\u5bfc\u4e2d\u7528\u5230\uff1a\u3002<\/section>\n<section><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-650\" src=\"https:\/\/aif.amtbbs.org\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-33.png\" width=\"947\" height=\"552\" alt=\"\u56fe\u7247\" srcset=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-33.png 947w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-33-300x175.png 300w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-33-768x448.png 768w\" sizes=\"auto, (max-width: 947px) 100vw, 947px\" \/><\/section>\n<section>\u8fd9\u4e2a\u524d\u95e8\u8def\u5f84\u770b\u4f3c\u5f88\u96be\u7406\u89e3\uff0c\u8bc1\u660e\u4f3c\u4e4e\u5f88\u4e0d\u76f4\u89c2\uff0c\u6070\u4f3c\u53d8\u9b54\u672f\u3002\u4f46\u662f\u5b83\u5176\u5b9e\u662f\u5f88\u663e\u7136\u7684\uff0c\u5728\u524d\u95e8\u8def\u5f84\u7684 DAG \u4e2d\uff0c\u6211\u4eec\u6709\uff1a\uff081\uff09X\u5bf9Z\u7684\u56e0\u679c\u4f5c\u7528\u53ef\u8bc6\u522b\uff0c\u56e0\u4e3aY\u963b\u65ad\u4e86\u5b83\u4eec\u4e4b\u95f4\u7684\u540e\u95e8\u8def\u5f84\uff1b\uff082\uff09Z\u5bf9Y\u7684\u56e0\u679c\u4f5c\u7528\u53ef\u8bc6\u522b\uff0c\u56e0\u4e3aX\u963b\u65ad\u4e86\u4ed6\u4eec\u7684\u540e\u95e8\u8def\u5f84\uff1b\uff083\uff09X\u5bf9Y\u7684\u4f5c\u7528\uff0c\u4ec5\u4ec5\u901a\u8fc7Z\u800c\u4ea7\u751f\u3002\u8fd9\u4e09\u70b9\u8574\u542b\u7740X\u5bf9Y\u7684\u56e0\u679c\u4f5c\u7528\u53ef\u8bc6\u522b\u2014\u2014\u8fd9\u6837\u770b\u6765\uff0c\u8fd9\u4e2a\u7ed3\u8bba\u5c31\u4e0d\u5947\u602a\u4e86\uff01<\/section>\n<section>Pearl \u5728\u4e66\u4e2d\u8bb2\u4e86\u4e00\u4e2a\u975e\u5e38\u6709\u8da3\u7684\u4f8b\u5b50\uff0c\u6765\u8bf4\u660e\u524d\u95e8\u51c6\u5219\u7684\u7528\u5904\u3002<\/section>\n<section><strong>\u4f8b\u5b50\uff1a<\/strong>\u6211\u4eec\u5173\u5fc3\u5438\u70df\u548c\u80ba\u764c\u4e4b\u95f4\u7684\u56e0\u679c\u5173\u7cfb\u3002\u7531\u4e8e\u4e00\u4e2a\u6f5c\u5728\u7684\u4e0d\u53ef\u89c2\u6d4b\u7684\u57fa\u56e0\u00a0\u00a0\u7684\u5b58\u5728\uff0c\u5438\u70df\u548c\u80ba\u764c\u4e4b\u95f4\u6709\u4e00\u6761\u201c\u6d3b\u201d\u7684\u540e\u95e8\u8def\u5f84\uff0c\u56e0\u6b64\u4e0d\u501f\u52a9\u5176\u4ed6\u7684\u6761\u4ef6\uff0c\u6211\u4eec\u65e0\u6cd5\u8bc6\u522b\u5438\u70df\u4e0e\u80ba\u764c\u7684\u56e0\u679c\u5173\u7cfb\u3002\u5982\u679c\u6211\u4eec\u6709\u8fd9\u6837\u7684\u77e5\u8bc6\u201c\u5438\u70df\u00a0\u00a0\u4ec5\u4ec5\u901a\u8fc7\u80ba\u90e8\u70df\u7126\u6cb9\u7684\u542b\u91cf\u00a0\u00a0\u6765\u5f71\u54cd\u80ba\u764c\u00a0\u00a0\u201d\uff0c\u90a3\u4e48\u5438\u70df\u5bf9\u80ba\u764c\u7684\u56e0\u679c\u4f5c\u7528\u5c31\u53ef\u4ee5\u4f30\u8ba1\u51fa\u6765\u4e86\u3002\u4e0d\u8fc7\uff0c\u8fd9\u91cc\u9700\u8981\u4e24\u4e2a\u6761\u4ef6\uff0c\u4e5f\u5c31\u662f\u5728\u8bc1\u660e\u4e2d\u4f7f\u7528\u7684\u4e24\u4e2a\u6761\u4ef6\u72ec\u7acb\u6027\uff0c\u4ed6\u4eec\u8868\u660e\uff1a\uff081\uff09\u5438\u70df\u00a0\u00a0 \u548c\u80ba\u90e8\u70df\u7126\u6cb9\u7684\u542b\u91cf\u00a0\u00a0 \u4e4b\u95f4\u6ca1\u6709\u201c\u6d3b\u201d\u7684\u540e\u95e8\u8def\u5f84\uff08\u6216\u8005\u6ca1\u6709\u6df7\u6742\u56e0\u7d20\uff09\uff1b\uff082\uff09\u5438\u70df\u00a0\u00a0\u5bf9\u80ba\u764c\u00a0\u00a0\u7684\u4f5c\u7528\u4ec5\u4ec5\u6765\u6e90\u4e8e\u5438\u70df\u00a0\u00a0\u5bf9\u80ba\u90e8\u70df\u7126\u6cb9\u00a0\u00a0\u7684\u4f5c\u7528\uff0c\u6216\u8005\u8bf4\uff0c\u5438\u70df\u00a0\u00a0\u5bf9\u80ba\u764c\u00a0\u00a0\u6ca1\u6709\u201c\u76f4\u63a5\u4f5c\u7528\u201d\u3002<\/section>\n<section><strong>\u4f8b\u5b50\uff1a<\/strong>\u5728 Figure 1 \u7684 DAG \u4e2d\uff0c\u00a0\u4e4b\u95f4\u7684\u540e\u95e8\u8def\u5f84\u88ab\u00a0\u00a0\u6216\u8005\u00a0\u00a0\u963b\u65ad\uff0c\u800c\u524d\u95e8\u8def\u5f84\u88ab\u00a0\u00a0\u963b\u65ad\u3002\u4e0a\u9762\u7684\u4e24\u4e2a\u51c6\u5219\u8868\u660e\uff0c<strong>\u8981\u8bc6\u522b\u4ece\u00a0<\/strong><strong>\u00a0\u5230\u00a0<\/strong><strong>\u00a0\u7684\u56e0\u679c\u4f5c\u7528\uff0c\u6211\u4eec\u4e0d\u9700\u8981\u89c2\u6d4b\u5230\u6240\u6709\u7684\u53d8\u91cf\uff0c\u53ea\u9700\u8981\u89c2\u6d4b\u5230\u5207\u65ad\u540e\u95e8\u8def\u5f84\u6216\u8005\u524d\u95e8\u8def\u5f84\u7684\u53d8\u91cf\u5373\u53ef\u3002<\/strong><\/section>\n<h1 data-tool=\"mdnice\u7f16\u8f91\u5668\">\u4e09\u3001\u00a0\u56de\u5230 Yule-Simpson\u2019s Paradox<\/h1>\n<section>\u5728\u7b2c\u4e00\u8282\u4e2d\uff0c\u6211\u4eec\u770b\u5230\u4e86\u7ecf\u5178\u7684 Yule-Simpson\u2019s Paradox\u3002\u8bb0\u00a0\u00a0\u4e3a\u5904\u7406\uff08\u5403\u836f\u4e0e\u5426\uff09\uff1b\u00a0\u00a0\u4e3a\u7ed3\u679c\uff08\u5b58\u6d3b\u4e0e\u5426\uff09\uff0c\u00a0\u00a0\u662f\u7528\u4e8e\u5206\u5c42\u7684\u53d8\u91cf\uff08\u5728\u6700\u5f00\u59cb\u7684\u4f8b\u5b50\u4e2d\uff0c\u00a0\u00a0\u662f\u6027\u522b\uff1b\u5728\u8fd9\u91cc\u6211\u4eec\u5148\u5c06\u00a0\u00a0\u7b80\u5355\u5730\u770b\u6210\u67d0\u4e2a\u7528\u4e8e\u5206\u5c42\u7684\u53d8\u91cf\uff09\u3002\u6096\u8bba\u5b58\u5728\uff0c\u662f\u56e0\u4e3a\u00a0\u00a0\u548c\u00a0\u00a0\u6b63\u76f8\u5173\uff1b\u4f46\u662f\u6309\u7167\u00a0\u7684\u503c\u5206\u5c42\u540e\uff0c\u00a0\u00a0\u548c\u00a0\u00a0\u8d1f\u76f8\u5173\u3002\u5206\uff0c\u8fd8\u662f\u4e0d\u5206\uff1f\u2014\u2013\u8fd9\u662f\u4e00\u4e2a\u95ee\u9898\uff01\u8fd9\u5728\u5b9e\u9645\u5e94\u7528\u662f\u975e\u5e38\u91cd\u8981\u7684\u95ee\u9898\u3002<\/section>\n<section>\u4e0d\u8fc7\uff0c\u4ec5\u4ec5\u4ece\u201c\u76f8\u5173\u201d\uff08association\uff09\u7684\u89d2\u5ea6\u8ba8\u8bba\u8fd9\u4e2a\u95ee\u9898\uff0c\u662f\u6ca1\u6709\u7b54\u6848\u7684\u3002\u4ece\u201c\u56e0\u679c\u201d\uff08causation\uff09\u7684\u89d2\u5ea6\u6765\u770b\uff0c\u624d\u80fd\u6709\u786e\u5207\u7684\u56de\u7b54\u3002\u89e3\u91ca Yule-Simpson\u2019s Paradox\uff0c\u7b97\u662f\u56e0\u679c\u56fe\u7684\u7b2c\u4e00\u4e2a\u91cd\u8981\u5e94\u7528\u3002<\/section>\n<section><img decoding=\"async\" class=\"rich_pages img_loading\" src=\"data:image\/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVQImWNgYGBgAAAABQABh6FO1AAAAABJRU5ErkJggg==\" alt=\"\u56fe\u7247\" crossorigin=\"anonymous\" data-ratio=\"1.160092807424594\" data-s=\"300,640\" data-type=\"png\" data-w=\"431\" data-src=\"https:\/\/mmbiz.qpic.cn\/mmbiz_png\/dMFkbmlFTgd6FibE9qxxMQiaxziacZqCQgMpBKBLib45MGPdlFd9bUhCjawCiaJ7GaZevMVwqibScv29Z8hFgHssE4iaw\/640?wx_fmt=png\" \/><\/section>\n<section>\u4e0b\u9762\uff0c\u6211\u5c06\u4ee5\u4e0a\u9762\u7684 Figure 4 \u4e2d\u7684\u56db\u4e2a\u56fe\u4e3a\u4f8b\u8bf4\u660e\uff0c\u4e09\u4e2a\u53d8\u91cf\u4e4b\u95f4\u7684\u5173\u7cfb\u7684\u590d\u6742\u6027\u3002<\/section>\n<section>\u56fe\uff08a\uff09\uff1a\u6839\u636e\u540e\u95e8\u51c6\u5219\uff0c\u00a0\u00a0\u963b\u65ad\u4e86\u00a0\u00a0\u5230\u00a0\u00a0\u7684\u540e\u95e8\u8def\u5f84\uff0c\u56e0\u6b64\uff0c\u6839\u636e\u00a0\u00a0\u505a\u8c03\u6574\u53ef\u4ee5\u5f97\u5230\u00a0\u00a0\u5bf9\u00a0\u7684\u56e0\u679c\u4f5c\u7528\u3002\u5982\u679c\u5b9e\u9645\u95ee\u9898\u7b26\u5408\u56fe\uff08a\uff09\uff0c\u90a3\u4e48\u6211\u4eec\u9700\u8981\u7528\u8c03\u6574\u540e\u7684\u4f30\u8ba1\u91cf\u3002<\/section>\n<section>\u56fe\uff08b\uff09\uff1a\u00a0\u662f\u00a0\u7684\u201c\u540e\u4ee3\u201d\u4e14\u662f\u00a0\u00a0\u7684\u201c\u7236\u4eb2\u201d\u3002\u5f88\u591a\u5730\u65b9\u79f0\uff0c\u6b64\u65f6\u00a0\u00a0\u5904\u4e8e\u00a0\u00a0\u5230\u00a0\u00a0\u7684\u56e0\u679c\u8def\u5f84\u4e0a\u3002\u76f4\u89c2\u7684\u770b\uff0c\u5982\u679c\u5ffd\u7565\u00a0\uff0c\u90a3\u4e48\u00a0\u00a0\u548c\u00a0\u00a0\u4e4b\u95f4\u7684\u76f8\u5173\u6027\u5c31\u662f \u00a0\u00a0\u5bf9 \u00a0\u00a0\u7684\u56e0\u679c\u4f5c\u7528\uff0c\u56e0\u4e3a\u00a0\u00a0\u548c\u00a0\u00a0\u4e4b\u95f4\u7684\u540e\u95e8\u8def\u5f84\u88ab\u7a7a\u96c6\u963b\u65ad\uff0c\u6211\u4eec\u65e0\u987b\u8c03\u6574\u3002\u5982\u679c\u6b64\u65f6\u6211\u4eec\u7528\u00a0\u00a0\u8fdb\u884c\u8c03\u6574\uff0c\u90a3\u4e48\u5f97\u5230\u7684\u662f\u00a0\u00a0\u5230\u00a0\u00a0\u7684\u201c\u76f4\u63a5\u4f5c\u7528\u201d\u3002\u4e0d\u8fc7\uff0c\u4ec0\u4e48\u662f\u201c\u76f4\u63a5\u4f5c\u7528\u201d\uff0c\u6211\u4eec\u5c06\u4f1a\u5728\u540e\u9762\u8ba8\u8bba\uff1b\u8fd9\u91cc\u53ea\u662f\u7ed9\u4e00\u4e2a\u5f62\u8c61\u7684\u540d\u5b57\u3002<\/section>\n<section>\u56fe\uff08c\uff09\uff1a\u548c\u56fe\uff08b\uff09\u76f8\u540c\uff0c\u00a0\u00a0\u548c\u00a0\u00a0\u4e4b\u95f4\u7684\u76f8\u5173\u6027\u5c31\u662f\u56e0\u679c\u4f5c\u7528\u3002\u4f46\u662f\uff0c\u590d\u6742\u6027\u5728\u4e8e\u00a0\u00a0\u548c\u00a0\u00a0\u4e4b\u95f4\u6709\u4e00\u4e2a\u5171\u540c\u7684\u4f46\u662f\u4e0d\u53ef\u89c2\u6d4b\u7684\u539f\u56e0\u00a0\u3002\u6b64\u65f6\uff0c\u4e0d\u8c03\u6574\u7684\u76f8\u5173\u6027\uff0c\u662f\u4e00\u4e2a\u56e0\u679c\u5173\u7cfb\u7684\u5ea6\u91cf\u3002\u4f46\u662f\uff0c\u5982\u679c\u6211\u4eec\u7528\u00a0\u00a0\u8fdb\u884c\u8c03\u6574\uff0c\u90a3\u4e48\u7ed9\u5b9a\u00a0\u00a0\u540e\uff0c\u00a0\u548c\u00a0\u00a0\u76f8\u5173\uff0c\u00a0\u548c\u00a0\u00a0\u4e4b\u95f4\u7684\u540e\u95e8\u8def\u5f84\u88ab\u6253\u901a\uff0c\u6211\u4eec\u5f97\u5230\u7684\u4f30\u8ba1\u91cf\u4e0d\u518d\u5177\u6709\u56e0\u679c\u7684\u542b\u4e49\u3002\u8fd9\u79cd\u73b0\u8c61\u53d1\u751f\u7684\u539f\u56e0\u662f\uff0c\u00a0\u4e4b\u95f4\u5f62\u6210\u4e86\u4e00\u4e2a\u00a0\u7ed3\u6784\uff1a\u867d\u7136\u00a0\u00a0\u548c\u00a0\u4e4b\u95f4\u662f\u72ec\u7acb\u7684\uff0c\u4f46\u662f\u7ed9\u5b9a\u00a0\u00a0\u4e4b\u540e\uff0c\u00a0\u548c\u00a0\u00a0\u4e0d\u518d\u72ec\u7acb\u3002<\/section>\n<section>\u56fe\uff08d\uff09\uff1a\u8fd9\u4e2a\u56fe\u5e38\u5e38\u88ab Judea Pearl \u7528\u6765\u6279\u8bc4 Donald Rubin\uff0c\u56e0\u4e3a\u5b83\u5b58\u5728\u4e00\u4e2a\u6709\u8da3\u7684\u00a0\u00a0\u7ed3\u6784\u3002\u5728\u8fd9\u4e2a\u56fe\u4e2d\uff0c\u7531\u4e8e\u00a0\u00a0\u7ed3\u6784\u7684\u5b58\u5728\uff0c\u00a0\u548c\u00a0\u00a0\u4e4b\u95f4\u7684\u540e\u95e8\u8def\u5f84\u88ab\u7a7a\u96c6\u963b\u65ad\uff0c\u56e0\u6b64\u00a0\u00a0\u548c\u00a0\u00a0\u4e4b\u95f4\u7684\u76f8\u5173\u6027\u5c31\u662f\u56e0\u679c\u6027\u3002\u4f46\u662f\u7531\u4e8e\u00a0\u00a0\u7ed3\u6784\u7684\u5b58\u5728\uff0c\u5f53\u6211\u4eec\u7528\u00a0\u00a0\u8fdb\u884c\u8c03\u6574\u7684\u65f6\u5019\uff0c\u00a0\u00a0\u548c\u00a0\u00a0\u4e4b\u95f4\u6253\u5f00\u4e86\u4e00\u6761\u201c\u901a\u8def\u201d\uff08\u5b83\u4eec\u4e0d\u518d\u72ec\u7acb\uff09\uff0c\u56e0\u6b64\u00a0\u00a0\u548c\u00a0\u00a0\u4e4b\u95f4\u7684\u540e\u95e8\u8def\u5f84\u88ab\u6253\u901a\uff0c\u6b64\u65f6\u00a0\u00a0\u548c\u00a0\u00a0\u4e4b\u95f4\u7684\u76f8\u5173\u6027\u4e0d\u518d\u5177\u6709\u56e0\u679c\u7684\u542b\u4e49\u3002<\/section>\n<section>\u6211\u4e2a\u4eba\u8ba4\u4e3a\uff0c\u56e0\u679c\u56fe\u662f\u63ed\u5f00 Yule-Simpson\u2019s Paradox \u795e\u79d8\u9762\u7eb1\u7684\u6709\u529b\u5de5\u5177\u3002\u6b63\u5982 Judea Pearl \u5728\u4ed6\u7684\u4e66\u4e2d\u5199\u5230\uff0c\u4e0d\u7528\u56e0\u679c\u7684\u8bed\u8a00\u6765\u63cf\u8ff0\u8fd9\u4e2a\u95ee\u9898\uff0c\u6211\u4eec\u662f\u8bb2\u4e0d\u6e05\u695a\u8fd9\u4e2a\u6096\u8bba\u7684\u3002\u5f53\u7136\uff0c\u56e0\u679c\u7684\u8bed\u8a00\u4e0d\u6b62\u56e0\u679c\u56fe\uff0cJudea Pearl \u7684\u89e3\u91ca\u59cb\u7ec8\u4e0d\u80fd\u5f97\u5230 Donald Rubin \u7684\u8ba4\u53ef\u3002<\/section>\n<h1 data-tool=\"mdnice\u7f16\u8f91\u5668\">\u56db\u3001\u00a0\u8ba8\u8bba<\/h1>\n<section>\u7528\u4e00\u4e2a\u56fe\u6765\u63cf\u8ff0\u53d8\u91cf\u4e4b\u95f4\u7684\u56e0\u679c\u5173\u7cfb\uff0c\u662f\u5f88\u81ea\u7136\u548c\u76f4\u89c2\u7684\u4e8b\u60c5\u3002\u4f46\u662f\uff0c\u8fd9\u5e76\u4e0d\u610f\u5473\u7740 Pearl \u7684\u7406\u8bba\u662f\u8001\u59aa\u80fd\u89e3\u7684\u3002\u4e8b\u5b9e\u4e0a\uff0c\u8fd9\u5957\u57fa\u4e8e DAG \u7684\u56e0\u679c\u63a8\u65ad\u7684\u8bed\u8a00\uff0c\u6bd4\u4f20\u7edf\u7684 Neyman-Rubin \u6a21\u578b\u8981\u6666\u6da9\u5f88\u591a\u3002DAG \u5728\u63cf\u8ff0\u56e0\u679c\u5173\u7cfb\u7684\u65f6\u5019\uff0c\u5e38\u5e38\u57fa\u4e8e\u5f88\u591a\u6697\u542b\u7684\u5047\u5b9a\u800c\u5e76\u4e0d\u660e\u8bf4\uff0c\u8fd9\u4e5f\u662f DAG \u5e76\u6ca1\u6709\u88ab\u5927\u5bb6\u5b8c\u5168\u63a5\u53d7\u7684\u539f\u56e0\u3002\u4f20\u7edf\u7684\u56e0\u679c\u63a8\u65ad\u7684\u8bed\u8a00\uff0c\u5f00\u59cb\u4e8e Jerzy Neyman \u7684\u535a\u58eb\u8bba\u6587\uff1bDonald Rubin \u53d1\u5c55\u8fd9\u5957\u201c\u6f5c\u5728\u7ed3\u679c\u201d\u7684\u8bed\u8a00\uff0c\u5e76\u5c06\u5b83\u548c\u7f3a\u5931\u6570\u636e\u7684\u7406\u8bba\u8054\u7cfb\u5728\u4e00\u8d77\uff0c\u6210\u4e3a\u7edf\u8ba1\u754c\u66f4\u591a\u4f7f\u7528\u7684\u8bed\u8a00\u3002<\/section>\n<section>\u5728\u5b9e\u9645\u4e2d\uff0c\u4eba\u4eec\u5bf9\u4e8e\u56fe\u6a21\u578b\u7684\u6279\u8bc4\u4ece\u672a\u4e2d\u65ad\u3002\u4e3b\u8981\u7684\u95ee\u9898\u96c6\u4e2d\u5728\u5982\u4e0b\u7684\u65b9\u9762\uff1a<\/section>\n<ol class=\"list-paddingleft-2\" data-tool=\"mdnice\u7f16\u8f91\u5668\">\n<li>\n<section>\u73b0\u5b9e\u7684\u95ee\u9898\uff0c\u662f\u5426\u80fd\u7528\u4e00\u4e2a\u6709\u5411\u65e0\u73af\u56fe\u8868\u793a\uff1f\u5927\u591a\u6570\u751f\u7269\u5b66\u5bb6\u770b\u5230 DAG \u7684\u53cd\u5e94\u662f\u201c\u80fd\u4e0d\u80fd\u7528\u56fe\u8868\u793a\u53cd\u9988\uff1f\u201d\u7684\u786e\uff0cDAG \u4f5c\u4e3a\u4e00\u79cd\u7b80\u5316\u7684\u6a21\u578b\uff0c\u5728\u590d\u6742\u7cfb\u7edf\u4e2d\u53ef\u80fd\u4e0d\u5b8c\u5168\u9002\u7528\u3002\u8981\u60f3\u5c06 DAG \u63a8\u5e7f\u5230\u52a8\u6001\u7684\u7cfb\u7edf\uff0c\u6216\u8005\u65f6\u95f4\u5e8f\u5217\u4e2d\uff0c\u8fd8\u6709\u5f85\u7814\u7a76\u3002<\/section>\n<\/li>\n<li>\n<section>Pearl \u5f15\u5165\u7684 do \u7b97\u5b50\uff0c\u662f\u4ed6\u5728\u56e0\u679c\u63a8\u65ad\u9886\u57df\u6700\u4e3b\u8981\u7684\u8d21\u732e\u3002\u6240\u8c13 \u201cdo\u201d\uff0c\u5c31\u662f\u201c\u5e72\u9884\u201d\uff0cPearl \u8ba4\u4e3a\u5e72\u9884\u5c31\u662f\u4ece\u7cfb\u7edf\u4e4b\u5916\u4eba\u4e3a\u7684\u63a7\u5236\u67d0\u4e9b\u53d8\u91cf\u3002\u4f46\u662f\uff0c\u8fd9\u4f9d\u8d56\u4e8e\u4e00\u4e2a\u5047\u5b9a\uff1a\u5e72\u9884\u67d0\u4e9b\u53d8\u91cf\u5e76\u4e0d\u4f1a\u5f15\u8d77 DAG \u4e2d\u5176\u4ed6\u7ed3\u6784\u7684\u53d8\u5316\u3002\u8fd9\u4e2a\u5047\u5b9a\u5e38\u5e38\u4f1a\u53d7\u5230\u8d28\u7591\uff0c\u4f46\u662f\u8d28\u7591\u5f52\u8d28\u7591\uff0cPearl \u7684\u8fd9\u4e2a\u5047\u5b9a\u867d\u7136\u770b\u4f3c\u5f88\u5f3a\uff0c\u4f46\u6839\u636e\u89c2\u6d4b\u6570\u636e\u5374\u4e0d\u53ef\u68c0\u9a8c\u3002\u8fd9\u79cd\u8d28\u7591\u5e76\u4e0d\u662f Pearl \u7684\u7406\u8bba\u72ec\u6709\u7684\u7f3a\u9677\uff0c\u8fd9\u4e8b\u5b9e\u4e0a\u662f\u4e00\u5207\u7814\u7a76\u7684\u7f3a\u9677\u3002\u6bd4\u5982\uff0c\u6211\u4eec\u7528\u5b8c\u5168\u968f\u673a\u5316\u8bd5\u9a8c\u6765\u7814\u7a76\u5904\u7406\u7684\u4f5c\u7528\uff0c\u6211\u4eec\u8981\u60f3\u5c06\u5b9e\u9a8c\u63a8\u5e7f\u5230\u89c2\u5bdf\u6027\u7684\u6570\u636e\u6216\u8005\u66f4\u5927\u7684\u4eba\u7fa4\u4e2d\u53bb\uff0c\u4e5f\u5fc5\u987b\u7528\u5230\u4e00\u4e9b\u4e0d\u53ef\u9a8c\u8bc1\u7684\u5047\u5b9a\u3002<\/section>\n<\/li>\n<li>\n<section>\u5f88\u591a\u4eba\u770b\u4e86 Pearl \u7684\u7406\u8bba\u540e\u5c31\u5632\u7b11\u4ed6\uff1a\u96be\u9053\u6211\u4eec\u53ef\u4ee5\u5728 DAG \u4e2d\u5e72\u9884\u201c\u6027\u522b\u201d\uff1f\u786e\u5b9e\uff0c\u79bb\u5f00\u4e86\u5b9e\u9645\u7684\u80cc\u666f\uff0c\u5e72\u9884\u6027\u522b\u4f3c\u4e4e\u662f\u4e0d\u592a\u5408\u7406\u7684\u3002\u90a3\u8fd9\u4e2a\u65f6\u5019\uff0c\u6839\u636e Pearl \u7684 do\u7b97\u5b50\u5f97\u5230\u7684\u56e0\u679c\u4f5c\u7528\u610f\u5473\u7740\u4ec0\u4e48\u5462\uff1f\u53ef\u4ee5\u4ece\u51e0\u4e2a\u65b9\u9762\u56de\u7b54\u8fd9\u4e2a\u95ee\u9898\u3002<\/section>\n<ul class=\"list-paddingleft-2\">\n<li>\n<section>\u5f88\u591a\u95ee\u9898\uff0c\u6211\u4eec\u4e0d\u80fd\u8c08\u8bba\u201c\u5e72\u9884\u6027\u522b\u201d\uff0c\u4e5f\u4e0d\u80fd\u8c08\u8bba\u201c\u6027\u522b\u201d\u7684\u201c\u56e0\u679c\u4f5c\u7528\u201d\u3002\u201c\u6027\u522b\u201d\u7684\u7279\u6027\u662f\u201c\u534f\u53d8\u91cf\u201d\uff08covariate\uff09\uff0c\u5bf9\u4e8e\u8fd9\u7c7b\u53d8\u91cf\uff08\u5982\u8eab\u9ad8\u3001\u80a4\u8272\u7b49\uff09\uff0c\u8c08\u8bba\u56e0\u679c\u4f5c\u7528\u4e0d\u5408\u9002\uff0c\u56e0\u4e3a\u6211\u4eec\u4e0d\u80fd\u60f3\u8c61\u51fa\u4e00\u4e2a\u53ef\u80fd\u7684\u201c\u5b9e\u9a8c\u201d\uff0c\u5e72\u9884\u8fd9\u4e9b\u53d8\u91cf\u3002<\/section>\n<\/li>\n<li>\n<section>\u4e0a\u9762\u7684\u56de\u7b54\u57fa\u4e8e\u201c\u5b9e\u9a8c\u5b66\u6d3e\u201d\uff08experimentalists\u2019\uff09\u7684\u89c2\u70b9\uff0c\u8ba4\u4e3a\u4e0d\u53ef\u5e72\u9884\uff0c\u5c31\u6ca1\u6709\u201c\u56e0\u679c\u201d\u3002\u4f46\u662f\uff0c\u5982\u679c\u8ba4\u4e3a\u53ea\u8981\u6709\u6570\u636e\u7684\u751f\u6210\u673a\u5236\uff0c\u5c31\u6709\u56e0\u679c\u5173\u7cfb\uff0c\u90a3\u4e48\u7b97\u51fa\u6027\u522b\u7684\u56e0\u679c\u4f5c\u7528\u4e5f\u4e0d\u5947\u602a\u3002\uff08\u8ba1\u91cf\u7ecf\u5c31\u5b66\u4e00\u76f4\u6709\u4e89\u8bae\uff0c\u4ee5 Joshua Angrist\u3001Guido Imbens \u7b49\u4e3a\u9996\u7684\u201c\u5b9e\u9a8c\u6d3e\u201d\uff0c\u548c\u4ee5 James Heckman \u4e3a\u9996\u7684\u201c\u7ed3\u6784\u65b9\u7a0b\u6a21\u578b\u201d\u6d3e\uff0c\u6709\u8fc7\u5f88\u6fc0\u70c8\u7684\u8ba8\u8bba\u3002\uff09<\/section>\n<\/li>\n<li>\n<section>\u6709\u4e9b\u95ee\u9898\u4e2d\u6027\u522b\u7684\u56e0\u679c\u4f5c\u7528\u662f\u826f\u597d\u5b9a\u4e49\u7684\u3002\u6bd4\u5982\uff0c\u6211\u4eec\u53ef\u4ee5\u4eba\u5de5\u7684\u4fee\u6539\u5e94\u8058\u8005\u7b80\u5386\u4e0a\u7684\u540d\u5b57\uff08\u968f\u673a\u7684\u4f7f\u7528\u7537\u6027\u548c\u5973\u6027\u540d\u5b57\uff09\uff0c\u4fbf\u53ef\u4ee5\u7814\u7a76\u6027\u522b\u5bf9\u4e8e\u6c42\u804c\u7684\u5f71\u54cd\uff0c\u662f\u5426\u5b58\u5728\u6027\u522b\u6b67\u89c6\u7b49\u7b49\uff08\u5df2\u6709\u7814\u7a76\u4f7f\u7528\u8fc7\u8fd9\u79cd\u5b9e\u9a8c\u8bbe\u8ba1\uff09\u3002<\/section>\n<\/li>\n<\/ul>\n<\/li>\n<li>\n<section>\u4e00\u4e2a\u66f4\u4e3a\u4e25\u91cd\u7684\u95ee\u9898\u662f\uff0c\u5b9e\u9645\u5de5\u4f5c\u4e2d\uff0c\u6211\u4eec\u5f88\u96be\u5f97\u5230\u4e00\u4e2a\u5b8c\u6574\u7684 DAG\uff0c\u7528\u4e8e\u9610\u8ff0\u53d8\u91cf\u4e4b\u95f4\u7684\u56e0\u679c\u5173\u7cfb\u6216\u8005\u6570\u636e\u751f\u6210\u673a\u5236\uff0c\u4f7f\u5f97 DAG \u7684\u5e94\u7528\u53d7\u5230\u7684\u5de8\u5927\u7684\u963b\u788d\u3002\u4e0d\u8fc7\uff0c\u4ece\u89c2\u6d4b\u6570\u636e\u5b66\u4e60 DAG \u7684\u7ed3\u6784\uff0c\u786e\u5b9e\u662f\u4e00\u4e2a\u5f88\u6709\u8da3\u4e14\u91cd\u8981\u7684\u95ee\u9898\uff0c\u8fd9\u7559\u5f85\u4e0b\u56de\u5206\u89e3\u3002<\/section>\n<\/li>\n<\/ol>\n<section>\u5728\u7ed3\u675f\u65f6\uff0c\u7559\u4e9b\u4e00\u4e9b\u601d\u8003\u7684\u95ee\u9898\uff1a<\/section>\n<ul class=\"list-paddingleft-2\" data-tool=\"mdnice\u7f16\u8f91\u5668\">\n<li>\n<section>\u5728\u4f55\u79cd\u610f\u4e49\u4e0b\uff0c\u540e\u95e8\u51c6\u5219\u7684\u6761\u4ef6\uff0c\u7b49\u4ef7\u4e8e\u53ef\u5ffd\u7565\u6027\uff0c\u5373\u00a0\uff1f<\/section>\n<\/li>\n<li>\n<section>\u5728\u7b2c\u4e00\u8282\u7684 Yule-Simpson\u2019s Paradox \u4e2d\uff0c\u6211\u4eec\u6700\u7ec8\u9009\u62e9\u8c03\u6574\u7684\u4f30\u8ba1\u91cf\uff0c\u8fd8\u662f\u4e0d\u8c03\u6574\u7684\u4f30\u8ba1\u91cf\uff1f<\/section>\n<\/li>\n<\/ul>\n<\/section>\n<section>\n<section>\n<section>\n<section>\n<section><\/section>\n<section><\/section>\n<section>\n<section><\/section>\n<\/section>\n<\/section>\n<section><strong>6. \u56e0\u679c\u63a8\u65ad\u7b80\u4ecb\u4e4b\u516d\uff1a<\/strong><\/p>\n<p><strong>\u5de5\u5177\u53d8\u91cf\uff08instrumental variable\uff09\u00a0<\/strong><\/p>\n<\/section>\n<section>\n<section><\/section>\n<section><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<p>\u4e3a\u4e86\u4ecb\u7ecd\u5de5\u5177\u53d8\u91cf\uff0c\u6211\u4eec\u9996\u5148\u8981\u4ece\u7ebf\u6027\u6a21\u578b\u51fa\u53d1\u3002\u6beb\u65e0\u7591\u95ee\uff0c\u7ebf\u6027\u6a21\u578b\u662f\u7406\u8bba\u548c\u5e94\u7528\u7edf\u8ba1\uff08\u5305\u62ec\u8ba1\u91cf\u7ecf\u6d4e\u5b66\u548c\u6d41\u884c\u75c5\u5b66\u7b49\uff09\u6700\u91cd\u8981\u7684\u5de5\u5177\uff1b\u5bf9\u7ebf\u6027\u6a21\u578b\u7684\u6df1\u523b\u7406\u89e3\uff0c\u53ef\u4ee5\u8bf4\u5c31\u662f\u5bf9\u4e00\u5927\u534a\u7edf\u8ba1\u7406\u8bba\u7684\u7406\u89e3\u3002\u4e0b\u9762\u7684\u7b2c\u4e00\u90e8\u5206\u5148\u5bf9\u7ebf\u6027\u6a21\u578b\uff0c\u5c24\u5176\u662f\u7ebf\u6027\u6a21\u578b\u80cc\u540e\u7684\u5047\u8bbe\u505a\u4e00\u4e2a\u56de\u987e\u3002<\/p>\n<p><strong>\u4e00\u3001\u7ebf\u6027\u56de\u5f52\u548c\u6700\u5c0f\u4e8c\u4e58\u6cd5<\/strong><\/p>\n<section>\u7ebf\u6027\u6a21\u578b\u548c\u6700\u5c0f\u4e8c\u4e58\u7684\u7406\u8bba\u8d77\u6e90\u4e8e\u9ad8\u65af\u7684\u5929\u6587\u5b66\u7814\u7a76\uff0c\u201c\u56de\u5f52\u201d\uff08regression\uff09\u8fd9\u4e2a\u540d\u5b57\u5219\u662f Francis Galton \u5728\u7814\u7a76\u4f18\u751f\u5b66\u7684\u65f6\u5019\u63d0\u51fa\u6765\u7684\u3002\u4e3a\u4e86\u63cf\u8ff0\u7684\u65b9\u4fbf\uff0c\u6211\u4eec\u5047\u5b9a\u56de\u5f52\u7684\u81ea\u53d8\u91cf\u53ea\u6709\u4e00\u7ef4\uff0c\u6bd4\u5982\u4e2a\u4f53 ii \u662f\u5426\u63a5\u53d7\u67d0\u79cd\u5904\u7406\uff08\u5438\u70df\u4e0e\u5426\uff1b\u53c2\u52a0\u67d0\u4e2a\u5de5\u4f5c\uff1b\u7b49\u7b49\uff09\uff0c\u8bb0\u4e3a Di\u3002\u56de\u5f52\u7684\u56e0\u53d8\u91cf\u4e5f\u662f\u4e00\u7ef4\uff0c\u8868\u793a\u6211\u4eec\u5173\u5fc3\u7684\u7ed3\u679c\uff08\u662f\u5426\u6709\u80ba\u764c\uff1b\u662f\u5426\u627e\u5230\u5de5\u4f5c\u57f9\u8bad\u4e0e\u5426\uff1b\u7b49\u7b49\uff09\uff0c\u8bb0\u4e3aYi\u3002\u5047\u5b9a\u6211\u4eec\u7684\u7814\u7a76\u4e2d\u6709 n \u4e2a\u4e2a\u4f53\uff0c\u4e0b\u9762\u7684\u7ebf\u6027\u6a21\u578b\u7528\u4e8e\u63cf\u8ff0 D \u548c Y \u4e4b\u95f4\u7684 \u201c\u5173\u7cfb\u201d\uff1a<\/section>\n<p><span aria-hidden=\"true\">Yi=\u03b1+\u03b2Di+\u03b5i,i=1,\u22ef,n.(1)<\/span><\/p>\n<\/section>\n<section>\u4e00\u822c\u60c5\u5f62\u4e0b\uff0c\u6211\u4eec\u5047\u5b9a\u4e2a\u4f53\u95f4\u662f\u72ec\u7acb\u7684\u3002\u6a21\u578b\u867d\u7b80\u5355\uff0c\u6211\u4eec\u8fd8\u662f\u6709\u5fc5\u8981\u505a\u4e00\u4e9b\u89e3\u91ca\u3002\u9996\u5148\uff0c\u6211\u4eec\u8fd9\u91cc\u7684\u8ba8\u8bba\u90fd\u5047\u5b9a\u00a0<span tabindex=\"0\" role=\"presentation\">Di<\/span>\u00a0\u662f\u968f\u673a\u53d8\u91cf\uff0c\u5bf9\u5e94\u7edf\u8ba1\u5b66\u4e2d\u7684\u968f\u673a\u8bbe\u8ba1\u00a0\uff08random design\uff09\u7684\u60c5\u5f62\uff1b\u8fd9\u548c\u4f20\u7edf\u7edf\u8ba1\u5b66\u4e2d\u504f\u597d\u7684\u56fa\u5b9a\u8bbe\u8ba1\uff08fixed design\uff09\u6709\u70b9\u4e0d\u540c\u2014\u90a3\u91cc\u5047\u5b9a\u00a0<span tabindex=\"0\" role=\"presentation\">Di<\/span>\u603b\u662f\u56fa\u5b9a\u7684\u3002\uff08\u7edf\u8ba1\u5b66\u6e90\u4e8e\u5b9e\u9a8c\u8bbe\u8ba1\uff0c\u90a3\u91cc\u7684\u89e3\u91ca\u53d8\u91cf\u90fd\u662f\u53ef\u4ee5\u63a7\u5236\u7684\uff0c\u56e0\u6b64\u7edf\u8ba1\u5b66\u6559\u79d1\u4e66\u6709\u5047\u5b9a\u56fa\u5b9a\u8bbe\u8ba1\u7684\u4f20\u7edf\u3002\uff09\u5047\u5b9a\u00a0<span tabindex=\"0\" role=\"presentation\">Di<\/span>\u662f\u968f\u673a\u7684\uff0c\u65e2\u7b26\u5408\u5f88\u591a\u793e\u4f1a\u79d1\u5b66\u548c\u6d41\u884c\u75c5\u5b66\u7684\u80cc\u666f\uff0c\u53c8\u4f1a\u7b80\u5316\u540e\u9762\u7684\u8ba8\u8bba\u3002\u53e6\u5916\u4e00\u4e2a\u95ee\u9898\u662f\u00a0<span tabindex=\"0\" role=\"presentation\">\u03b5i<\/span>\uff0c\u5b83\u5230\u5e95\u662f\u4ec0\u4e48\u542b\u4e49\uff1fRubin \u66fe\u7ecf\u5632\u7b11\u8ba1\u91cf\u7ecf\u6d4e\u5b66\u5bb6\u7684\u00a0<span tabindex=\"0\" role=\"presentation\">\u03b5i<\/span>\u9053\uff1a\u4e3a\u4e86\u4f7f\u5f97\u7ebf\u6027\u6a21\u578b\u7684\u7b49\u5f0f\u6210\u7acb\uff0c\u8ba1\u91cf\u7ecf\u6d4e\u5b66\u5bb6\u5fc5\u987b\u52a0\u7684\u4e00\u9879\uff0c\u5c31\u53eb\u00a0<span tabindex=\"0\" role=\"presentation\">\u03b5i<\/span>\u3002\u6279\u8bc4\u7684\u5b58\u5728\u5e76\u4e0d\u5f71\u54cd\u8fd9\u4e2a\u7ebf\u6027\u6a21\u578b\u7684\u5e94\u7528\uff1b\u5173\u952e\u7684\u95ee\u9898\u5728\u4e8e\uff0c\u6211\u4eec\u5728\u8fd9\u4e2a\u00a0<span tabindex=\"0\" role=\"presentation\">\u03b5i<\/span>\u4e0a\u52a0\u4e86\u4ec0\u4e48\u5047\u5b9a\u5462\uff1f\u6700\u6839\u672c\u7684\u5047\u5b9a\u662f\uff1a<\/section>\n<section><img decoding=\"async\" class=\"rich_pages wxw-img img_loading\" src=\"data:image\/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVQImWNgYGBgAAAABQABh6FO1AAAAABJRU5ErkJggg==\" alt=\"\u56fe\u7247\" crossorigin=\"anonymous\" data-galleryid=\"\" data-ratio=\"0.12183908045977011\" data-s=\"300,640\" data-type=\"png\" data-w=\"435\" data-src=\"https:\/\/mmbiz.qpic.cn\/mmbiz_png\/wibWV1DB7tWIO90r3UsHjHlftibAW0QN6HkHLOYicyyguujXxeHKz47BxXNfrtystnGbuLyaANCEYpoibCEjCiaChNQ\/640?wx_fmt=png\" \/><\/section>\n<section><\/section>\n<section>\u4e0d\u540c\u7684\u6559\u79d1\u4e66\u7a0d\u6709\u4e0d\u540c\uff0c\u6bd4\u5982 Wooldridge \u7684\u4e66\u4e0a\u5047\u5b9aE(\u03b5i\u2223Di)=0\uff0c\u5f88\u663e\u7136\uff0c\u8fd9\u8574\u542b\u7740\u4e0a\u9762\u4e24\u4e2a\u5047\u5b9a\u3002\u96f6\u5747\u503c\u7684\u5047\u5b9a\u5e76\u4e0d\u5f3a\uff0c\u56e0\u4e3a\u00a0\u03b1\u03b1\u201c\u5438\u6536\u201d\u4e86\u00a0\u03b5i\u03b5i\u7684\u5747\u503c\uff1b\u5173\u952e\u5728\u7b2c\u4e8c\u4e2a\u534f\u65b9\u5dee\u4e3a\u96f6\u7684\u5047\u5b9a\u2014\u5b83\u901a\u5e38\u88ab\u79f0\u4e3a \u201c\u5916\u751f\u6027\u201d\uff08exogeneity\uff09\u5047\u5b9a\u3002\u5728\u8fd9\u4e2a\u5047\u5b9a\u4e0b\uff0c\u6211\u4eec\u5728 (1) \u7684\u4e24\u8fb9\u5173\u4e8e\u00a0Di\u00a0\u53d6\u534f\u65b9\u5dee\uff0c\u4fbf\u53ef\u4ee5\u5f97\u5230\uff1a<\/section>\n<p><span aria-hidden=\"true\">cov(Yi,Di)=\u03b2var(Di),<\/span><span role=\"presentation\"><br \/>\n<\/span><\/p>\n<p>&nbsp;<\/p>\n<p>\u56e0\u6b64\uff0c<span tabindex=\"0\" role=\"presentation\">\u03b2=cov(Yi,Di)\/var(Di)<\/span>\uff0c\u6211\u4eec\u7acb\u523b\u5f97\u5230\u4e86\u77e9\u4f30\u8ba1\uff1a<\/p>\n<p><img decoding=\"async\" class=\"rich_pages wxw-img img_loading\" src=\"data:image\/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVQImWNgYGBgAAAABQABh6FO1AAAAABJRU5ErkJggg==\" alt=\"\u56fe\u7247\" crossorigin=\"anonymous\" data-galleryid=\"\" data-ratio=\"0.24345549738219896\" data-s=\"300,640\" data-type=\"png\" data-w=\"382\" data-src=\"https:\/\/mmbiz.qpic.cn\/mmbiz_png\/wibWV1DB7tWIO90r3UsHjHlftibAW0QN6H4iaqYnpPWvbib9uEIU1RfOzj4IGF3PBcXtFQqEuHnBfB2jtflAx6f0rQ\/640?wx_fmt=png\" \/><\/p>\n<p>\u4e0a\u9762\u7684\u4f30\u8ba1\u5f0f\u4e5f\u662f\u901a\u5e38\u7684\u6700\u5c0f\u4e8c\u4e58\u89e3\uff0c\u8fd9\u91cc\u53ea\u662f\u6362\u4e86\u4e00\u4e2a\u63a8\u5bfc\u65b9\u5f0f\u3002\u5982\u679c\u5c06 (1) \u770b\u6210\u4e00\u4e2a\u6570\u636e\u751f\u6210\u7684\u673a\u5236\uff0c\u5728\u5047\u5b9a (2) \u4e0b\u6211\u4eec\u7684\u786e\u53ef\u4ee5\u4f30\u8ba1\u51fa\u56e0\u679c\u4f5c\u7528\u00a0\u03b2.<\/p>\n<section><strong>\u4e8c\u3001\u5185\u751f\u6027\u548c\u5de5\u5177\u53d8\u91cf<\/strong><\/section>\n<p>\u95ee\u9898\u7684\u5173\u952e\u662f\u5047\u5b9a (2) \u5f88\u591a\u65f6\u5019\u5e76\u4e0d\u6210\u7acb\uff08cov(Di,\u03b5i)\u22600\uff09\uff0c\u6bd4\u5982\uff0c\u5438\u70df\u7684\u4eba\u7fa4\u548c\u4e0d\u5438\u70df\u7684\u4eba\u7fa4\u672c\u8eab\u5f88\u4e0d\u76f8\u540c\uff0c\u53c2\u52a0\u5de5\u4f5c\u57f9\u8bad\u7684\u4eba\u53ef\u80fd\u6bd4\u4e0d\u53c2\u52a0\u5de5\u4f5c\u57f9\u8bad\u7684\u4eba\u6709\u66f4\u5f3a\u7684\u627e\u5de5\u4f5c\u52a8\u673a\uff0c\u7b49\u7b49\u3002\u56e0\u6b64\uff0c\u5305\u542b\u4e2a\u4f53 ii\u5176\u4ed6\u6240\u6709\u9690\u85cf\u4fe1\u606f\u7684\u53d8\u91cf\u00a0\u03b5i\u03b5i\u4e0d\u518d\u4e0e DiDi\u4e0d\u76f8\u5173\u4e86\u2014\u8fd9\u88ab\u79f0\u4e3a \u201c\u5185\u751f\u6027\u201d\uff08endogeneity\uff09\u3002\u8fd9\u4e2a\u65f6\u5019\uff0c\u6700\u5c0f\u4e8c\u4e58\u4f30\u8ba1\u6536\u655b\u5230\u00a0\u03b2+cov(D,\u03b5)\/var(D), \u56e0\u800c\u5728 cov(D,\u03b5)\u22600\u65f6\u4e0d\u518d\u662f\u03b2\u7684\u76f8\u5408\u4f30\u8ba1\u3002<\/p>\n<section>\u524d\u9762\u51e0\u6b21\u56e0\u679c\u63a8\u65ad\u7684\u4ecb\u7ecd\u4e2d\u63d0\u5230\uff0c\u5b8c\u5168\u7684\u968f\u673a\u5316\u5b9e\u9a8c\uff0c\u53ef\u4ee5\u7ed9\u6211\u4eec\u6709\u6548\u7684\u56e0\u679c\u63a8\u65ad\u3002\u4f46\u662f\u5f88\u591a\u95ee\u9898\u4e2d\uff0c\u5f3a\u5236\u6027\u7684\u968f\u673a\u5316\u5b9e\u9a8c\u662f\u4e0d\u73b0\u5b9e\u6216\u8005\u4e0d\u7b26\u5408\u4f26\u7406\u7684\u3002\u6bd4\u5982\uff0c\u6211\u4eec\u4e0d\u80fd\u5f3a\u5236\u67d0\u4e9b\u4eba\u5438\u70df\uff0c\u6216\u8005\u4e0d\u5438\u70df\u3002\u4f46\u662f\uff0c\u201c\u9f13\u52b1\u6027\u5b9e\u9a8c\u201d\u4f9d\u7136\u53ef\u884c\u3002\u6211\u4eec\u53ef\u4ee5\u968f\u673a\u5730\u7ed9\u5438\u70df\u7684\u4eba\u4ee5\u67d0\u79cd\u91d1\u94b1\u7684\u5956\u52b1\uff0c\u5982\u679c\u4ed6\u4eec\u653e\u5f03\u5438\u70df\uff0c\u5219\u83b7\u5f97\u67d0\u79cd\u7ecf\u6d4e\u4e0a\u7684\u4f18\u60e0\u3002\u5c06\u8fd9\u4e2a \u201c\u9f13\u52b1\u6027\u201d \u7684\u53d8\u91cf\u8bb0\u4e3a Zi\uff0c\u5b83\u5b9a\u4e49\u4e3a\u662f\u5426\u88ab\u9f13\u52b1\u7684\u793a\u6027\u53d8\u91cf\uff0c\u53d6\u503c 0-1\u3002\u7531\u4e8e\u6211\u4eec\u7684\u9f13\u52b1\u662f\u5b8c\u5168\u968f\u673a\u7684\uff0c\u6709\u7406\u7531\u5047\u5b9a cov(Zi,\u03b5i)=0\u3002<\/section>\n<p>\u4ee5\u4e0a\u7684\u5404\u4e2a\u5047\u5b9a\uff0c\u53ef\u4ee5\u7528\u4e0b\u9762\u7684\u4e00\u4e2a\u56fe\u6765\u5f62\u8c61\u7684\u63cf\u8ff0\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-651\" src=\"https:\/\/aif.amtbbs.org\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-34.png\" width=\"413\" height=\"257\" alt=\"\u56fe\u7247\" srcset=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-34.png 413w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-34-300x187.png 300w\" sizes=\"auto, (max-width: 413px) 100vw, 413px\" \/><\/p>\n<p>\u5982\u56fe\u6240\u793a\uff0c\u7531\u4e8e<span style=\"margin: 0px; padding: 1px 0px; outline: 0px; max-width: none; box-sizing: border-box !important; overflow-wrap: normal; display: inline-block; line-height: 0; word-spacing: normal; float: none; direction: ltr; max-height: none; min-width: 0px; min-height: 0px; border: 0px initial initial;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mi&gt;D&lt;\/mi&gt;&lt;\/math&gt;\"><span aria-hidden=\"true\">D<\/span><span role=\"presentation\">D<\/span><\/span>\u548c<span style=\"margin: 0px; padding: 1px 0px; outline: 0px; max-width: none; box-sizing: border-box !important; overflow-wrap: normal; display: inline-block; line-height: 0; word-spacing: normal; float: none; direction: ltr; max-height: none; min-width: 0px; min-height: 0px; border: 0px initial initial;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mi&gt;Y&lt;\/mi&gt;&lt;\/math&gt;\"><span aria-hidden=\"true\">Y<\/span><span role=\"presentation\">Y<\/span><\/span>\u4e4b\u95f4\u5b58\u5728\u4e00\u4e2a\u6df7\u6742\u56e0\u7d20<span style=\"margin: 0px; padding: 1px 0px; outline: 0px; max-width: none; box-sizing: border-box !important; overflow-wrap: normal; display: inline-block; line-height: 0; word-spacing: normal; float: none; direction: ltr; max-height: none; min-width: 0px; min-height: 0px; border: 0px initial initial;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mi&gt;U&lt;\/mi&gt;&lt;\/math&gt;\"><span aria-hidden=\"true\">U<\/span><span role=\"presentation\">U<\/span><\/span>\uff0c\u4e24\u8005\u4e4b\u95f4\u7684\u56e0\u679c\u4f5c\u7528\u662f\u4e0d\u53ef\u4ee5\u7528\u7ebf\u6027\u56de\u5f52\u76f8\u5408\u4f30\u8ba1\u7684\u3002\u5de5\u5177\u53d8\u91cf<span style=\"margin: 0px; padding: 1px 0px; outline: 0px; max-width: none; box-sizing: border-box !important; overflow-wrap: normal; display: inline-block; line-height: 0; word-spacing: normal; float: none; direction: ltr; max-height: none; min-width: 0px; min-height: 0px; border: 0px initial initial;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mi&gt;Z&lt;\/mi&gt;&lt;\/math&gt;\"><span aria-hidden=\"true\">Z<\/span><span role=\"presentation\">Z<\/span><\/span>\u7684\u5b58\u5728\uff0c\u4f7f\u5f97<span style=\"margin: 0px; padding: 1px 0px; outline: 0px; max-width: none; box-sizing: border-box !important; overflow-wrap: normal; display: inline-block; line-height: 0; word-spacing: normal; float: none; direction: ltr; max-height: none; min-width: 0px; min-height: 0px; border: 0px initial initial;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mi&gt;D&lt;\/mi&gt;&lt;\/math&gt;\"><span aria-hidden=\"true\">D<\/span><span role=\"presentation\">D<\/span><\/span>\u5230<span style=\"margin: 0px; padding: 1px 0px; outline: 0px; max-width: none; box-sizing: border-box !important; overflow-wrap: normal; display: inline-block; line-height: 0; word-spacing: normal; float: none; direction: ltr; max-height: none; min-width: 0px; min-height: 0px; border: 0px initial initial;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mi&gt;Y&lt;\/mi&gt;&lt;\/math&gt;\"><span aria-hidden=\"true\">Y<\/span><span role=\"presentation\">Y<\/span><\/span>\u7684\u56e0\u679c\u4f5c\u7528\u7684\u8bc6\u522b\u6210\u4e3a\u4e86\u53ef\u80fd\u3002\u8fd9\u91cc\u7684\u5de5\u5177\u53d8\u91cf<span style=\"margin: 0px; padding: 1px 0px; outline: 0px; max-width: none; box-sizing: border-box !important; overflow-wrap: normal; display: inline-block; line-height: 0; word-spacing: normal; float: none; direction: ltr; max-height: none; min-width: 0px; min-height: 0px; border: 0px initial initial;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mi&gt;Z&lt;\/mi&gt;&lt;\/math&gt;\"><span aria-hidden=\"true\">Z<\/span><span role=\"presentation\">Z<\/span><\/span>\u6ee1\u8db3\u5982\u4e0b\u7684\u6761\u4ef6:\u00a0\u00a0<span style=\"margin: 0px; padding: 1px 0px; outline: 0px; max-width: none; box-sizing: border-box !important; overflow-wrap: normal; display: inline-block; line-height: 0; text-align: left; font-size: 19.04px; float: none; direction: ltr; max-height: none; min-width: 0px; min-height: 0px; font-family: Optima, 'Lucida Sans', Calibri, Candara, Arial, source-han-serif-sc, 'Source Han Serif SC', 'Source Han Serif CN', 'Source Han Serif TC', 'Source Han Serif TW', 'Source Han Serif', 'Songti SC', 'Microsoft YaHei', sans-serif; border: 0px initial initial;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mi&gt;Z&lt;\/mi&gt;&lt;mo&gt;&amp;#x22A5;&lt;\/mo&gt;&lt;mi&gt;U&lt;\/mi&gt;&lt;mo&gt;,&lt;\/mo&gt;&lt;mi&gt;Z&lt;\/mi&gt;&lt;mo&gt;&amp;#x22A5;&amp;#x338;&lt;\/mo&gt;&lt;mi&gt;D&lt;\/mi&gt;&lt;\/math&gt;\"><span aria-hidden=\"true\">Z\u22a5U,Z\u22a5D<\/span><span role=\"presentation\">Z\u22a5U,Z\u22a5\u0338D<\/span><\/span>\uff0c\u5e76\u4e14\u00a0<span style=\"margin: 0px; padding: 1px 0px; outline: 0px; max-width: none; box-sizing: border-box !important; overflow-wrap: normal; display: inline-block; line-height: 0; text-align: left; font-size: 19.04px; float: none; direction: ltr; max-height: none; min-width: 0px; min-height: 0px; font-family: Optima, 'Lucida Sans', Calibri, Candara, Arial, source-han-serif-sc, 'Source Han Serif SC', 'Source Han Serif CN', 'Source Han Serif TC', 'Source Han Serif TW', 'Source Han Serif', 'Songti SC', 'Microsoft YaHei', sans-serif; border: 0px initial initial;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mi&gt;Z&lt;\/mi&gt;&lt;mo&gt;&amp;#x22A5;&lt;\/mo&gt;&lt;mi&gt;Y&lt;\/mi&gt;&lt;mrow&gt;&lt;mo stretchy=&quot;false&quot;&gt;|&lt;\/mo&gt;&lt;\/mrow&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;\/mo&gt;&lt;mi&gt;D&lt;\/mi&gt;&lt;mo&gt;,&lt;\/mo&gt;&lt;mi&gt;U&lt;\/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;\/mo&gt;&lt;\/math&gt;\"><span aria-hidden=\"true\">Z\u22a5Y|(D,U)<\/span><span role=\"presentation\">Z\u22a5Y|(D,U)<\/span><\/span>\u3002\u7b2c\u4e09\u4e2a\u6761\u4ef6\uff0c\u53ef\u4ee5\u7406\u89e3\u6210\u4e3a \u201c\u65e0\u00a0Z\u5230\u00a0Y\u7684\u76f4\u63a5\u4f5c\u7528\u201d\u3002<\/p>\n<p>\u6b64\u65f6\uff0c\u6211\u4eec\u5728\u7ebf\u6027\u6a21\u578b (1) \u4e24\u8fb9\u5173\u4e8e\u00a0<span style=\"margin: 0px; padding: 1px 0px; outline: 0px; max-width: none; box-sizing: border-box !important; overflow-wrap: normal; display: inline-block; line-height: 0; text-align: left; font-size: 19.04px; float: none; direction: ltr; max-height: none; min-width: 0px; min-height: 0px; font-family: Optima, 'Lucida Sans', Calibri, Candara, Arial, source-han-serif-sc, 'Source Han Serif SC', 'Source Han Serif CN', 'Source Han Serif TC', 'Source Han Serif TW', 'Source Han Serif', 'Songti SC', 'Microsoft YaHei', sans-serif; border: 0px initial initial;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;msub&gt;&lt;mi&gt;Z&lt;\/mi&gt;&lt;mi&gt;i&lt;\/mi&gt;&lt;\/msub&gt;&lt;\/math&gt;\"><span aria-hidden=\"true\">Zi<\/span><span role=\"presentation\">Zi<\/span><\/span>\u00a0<span style=\"margin: 0px; padding: 1px 0px; outline: 0px; max-width: none; box-sizing: border-box !important; overflow-wrap: normal; display: inline-block; line-height: 0; text-align: left; font-size: 19.04px; float: none; direction: ltr; max-height: none; min-width: 0px; min-height: 0px; font-family: Optima, 'Lucida Sans', Calibri, Candara, Arial, source-han-serif-sc, 'Source Han Serif SC', 'Source Han Serif CN', 'Source Han Serif TC', 'Source Han Serif TW', 'Source Han Serif', 'Songti SC', 'Microsoft YaHei', sans-serif; border: 0px initial initial;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;msub&gt;&lt;mi&gt;Z&lt;\/mi&gt;&lt;mi&gt;i&lt;\/mi&gt;&lt;\/msub&gt;&lt;\/math&gt;\"><span role=\"presentation\">Zi<\/span><\/span>\u00a0\u53d6\u534f\u65b9\u5dee\uff0c\u5f97\u5230<\/p>\n<p>cov(Zi,Yi)=\u03b2cov(Zi,Di)<\/p>\n<p>\u56e0\u6b64\uff0c<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-652\" src=\"https:\/\/aif.amtbbs.org\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-35.png\" width=\"125\" height=\"55\" alt=\"\u56fe\u7247\" \/><\/p>\n<p><span style=\"margin: 0px; padding: 1px 0px; outline: 0px; max-width: none; box-sizing: border-box !important; overflow-wrap: normal; display: inline-block; line-height: 0; font-size: 19.04px; float: none; direction: ltr; max-height: none; min-width: 0px; min-height: 0px; font-family: Optima, 'Lucida Sans', Calibri, Candara, Arial, source-han-serif-sc, 'Source Han Serif SC', 'Source Han Serif CN', 'Source Han Serif TC', 'Source Han Serif TW', 'Source Han Serif', 'Songti SC', 'Microsoft YaHei', sans-serif; border: 0px initial initial;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mi&gt;&amp;#x03B2;&lt;\/mi&gt;&lt;mo&gt;=&lt;\/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mtext&gt;cov&lt;\/mtext&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;\/mo&gt;&lt;msub&gt;&lt;mi&gt;Z&lt;\/mi&gt;&lt;mi&gt;i&lt;\/mi&gt;&lt;\/msub&gt;&lt;mo&gt;,&lt;\/mo&gt;&lt;msub&gt;&lt;mi&gt;Y&lt;\/mi&gt;&lt;mi&gt;i&lt;\/mi&gt;&lt;\/msub&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;\/mo&gt;&lt;\/mrow&gt;&lt;mrow&gt;&lt;mtext&gt;cov&lt;\/mtext&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;\/mo&gt;&lt;msub&gt;&lt;mi&gt;Z&lt;\/mi&gt;&lt;mi&gt;i&lt;\/mi&gt;&lt;\/msub&gt;&lt;mo&gt;,&lt;\/mo&gt;&lt;msub&gt;&lt;mi&gt;D&lt;\/mi&gt;&lt;mi&gt;i&lt;\/mi&gt;&lt;\/msub&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;\/mo&gt;&lt;\/mrow&gt;&lt;\/mfrac&gt;&lt;\/math&gt;\"><span role=\"presentation\">\u03b2=cov(Zi,Yi)cov(Zi,Di)<\/span><\/span>\uff0c\u6211\u4eec\u7acb\u523b\u5f97\u5230\u5982\u4e0b\u7684\u77e9\u4f30\u8ba1\uff1a<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-653\" src=\"https:\/\/aif.amtbbs.org\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-36.png\" width=\"426\" height=\"84\" alt=\"\u56fe\u7247\" srcset=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-36.png 426w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-36-300x59.png 300w\" sizes=\"auto, (max-width: 426px) 100vw, 426px\" \/><\/p>\n<section><\/section>\n<section>\u6839\u636e\u5927\u6570\u5b9a\u5f8b\uff0c\u8fd9\u4e2a \u201c\u5de5\u5177\u53d8\u91cf\u4f30\u8ba1\u201d \u662f\u00a0<span tabindex=\"0\" role=\"presentation\">\u03b2<\/span>\u7684\u76f8\u5408\u4f30\u8ba1\u91cf\u3002\u4e0a\u9762\u7684\u5f0f\u5b50\u5bf9\u4e00\u822c\u7684\u00a0<span tabindex=\"0\" role=\"presentation\">Zi<\/span>\u90fd\u662f\u6210\u7acb\u7684\uff1b\u5f53\u00a0<span tabindex=\"0\" role=\"presentation\">Zi<\/span>\u662f\u00a00-1 \u53d8\u91cf\u65f6\uff0c\u4e0a\u9762\u7684\u5f0f\u5b50\u53ef\u5316\u7b80\u6210\uff1a<\/section>\n<p><img decoding=\"async\" class=\"rich_pages wxw-img img_loading\" src=\"data:image\/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVQImWNgYGBgAAAABQABh6FO1AAAAABJRU5ErkJggg==\" alt=\"\u56fe\u7247\" crossorigin=\"anonymous\" data-galleryid=\"\" data-ratio=\"0.2755102040816326\" data-s=\"300,640\" data-type=\"png\" data-w=\"294\" data-src=\"https:\/\/mmbiz.qpic.cn\/mmbiz_png\/wibWV1DB7tWIO90r3UsHjHlftibAW0QN6HkY3JXl9LfibaFKDclURwuT9BvaC4mn5R4g4aJ7BiaoFaiaJH5nLW0J2Ug\/640?wx_fmt=png\" \/><\/p>\n<section>\u5176\u4e2d<span style=\"margin: 0px; padding: 1px 0px; outline: 0px; max-width: none; box-sizing: border-box !important; overflow-wrap: normal; display: inline-block; line-height: 0; font-size: 19.04px; float: none; direction: ltr; max-height: none; min-width: 0px; min-height: 0px; border: 0px initial initial;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mover&gt;&lt;mi&gt;Y&lt;\/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x00AF;&lt;\/mo&gt;&lt;\/mover&gt;&lt;\/mrow&gt;&lt;mn&gt;1&lt;\/mn&gt;&lt;\/msub&gt;&lt;\/math&gt;\"><span aria-hidden=\"true\">\u00afY1<\/span><span role=\"presentation\">Y\u00af1<\/span><\/span>\u8868\u793a\u00a0Zi=1\u7ec4\u7684\u5e73\u5747\u7ed3\u679c\uff0c<span style=\"margin: 0px; padding: 1px 0px; outline: 0px; max-width: none; box-sizing: border-box !important; overflow-wrap: normal; display: inline-block; line-height: 0; font-size: 19.04px; float: none; direction: ltr; max-height: none; min-width: 0px; min-height: 0px; border: 0px initial initial;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mover&gt;&lt;mi&gt;Y&lt;\/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x00AF;&lt;\/mo&gt;&lt;\/mover&gt;&lt;\/mrow&gt;&lt;mn&gt;1&lt;\/mn&gt;&lt;\/msub&gt;&lt;\/math&gt;\"><span aria-hidden=\"true\">\u00afY1<\/span><span role=\"presentation\">Y\u00af1<\/span><\/span>\u8868\u793a Zi=0\u7ec4\u7684\u5e73\u5747\u7ed3\u679c\uff0c\u5173\u4e8e DD\u7684\u5b9a\u4e49\u7c7b\u4f3c\u3002\u4e0a\u9762\u7684\u4f30\u8ba1\u91cf\uff0c\u5f88\u591a\u65f6\u5019\u88ab\u79f0\u4e3a Wald \u4f30\u8ba1\u91cf\uff08\u5b83\u7684\u76f4\u89c2\u542b\u4e49\u662f\u4ec0\u4e48\u5462\uff1f\uff09\u00a0\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c(3) \u8981\u6c42 cov(Zi,Di)\u22600\uff0c\u5373 \u201c\u9f13\u52b1\u201d \u5bf9\u4e8e\u6539\u53d8\u4eba\u7684\u5438\u70df\u884c\u4e3a\u662f\u6709\u6548\u7684\uff1b\u5426\u5219\u4e0a\u9762\u7684\u5de5\u5177\u53d8\u91cf\u4f30\u8ba1\u91cf\u5728\u5927\u6837\u672c\u4e0b\u8d8b\u4e8e\u65e0\u7a77\u5927\u3002<\/section>\n<p><strong>\u4e09\u3001\u6f5c\u5728\u7ed3\u679c\u89c6\u89d2\u4e0b\u7684\u56e0\u679c\u4f5c\u7528<\/strong><\/p>\n<p>\u5de5\u5177\u53d8\u91cf\u4f30\u8ba1\u91cf\u5728\u6587\u732e\u4e2d\u5b58\u5728\u5df2\u6709\u5f88\u591a\u5e74\u4e86\uff0c\u4e00\u76f4\u5230\u4e86 Angrist, Imbens and Rubin\u00a0(1996)\u00a0\u5e74\u7684\u6587\u7ae0\u51fa\u73b0\uff0c\u624d\u5c06\u5b83\u548c\u6f5c\u5728\u7ed3\u679c\u89c6\u89d2\u4e0b\u7684\u56e0\u679c\u63a8\u65ad\u8054\u7cfb\u8d77\u6765\u3002\u5173\u4e8e Neyman \u5f15\u8fdb\u7684\u6f5c\u5728\u7ed3\u679c\uff0c\u9700\u8981\u56de\u987e\u8fd9\u4e00\u7cfb\u5217\u7684\u7b2c\u4e8c\u7bc7\u6587\u7ae0\u3002<\/p>\n<p>\u4e00\u822c\u5730\uff0c\u00a0<span tabindex=\"0\" role=\"presentation\">Z<\/span>\u00a0\u8868\u793a\u4e00\u4e2a 0-1 \u7684\u53d8\u91cf\uff0c\u8868\u793a\u968f\u673a\u5316\u7684\u53d8\u91cf\uff081 \u8868\u793a\u968f\u673a\u5316\u5206\u5230\u975e\u9f13\u52b1\u7ec4\uff1b0 \u8868\u793a\u968f\u673a\u5316\u5206\u5230\u9f13\u52b1\u7ec4\uff09\uff1b<span tabindex=\"0\" role=\"presentation\">D<\/span>\u00a0\u8868\u793a\u6700\u7ec8\u63a5\u53d7\u5904\u7406\u4e0e\u5426\uff081 \u8868\u793a\u63a5\u53d7\u5904\u7406\uff1b0 \u8868\u793a\u63a5\u53d7\u5bf9\u7167\uff09\uff1b<span tabindex=\"0\" role=\"presentation\">Y<\/span>\u00a0\u662f\u7ed3\u679c\u53d8\u91cf\u3002\u4e3a\u4e86\u5b9a\u4e49\u56e0\u679c\u4f5c\u7528\uff0c\u6211\u4eec\u5f15\u8fdb\u5982\u4e0b\u7684\u6f5c\u5728\u7ed3\u679c\uff1a<span tabindex=\"0\" role=\"presentation\">(Yi(1),Yi(0))<\/span>\u00a0\u8868\u793a\u4e2a\u4f53\u00a0<span tabindex=\"0\" role=\"presentation\">i<\/span>\u00a0\u63a5\u53d7\u5904\u7406\u548c\u5bf9\u7167\u4e0b\u00a0<span tabindex=\"0\" role=\"presentation\">Y<\/span>\u00a0\u7684\u6f5c\u5728\u7ed3\u679c\uff1b<span tabindex=\"0\" role=\"presentation\">(Di(1),Di(0))<\/span>\u00a0\u8868\u793a\u4e2a\u4f53\u00a0<span tabindex=\"0\" role=\"presentation\">i\u00a0<\/span>\u975e\u9f13\u52b1\u7ec4\u548c\u9f13\u52b1\u7ec4\u4e0b\u00a0<span tabindex=\"0\" role=\"presentation\">D<\/span>\u00a0\u7684\u6f5c\u5728\u7ed3\u679c\u3002\u7531\u4e8e\u968f\u673a\u5316\uff0c\u4e0b\u9762\u7684\u5047\u5b9a\u81ea\u7136\u7684\u6210\u7acb\uff1a<\/p>\n<section>\uff08\u968f\u673a\u5316\uff09Zi\u22a5{Di(1),Di(0),Yi(1),Yi(0)}.<\/section>\n<section>\u6839\u636e\u9f13\u52b1\u6027\u5b9e\u9a8c\u7684\u673a\u5236\uff0c\u4e2a\u4f53\u5728\u53d7\u5230\u9f13\u52b1\u7684\u65f6\u5019\uff0c\u66f4\u52a0\u4e0d\u53ef\u80fd\u5438\u70df\uff0c\u56e0\u4e3a\u4e0b\u9762\u7684\u5355\u8c03\u6027\u4e5f\u662f\u5f88\u5408\u7406\u7684\uff1a<\/section>\n<section>\uff08\u5355\u8c03\u6027\uff09Di(1)\u2264Di(0).<\/section>\n<section>\u7531\u4e8e\u4e2a\u4f53\u7684\u7ed3\u679c\u00a0YY\u00a0\u76f4\u63a5\u53d7\u5230\u6240\u53d7\u7684\u5904\u7406\u00a0DD\u00a0\u7684\u5f71\u54cd\uff0c\u800c\u4e0d\u4f1a\u53d7\u5230\u662f\u5426\u53d7\u9f13\u52b1\u00a0ZZ\u00a0\u7684\u5f71\u54cd\uff0c\u4e0b\u9762\u7684\u6392\u9664\u7ea6\u675f\uff08exclusion restriction\uff09\u7684\u5047\u5b9a\uff0c\u5f88\u591a\u65f6\u5019\u4e5f\u662f\u5408\u7406\u7684\uff1a<\/section>\n<section>\uff08\u6392\u9664\u7ea6\u675f\uff09Di(1)=Di(0)\u00a0\u8574\u542b\u7740\u00a0Yi(1)=Yi(0).<\/section>\n<section>\u4e0a\u9762\u7684\u5047\u5b9a\u8868\u660e\uff0c\u5f53\u968f\u673a\u5316\u7684 \u201c\u9f13\u52b1\u201d<span style=\"margin: 0px; padding: 1px 0px; outline: 0px; max-width: none; box-sizing: border-box !important; overflow-wrap: normal; display: inline-block; line-height: 0; word-spacing: normal; float: none; direction: ltr; max-height: none; min-width: 0px; min-height: 0px; border: 0px initial initial;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mi&gt;Z&lt;\/mi&gt;&lt;\/math&gt;\"><span aria-hidden=\"true\">Z<\/span><span role=\"presentation\">Z<\/span><\/span>\u00a0\u4e0d\u4f1a\u5f71\u54cd\u662f\u5426\u63a5\u53d7\u5904\u7406\u00a0<span style=\"margin: 0px; padding: 1px 0px; outline: 0px; max-width: none; box-sizing: border-box !important; overflow-wrap: normal; display: inline-block; line-height: 0; word-spacing: normal; float: none; direction: ltr; max-height: none; min-width: 0px; min-height: 0px; border: 0px initial initial;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mi&gt;D&lt;\/mi&gt;&lt;\/math&gt;\"><span aria-hidden=\"true\">D<\/span><span role=\"presentation\">D<\/span><\/span>\u65f6\uff0c\u968f\u673a\u5316\u7684 \u201c\u9f13\u52b1\u201d\u00a0<span style=\"margin: 0px; padding: 1px 0px; outline: 0px; max-width: none; box-sizing: border-box !important; overflow-wrap: normal; display: inline-block; line-height: 0; word-spacing: normal; float: none; direction: ltr; max-height: none; min-width: 0px; min-height: 0px; border: 0px initial initial;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mi&gt;Z&lt;\/mi&gt;&lt;\/math&gt;\"><span aria-hidden=\"true\">Z<\/span><span role=\"presentation\">Z<\/span><\/span>\u00a0\u4e5f\u4e0d\u4f1a\u5f71\u54cd\u7ed3\u679c\u53d8\u91cf\u00a0<span style=\"margin: 0px; padding: 1px 0px; outline: 0px; max-width: none; box-sizing: border-box !important; overflow-wrap: normal; display: inline-block; line-height: 0; word-spacing: normal; float: none; direction: ltr; max-height: none; min-width: 0px; min-height: 0px; border: 0px initial initial;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mi&gt;Y&lt;\/mi&gt;&lt;\/math&gt;\"><span aria-hidden=\"true\">Y<\/span><span role=\"presentation\">Y<\/span><\/span>\u3002\u4e5f\u53ef\u4ee5\u7406\u89e3\u6210\uff0c\u968f\u673a\u5316\u7684 \u201c\u9f13\u52b1\u201d\u00a0<span style=\"margin: 0px; padding: 1px 0px; outline: 0px; max-width: none; box-sizing: border-box !important; overflow-wrap: normal; display: inline-block; line-height: 0; word-spacing: normal; float: none; direction: ltr; max-height: none; min-width: 0px; min-height: 0px; border: 0px initial initial;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mi&gt;Z&lt;\/mi&gt;&lt;\/math&gt;\"><span aria-hidden=\"true\">Z<\/span><span role=\"presentation\">Z<\/span><\/span>\u00a0\u4ec5\u4ec5\u901a\u8fc7\u5f71\u54cd\u662f\u5426\u63a5\u53d7\u5904\u7406\u00a0<span style=\"margin: 0px; padding: 1px 0px; outline: 0px; max-width: none; box-sizing: border-box !important; overflow-wrap: normal; display: inline-block; line-height: 0; word-spacing: normal; float: none; direction: ltr; max-height: none; min-width: 0px; min-height: 0px; border: 0px initial initial;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mi&gt;D&lt;\/mi&gt;&lt;\/math&gt;\"><span aria-hidden=\"true\">D<\/span><span role=\"presentation\">D<\/span><\/span>\u00a0\u6765\u5f71\u54cd\u7ed3\u679c\u00a0<span style=\"margin: 0px; padding: 1px 0px; outline: 0px; max-width: none; box-sizing: border-box !important; overflow-wrap: normal; display: inline-block; line-height: 0; word-spacing: normal; float: none; direction: ltr; max-height: none; min-width: 0px; min-height: 0px; border: 0px initial initial;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mi&gt;Y&lt;\/mi&gt;&lt;\/math&gt;\"><span aria-hidden=\"true\">Y<\/span><span role=\"presentation\">Y<\/span><\/span>\uff0c\u6216\u8005\u8bf4\uff0c\u968f\u673a\u5316 \u201c\u9f13\u52b1\u201d\u00a0<span style=\"margin: 0px; padding: 1px 0px; outline: 0px; max-width: none; box-sizing: border-box !important; overflow-wrap: normal; display: inline-block; line-height: 0; word-spacing: normal; float: none; direction: ltr; max-height: none; min-width: 0px; min-height: 0px; border: 0px initial initial;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mi&gt;Z&lt;\/mi&gt;&lt;\/math&gt;\"><span aria-hidden=\"true\">Z<\/span><span role=\"presentation\">Z<\/span><\/span>\u00a0\u672c\u8eab\u5bf9\u4e0e\u7ed3\u679c\u53d8\u91cf\u00a0<span style=\"margin: 0px; padding: 1px 0px; outline: 0px; max-width: none; box-sizing: border-box !important; overflow-wrap: normal; display: inline-block; line-height: 0; word-spacing: normal; float: none; direction: ltr; max-height: none; min-width: 0px; min-height: 0px; border: 0px initial initial;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mi&gt;Y&lt;\/mi&gt;&lt;\/math&gt;\"><span aria-hidden=\"true\">Y<\/span><span role=\"presentation\">Y<\/span><\/span>\u6ca1\u6709\u201c\u76f4\u63a5\u4f5c\u7528\u201d\u3002<\/section>\n<section><\/section>\n<section>\u4ee5\u4e0a\u4e09\u4e2a\u5047\u5b9a\u4e0b\uff0c\u6211\u4eec\u5f97\u5230\uff1a<\/section>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-654\" src=\"https:\/\/aif.amtbbs.org\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-37.png\" width=\"731\" height=\"196\" alt=\"\u56fe\u7247\" srcset=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-37.png 731w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-37-300x80.png 300w\" sizes=\"auto, (max-width: 731px) 100vw, 731px\" \/><\/p>\n<section><\/section>\n<section>\u5355\u8c03\u4f7f\u5f97\u00a0<span tabindex=\"0\" role=\"presentation\">D<\/span>\u00a0\u7684\u6f5c\u5728\u7ed3\u679c\u7684\u7ec4\u5408\u53ea\u6709\u4e09\u79cd\uff1b\u6392\u9664\u7ea6\u675f\u5047\u5b9a\u4f7f\u5f97\u4e0a\u9762\u5206\u89e3\u7684\u540e\u4e24\u4e2a\u5f0f\u5b50\u4e3a<span tabindex=\"0\" role=\"presentation\">0<\/span>\u3002\u7531\u4e8e\u5bf9\u4e8e<span tabindex=\"0\" role=\"presentation\">(Di(1)=0,Di(0)=0)<\/span>\u00a0\u548c<span tabindex=\"0\" role=\"presentation\">(Di(1)=1,Di(0)=1)<\/span>\u4e24\u7c7b\u4eba\uff0c\u968f\u673a\u5316\u7684 \u201c\u9f13\u52b1\u201d \u5bf9\u4e8e\u00a0<span tabindex=\"0\" role=\"presentation\">D<\/span>\u7684\u4f5c\u7528\u4e3a\u00a0<span tabindex=\"0\" role=\"presentation\">0<\/span>\uff0c<span tabindex=\"0\" role=\"presentation\">(Di(1)=1,Di(0)=0)<\/span>\u4e00\u7c7b\u4eba\u7684\u6bd4\u4f8b\u5c31\u662f<span tabindex=\"0\" role=\"presentation\">Z<\/span>\u5bf9<span tabindex=\"0\" role=\"presentation\">D<\/span>\u5e73\u5747\u56e0\u679c\u4f5c\u7528\uff1a<span tabindex=\"0\" role=\"presentation\">ACE(Z\u2192D)=P{Di(1)=1,Di(0)=0}<\/span>. \u56e0\u6b64\uff0c<\/section>\n<section><\/section>\n<section><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-655\" src=\"https:\/\/aif.amtbbs.org\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-38.png\" width=\"771\" height=\"91\" alt=\"\u56fe\u7247\" srcset=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-38.png 771w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-38-300x35.png 300w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-38-768x91.png 768w\" sizes=\"auto, (max-width: 771px) 100vw, 771px\" \/><\/section>\n<section><\/section>\n<section>\u4e0a\u9762\u7684\u5f0f\u5b50\u88ab\u5b9a\u4e49\u4e3a\u00a0<span tabindex=\"0\" role=\"presentation\">CACE<\/span>\u00a0\u662f\u6709\u7406\u7531\u7684\u3002\u5b83\u8868\u793a\u7684\u662f\u5b50\u603b\u4f53\u00a0<span tabindex=\"0\" role=\"presentation\">(Di(1)=1,Di(0)=0)<\/span>\u00a0\u4e2d\uff0c\u968f\u673a\u5316\u5bf9\u4e8e\u7ed3\u679c\u7684\u56e0\u679c\u4f5c\u7528\uff1b\u7531\u4e8e\u8fd9\u7c7b\u4eba\u4e2d\u968f\u673a\u5316\u548c\u63a5\u53d7\u7684\u5904\u7406\u662f\u76f8\u540c\u7684\uff0c\u5b83\u4e5f\u8868\u793a\u5904\u7406\u5bf9\u7ed3\u679c\u7684\u56e0\u679c\u4f5c\u7528\u3002\u8fd9\u7c7b\u4eba\u63a5\u53d7\u5904\u7406\u4e0e\u5426\u5b8c\u5168\u7531\u4e8e\u662f\u5426\u63a5\u53d7\u9f13\u52b1\u800c\u5b9a\uff0c\u4ed6\u4eec\u88ab\u6210\u4e3a \u201c\u4f9d\u4ece\u8005\u201d\uff08complier\uff09\uff0c\u56e0\u4e3a\u8fd9\u7c7b\u4eba\u7fa4\u4e2d\u7684\u5e73\u5747\u56e0\u679c\u4f5c\u7528\u53c8\u88ab\u6210\u4e3a \u201c\u4f9d\u4ece\u8005\u5e73\u5747\u56e0\u679c\u4f5c\u7528\u201d\uff08CACE\uff1acomplier average causal effect\uff09; \u8ba1\u91cf\u7ecf\u6d4e\u5b66\u5bb6\u79f0\u5b83\u4e3a \u201c\u5c40\u90e8\u5904\u7406\u4f5c\u7528\u201d\uff08LATE\uff1alocal average treatment effect\uff09<\/section>\n<section><\/section>\n<section>\u7531\u4e8e<span style=\"margin: 0px; padding: 1px 0px; outline: 0px; max-width: none; box-sizing: border-box !important; overflow-wrap: normal; display: inline-block; line-height: 0; word-spacing: normal; float: none; direction: ltr; max-height: none; min-width: 0px; min-height: 0px; border: 0px initial initial;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mi&gt;Z&lt;\/mi&gt;&lt;\/math&gt;\"><span aria-hidden=\"true\">Z<\/span><span role=\"presentation\">Z<\/span><\/span>\u662f\u968f\u673a\u5316\u7684\uff0c\u5b83\u5bf9\u4e8e<span style=\"margin: 0px; padding: 1px 0px; outline: 0px; max-width: none; box-sizing: border-box !important; overflow-wrap: normal; display: inline-block; line-height: 0; word-spacing: normal; float: none; direction: ltr; max-height: none; min-width: 0px; min-height: 0px; border: 0px initial initial;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mi&gt;D&lt;\/mi&gt;&lt;\/math&gt;\"><span aria-hidden=\"true\">D<\/span><span role=\"presentation\">D<\/span><\/span>\u548c<span style=\"margin: 0px; padding: 1px 0px; outline: 0px; max-width: none; box-sizing: border-box !important; overflow-wrap: normal; display: inline-block; line-height: 0; word-spacing: normal; float: none; direction: ltr; max-height: none; min-width: 0px; min-height: 0px; border: 0px initial initial;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mi&gt;Y&lt;\/mi&gt;&lt;\/math&gt;\"><span aria-hidden=\"true\">Y<\/span><span role=\"presentation\">Y<\/span><\/span>\u7684\u5e73\u5747\u56e0\u679c\u4f5c\u7528\u90fd\u662f\u663e\u800c\u6613\u89c1\u53ef\u4ee5\u5f97\u5230\u7684\u3002<\/section>\n<section><\/section>\n<p>\u56e0\u4e3a<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-656\" src=\"https:\/\/aif.amtbbs.org\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-39.png\" width=\"470\" height=\"33\" alt=\"\u56fe\u7247\" srcset=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-39.png 470w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-39-300x21.png 300w\" sizes=\"auto, (max-width: 470px) 100vw, 470px\" \/>CACE \u7684\u4e00\u4e2a\u77e9\u4f30\u8ba1\u4fbf\u662f<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-657\" src=\"https:\/\/aif.amtbbs.org\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-40.png\" width=\"316\" height=\"79\" alt=\"\u56fe\u7247\" srcset=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-40.png 316w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-40-300x75.png 300w\" sizes=\"auto, (max-width: 316px) 100vw, 316px\" \/><\/p>\n<p>\u7531\u6b64\u53ef\u89c1\u5de5\u5177\u53d8\u91cf\u4f30\u8ba1\u91cf\u7684\u56e0\u679c\u542b\u4e49\u3002\u4e0a\u9762\u7684\u8ba8\u8bba\u65e2\u663e\u793a\u4e86\u5de5\u5177\u53d8\u91cf\u5bf9\u4e8e\u8bc6\u522b\u56e0\u679c\u4f5c\u7528\u7684\u6709\u6548\u6027\uff0c\u4e5f\u63ed\u793a\u4e86\u5b83\u7684\u5c40\u9650\u6027\uff1a\u6211\u4eec\u53ea\u80fd\u8bc6\u522b\u67d0\u4e2a\u5b50\u603b\u4f53\u7684\u5e73\u5747\u56e0\u679c\u4f5c\u7528\uff1b\u800c\u901a\u5e38\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u5e76\u4e0d\u77e5\u9053\u67d0\u4e2a\u4e2a\u4f53\u5177\u4f53\u5c5e\u4e8e\u54ea\u4e2a\u5b50\u603b\u4f53\u3002<\/p>\n<section><strong>\u56db\u3001\u5b9e\u4f8b<\/strong><\/section>\n<p>\u8fd9\u90e8\u5206\u7ed9\u51fa\u5177\u4f53\u7684\u4f8b\u5b50\u6765\u8bf4\u660e\u4e0a\u8ff0\u7406\u8bba\u7684\u5e94\u7528\uff0c\u5177\u4f53\u8ba1\u7b97\u7528\u5230\u4e86\u7b2c\u4e94\u90e8\u5206\u7684\u4e00\u4e2a\u51fd\u6570\uff08\u5176\u4e2d\u5305\u62ec\u7528 delta \u65b9\u6cd5\u7b97\u7684\u62bd\u6837\u65b9\u5dee\uff09\u3002\u8fd9\u91cc\u7528\u5230\u7684\u6570\u636e\u6765\u81ea\u4e00\u7bc7\u653f\u6cbb\u5b66\u7684\u6587\u7ae0 Green et al. (2003) \u201cGetting Out the Vote in Local Elections: Results from Six Door-to-Door Canvassing Experiments\u201d\uff0c\u6570\u636e\u70b9\u51fb\u6b64\u5904\u53ef\u4ee5\u5728\u6b64\u4e0b\u8f7d\u3002<\/p>\n<p>\u6587\u7ae0\u76ee\u7684\u662f\u7814\u7a76\u67d0\u4e2a\u793e\u4f1a\u5b9e\u9a8c\u662f\u5426\u80fd\u591f\u63d0\u9ad8\u6295\u7968\u7387\uff0c\u5b9e\u9a8c\u662f\u968f\u673a\u5316\u7684\uff0c\u4f46\u662f\u5e76\u975e\u6240\u6709\u7684\u5b9e\u9a8c\u7ec4\u7684\u4eba\u90fd\u4f9d\u4ece\u3002\u56e0\u6b64\u8fd9\u91cc\u7684\u53d8\u91cf\u00a0<span style=\"margin: 0px; padding: 1px 0px; outline: 0px; max-width: none; box-sizing: border-box !important; overflow-wrap: normal; display: inline-block; line-height: 0; word-spacing: normal; float: none; direction: ltr; max-height: none; min-width: 0px; min-height: 0px; border: 0px initial initial;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mi&gt;Z&lt;\/mi&gt;&lt;\/math&gt;\"><span aria-hidden=\"true\">Z<\/span><span role=\"presentation\">Z<\/span><\/span>\u00a0\u8868\u793a\u968f\u673a\u5316\u7684\u5b9e\u9a8c\uff0c<span style=\"margin: 0px; padding: 1px 0px; outline: 0px; max-width: none; box-sizing: border-box !important; overflow-wrap: normal; display: inline-block; line-height: 0; word-spacing: normal; float: none; direction: ltr; max-height: none; min-width: 0px; min-height: 0px; border: 0px initial initial;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mi&gt;D&lt;\/mi&gt;&lt;\/math&gt;\"><span aria-hidden=\"true\">D<\/span><span role=\"presentation\">D<\/span><\/span>\u00a0\u8868\u793a\u4f9d\u4ece\u4e0e\u5426\uff0c<span style=\"margin: 0px; padding: 1px 0px; outline: 0px; max-width: none; box-sizing: border-box !important; overflow-wrap: normal; display: inline-block; line-height: 0; word-spacing: normal; float: none; direction: ltr; max-height: none; min-width: 0px; min-height: 0px; border: 0px initial initial;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mi&gt;Y&lt;\/mi&gt;&lt;\/math&gt;\"><span aria-hidden=\"true\">Y<\/span><span role=\"presentation\">Y<\/span><\/span>\u00a0\u662f\u6295\u7968\u4e0e\u5426\u7684\u793a\u6027\u53d8\u91cf\u3002\u5177\u4f53\u7684\u6570\u636e\u63cf\u8ff0\uff0c\u53ef\u53c2\u52a0\u524d\u9762\u63d0\u5230\u7684\u6587\u7ae0\u3002<\/p>\n<p>\u539f\u59cb\u6570\u636e\u603b\u7ed3\u5982\u4e0b\uff1a<\/p>\n<p><img decoding=\"async\" class=\"rich_pages wxw-img img_loading\" src=\"data:image\/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVQImWNgYGBgAAAABQABh6FO1AAAAABJRU5ErkJggg==\" alt=\"\u56fe\u7247\" crossorigin=\"anonymous\" data-ratio=\"0.3371824480369515\" data-s=\"300,640\" data-type=\"png\" data-w=\"433\" data-src=\"https:\/\/mmbiz.qpic.cn\/mmbiz_png\/wibWV1DB7tWIO90r3UsHjHlftibAW0QN6HZbSicCSBJG0afPzfNAvIx1LOG47br1zAvYibyClz6fhzDQve0bYUMicicg\/640?wx_fmt=png\" \/><\/p>\n<p>\u6839\u636e\u4e0b\u4e00\u4e2a\u90e8\u5206\u7684\u51fd\u6570\uff0c\u6211\u4eec\u5f97\u5230\u5982\u4e0b\u7684\u7ed3\u679c\uff1a<\/p>\n<p>CACE.IV(Y, D, Z)<br \/>\n$CACE<br \/>\n[1] 0.07914375<\/p>\n<p>$se.CACE<br \/>\n[,1]<br \/>\n[1,] 0.02273439<\/p>\n<p>$p.value<br \/>\n[,1]<br \/>\n[1,] 0.0004991073<\/p>\n<p>$prob.complier<br \/>\n[1] 0.2925123<\/p>\n<p>$se.complier<br \/>\n[1] 0.004871619<\/p>\n<p>\u7531\u6b64\u53ef\u89c1\uff0c\u8fd9\u4e2a\u5b9e\u9a8c\u5bf9\u4e8e\u63d0\u9ad8\u6295\u7968\u7387\uff0c\u6709\u663e\u8457\u7684\u4f5c\u7528\u3002<\/p>\n<h1>\u4e94\u3001R code<\/h1>\n<p>## function for complier average causal effect<br \/>\nCACE.IV &lt;- function(outcome, treatment, instrument) {<br \/>\nY &lt;- outcome<br \/>\nD &lt;- treatment<br \/>\nZ &lt;- instrument<br \/>\nN &lt;- length(Y)<\/p>\n<p>Y1 &lt;- Y[Z == 1]<br \/>\nY0 &lt;- Y[Z == 0]<br \/>\nD1 &lt;- D[Z == 1]<br \/>\nD0 &lt;- D[Z == 0]<\/p>\n<p>mean.Y1 &lt;- mean(Y1)<br \/>\nmean.Y0 &lt;- mean(Y0)<br \/>\nmean.D1 &lt;- mean(D1)<br \/>\nmean.D0 &lt;- mean(D0)<\/p>\n<p>prob.complier &lt;- mean.D1 &#8211; mean.D0<br \/>\nvar.complier &lt;- var(D1) \/ length(D1) + var(D0) \/ length(D0)<br \/>\nse.complier &lt;- var.complier^0.5<\/p>\n<p>CACE &lt;- (mean.Y1 &#8211; mean.Y0) \/ (mean.D1 &#8211; mean.D0)<\/p>\n<p>## COV<br \/>\npi1 &lt;- mean(Z)<br \/>\npi0 &lt;- 1 &#8211; pi1<\/p>\n<p>Omega &lt;- c(<br \/>\nvar(Y1) \/ pi1, cov(Y1, D1) \/ pi1, 0, 0,<br \/>\ncov(Y1, D1) \/ pi1, var(D1) \/ pi1, 0, 0,<br \/>\n0, 0, var(Y0) \/ pi0, cov(Y0, D0) \/ pi0,<br \/>\n0, 0, cov(Y0, D0) \/ pi0, var(D0) \/ pi0<br \/>\n)<br \/>\nOmega &lt;- matrix(Omega, byrow = TRUE, nrow = 4)<\/p>\n<p>## Gradient<br \/>\nGrad &lt;- c(1, -CACE, -1, CACE) \/ (mean.D1 &#8211; mean.D0)<\/p>\n<p>COV.CACE &lt;- t(Grad) %*% Omega %*% Grad \/ N<\/p>\n<p>se.CACE &lt;- COV.CACE^0.5<\/p>\n<p>p.value &lt;- 2 * pnorm(abs(CACE \/ se.CACE), 0, 1, lower.tail = FALSE)<\/p>\n<p>## results<br \/>\nres &lt;- list(<br \/>\nCACE = CACE,<br \/>\nse.CACE = se.CACE,<br \/>\np.value = p.value,<br \/>\nprob.complier = prob.complier,<br \/>\nse.complier = se.complier<br \/>\n)<\/p>\n<p>return(res)<br \/>\n}<\/p>\n<section>\n<section>\n<section>\n<section>\n<section><\/section>\n<section><\/section>\n<section>\n<section><\/section>\n<\/section>\n<\/section>\n<section><strong>7. \u56e0\u679c\u63a8\u65ad\u7b80\u4ecb\u4e4b\u4e03\uff1aLord\u2019s Paradox<\/strong><\/p>\n<\/section>\n<section>\n<section><\/section>\n<section><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<p>\u5728\u5145\u6ee1\u968f\u673a\u6027\u7684\u7edf\u8ba1\u4e16\u754c\u4e2d\uff0c\u6096\u8bba\u65e0\u5904\u4e0d\u5728\u3002\u8fd9\u4e00\u8282\u4ecb\u7ecd\u4e00\u4e2a\u5f88\u6709\u540d\uff0c\u4f46\u662f\u5728\u4e2d\u6587\u7edf\u8ba1\u6559\u79d1\u4e66\u4e2d\u51e0\u4e4e\u4ece\u672a\u4ecb\u7ecd\u8fc7\u7684\u6096\u8bba\u3002\u8fd9\u4e2a\u6096\u8bba\u662f Educational Testing Service\u00a0(ETS)\u00a0\u7684\u7edf\u8ba1\u5b66\u5bb6 Frederic Lord \u4e8e 1967 \u5e74\u63d0\u51fa\u6765\u7684\uff1b\u6700\u7ec8\u7531\u540c\u5728 ETS \u5de5\u4f5c\u7684\u53e6\u5916\u4e24\u4f4d\u7edf\u8ba1\u5b66\u5bb6 Paul Holland \u548c Donald Rubin \u4e8e 1982 \u5e74\u5706\u6ee1\u5730\u627e\u51fa\u4e86\u8fd9\u4e2a\u6096\u8bba\u7684\u6839\u6e90\u3002\u8fd9\u90e8\u5206\u5148\u4ecb\u7ecd\u8fd9\u4e2a\u6096\u8bba\uff0c\u518d\u4ecb\u7ecd Holland \u548c Rubin \u7684\u89e3\u91ca\uff0c\u6700\u540e\u662f\u4e00\u4e9b\u7ed3\u8bba\u3002<\/p>\n<p><strong>\u4e00\u3001Lord&#8217;s Paradox<\/strong><\/p>\n<p>\u8003\u8651\u4e0b\u9762\u4e00\u4e2a\u7b80\u5355\u4f8b\u5b50\uff0c\u5177\u4f53\u7684\u6570\u5b57\u662f\u4f2a\u9020\u7684\u3002\u67d0\u4e2a\u5b66\u6821\u60f3\u7814\u7a76\u98df\u5802\u5bf9\u4e8e\u5b66\u751f\u4f53\u91cd\u662f\u5426\u6709\u5dee\u5f02\u6027\u7684\u5f71\u54cd\uff0c\u5c24\u5176\u5173\u5fc3\u98df\u5802\u5bf9\u4e8e\u7537\u5973\u5b66\u751f\u4f53\u91cd\u5f71\u54cd\u662f\u5426\u76f8\u540c\u3002\u4e8e\u662f\u7edf\u8ba1\u5b66\u5bb6\u4eec\u6536\u96c6\u4e86\u5982\u4e0b\u7684\u6570\u636e\uff1a\u5b66\u751f\u7684\u6027\u522b<span style=\"margin: 0px; padding: 1px 0px; outline: 0px; max-width: none; box-sizing: border-box !important; overflow-wrap: normal; display: inline-block; line-height: 0; word-spacing: normal; float: none; direction: ltr; max-height: none; min-width: 0px; min-height: 0px; border: 0px initial initial;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mi&gt;G&lt;\/mi&gt;&lt;\/math&gt;\"><span aria-hidden=\"true\">G<\/span><span role=\"presentation\">G<\/span><\/span>\uff1b\u5b66\u751f\u5728 1963 \u5e74 6 \u6708\u5165\u5b66\u65f6\u5019\u7684\u4f53\u91cd<span style=\"margin: 0px; padding: 1px 0px; outline: 0px; max-width: none; box-sizing: border-box !important; overflow-wrap: normal; display: inline-block; line-height: 0; word-spacing: normal; float: none; direction: ltr; max-height: none; min-width: 0px; min-height: 0px; border: 0px initial initial;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mi&gt;X&lt;\/mi&gt;&lt;\/math&gt;\"><span aria-hidden=\"true\">X<\/span><span role=\"presentation\">X<\/span><\/span>\uff1b\u5b66\u751f\u5728 1964 \u5e74 6 \u6708\u653e\u6691\u5047\u65f6\u5019\u7684\u4f53\u91cd<span style=\"margin: 0px; padding: 1px 0px; outline: 0px; max-width: none; box-sizing: border-box !important; overflow-wrap: normal; display: inline-block; line-height: 0; word-spacing: normal; float: none; direction: ltr; max-height: none; min-width: 0px; min-height: 0px; border: 0px initial initial;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mi&gt;Y&lt;\/mi&gt;&lt;\/math&gt;\"><span aria-hidden=\"true\">Y<\/span><span role=\"presentation\">Y<\/span><\/span>\u3002<\/p>\n<p>\u7b2c\u4e00\u4e2a\u7edf\u8ba1\u5b66\u5bb6\uff0c\u91c7\u53d6\u4e86\u4e00\u79cd\u5f88\u7b80\u5355\u7684\u65b9\u6cd5\u3002\u5982\u56fe\u6240\u793a\uff0c\u6a2a\u8f74\u8868\u793a 1963 \u5e74 6 \u6708\u5165\u5b66\u524d\u7684\u4f53\u91cdX\uff0c\u7eb5\u8f74\u8868\u793a 1964 \u5e74 6 \u6708\u524d\u653e\u5047\u7684\u4f53\u91cd<code>Y<\/code>\u3002\u4e2a\u4f53\u4e0a\u6765\u770b\uff0c\u7537\u5973\u5165\u5b66\u524d\u548c\u5165\u5b66\u540e\u4e00\u5e74\u4f53\u91cd\u90fd\u4f1a\u6709\u4e9b\u53d8\u5316\uff0c\u7537\u5973\u5b66\u751f\u4f53\u91cd\u7684\u6563\u70b9\u56fe\u5206\u522b\u7528\u7eff\u8272\u548c\u7ea2\u8272\u6807\u51fa\u3002\u4ece\u7537\u5973\u5b66\u751f\u751f\u5e73\u5747\u4f53\u91cd\u6765\u770b\uff0c\u7537\u751f\u5165\u5b66\u524d\u540e\u4e00\u5e74\u5e73\u5747\u4f53\u91cd\u5747\u662f 150 \u78c5\uff08\u56fe\u4e2d\u53f3\u4e0a\u89d2\u7684\u9ed1\u70b9\uff09\uff0c\u5973\u751f\u5165\u5b66\u524d\u540e\u4e00\u5e74\u5e73\u5747\u4f53\u91cd\u5747\u4e3a 130 \u78c5\uff08\u56fe\u4e2d\u5de6\u4e0b\u89d2\u7684\u9ed1\u70b9\uff09\u3002\u56fe\u4e2d\u7684\u865a\u7ebf\u662f\u5bf9\u89d2\u7ebf<code>Y=X<\/code>\uff0c\u4e24\u4e2a\u9ed1\u70b9\u5747\u4f4d\u4e8e\u5bf9\u89d2\u7ebf\u4e0a\u3002\u56e0\u6b64\uff0c\u7b2c\u4e00\u4e2a\u7edf\u8ba1\u5b66\u5bb6\u7684\u7ed3\u8bba\u662f\u98df\u5802\u5bf9\u4e8e\u7537\u5973\u5b66\u751f\u4f53\u91cd\u90fd\u6ca1\u6709\u5f71\u54cd\uff0c\u56e0\u6b64\u5bf9\u7537\u5973\u5b66\u751f\u4f53\u91cd\u7684\u4f5c\u7528\u76f8\u540c\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-658\" src=\"https:\/\/aif.amtbbs.org\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-41.png\" width=\"1080\" height=\"1080\" alt=\"\u56fe\u7247\" srcset=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-41.png 1080w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-41-300x300.png 300w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-41-1024x1024.png 1024w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-41-150x150.png 150w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-41-768x768.png 768w\" sizes=\"auto, (max-width: 1080px) 100vw, 1080px\" \/><\/p>\n<p>\u6ce8\uff1a\u6a2a\u8f74\u8868\u793a 1963 \u5e74 6 \u6708\u5165\u5b66\u524d\u7684\u4f53\u91cd<code>X<\/code>\uff0c\u7eb5\u8f74\u8868\u793a 1964 \u5e74 6 \u6708\u524d\u653e\u5047\u7684\u4f53\u91cd<code>Y<\/code>\uff1b\u865a\u7ebf\u662f\u5bf9\u89d2\u7ebf<code>Y=X<\/code>\uff1b\u7537\u5973\u5b66\u751f\u4f53\u91cd\u7684\u6563\u70b9\u56fe\u5206\u522b\u7528\u7eff\u8272\u548c\u7ea2\u8272\u6807\u51fa\u3002\u56fe\u4e2d\u6570\u636e\u751f\u6210\u673a\u5236\u5982\u4e0b\uff1a\u7537\u5b66\u751f<code>(X,Y)~<\/code>\u4e8c\u5143\u6b63\u6001\u5206\u5e03\uff0c\u5747\u503c<code>(150,150)<\/code>\uff0c\u534f\u65b9\u5dee\u77e9\u9635<img decoding=\"async\" class=\"rich_pages wxw-img\" src=\"data:image\/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVQImWNgYGBgAAAABQABh6FO1AAAAABJRU5ErkJggg==\" alt=\"\u56fe\u7247\" crossorigin=\"anonymous\" data-croporisrc=\"https:\/\/mmbiz.qlogo.cn\/mmbiz_png\/wibWV1DB7tWIO90r3UsHjHlftibAW0QN6HiasC0QgVuk28p8jMlr6tiaxDHMUS4MmiazO1f8QvHU8EawiaWAker7jsYw\/0?wx_fmt=png\" data-cropx1=\"0\" data-cropx2=\"107\" data-cropy1=\"7\" data-cropy2=\"64\" data-galleryid=\"\" data-ratio=\"0.5327102803738317\" data-s=\"300,640\" data-type=\"jpeg\" data-w=\"107\" data-src=\"https:\/\/mmbiz.qpic.cn\/mmbiz_jpg\/wibWV1DB7tWIO90r3UsHjHlftibAW0QN6HEnjR37XQbpMVKbvOdZa3KTpDClMXahQvSsvgf1LnMY63cia3iamWGSNQ\/640?wx_fmt=jpeg\" \/>;\u5973\u5b66\u751f<code>(X,Y)~<\/code>\u4e8c\u5143\u6b63\u6001\u5206\u5e03\uff0c\u5747\u503c<code>(130,130)<\/code>\uff0c\u534f\u65b9\u5dee\u77e9\u9635<img decoding=\"async\" class=\"rich_pages wxw-img\" src=\"data:image\/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVQImWNgYGBgAAAABQABh6FO1AAAAABJRU5ErkJggg==\" alt=\"\u56fe\u7247\" crossorigin=\"anonymous\" data-croporisrc=\"https:\/\/mmbiz.qlogo.cn\/mmbiz_png\/wibWV1DB7tWIO90r3UsHjHlftibAW0QN6HiasC0QgVuk28p8jMlr6tiaxDHMUS4MmiazO1f8QvHU8EawiaWAker7jsYw\/0?wx_fmt=png\" data-cropx1=\"0\" data-cropx2=\"107\" data-cropy1=\"7\" data-cropy2=\"64\" data-galleryid=\"\" data-ratio=\"0.5327102803738317\" data-s=\"300,640\" data-type=\"jpeg\" data-w=\"107\" data-src=\"https:\/\/mmbiz.qpic.cn\/mmbiz_jpg\/wibWV1DB7tWIO90r3UsHjHlftibAW0QN6HEnjR37XQbpMVKbvOdZa3KTpDClMXahQvSsvgf1LnMY63cia3iamWGSNQ\/640?wx_fmt=jpeg\" \/>\u3002\u751f\u6210\u8fd9\u5e45\u56fe\u7684 R \u4ee3\u7801\u53ef\u4ee5\u5728\u8fd9\u91cc\u4e0b\u8f7d\uff1aRcodehttps:\/\/uploads.cosx.org\/2013\/09\/Rcode2.txt\u3002\u7531\u4e8e\u6837\u672c\u91cf 3000\uff0c\u6837\u672c\u5747\u503c\u975e\u5e38\u63a5\u8fd1\u7406\u8bba\u5747\u503c\uff0c\u56e0\u6b64\u843d\u5728\u4e86\u5bf9\u89d2\u7ebf\u4e0a\u3002)<\/p>\n<p>(150,150)\u751f\u6210\u8fd9\u5e45\u56fe\u7684 R \u4ee3\u7801\u53ef\u4ee5\u5728\u8fd9\u91cc\u4e0b\u8f7d\uff1aRcode\u3002\u7531\u4e8e\u6837\u672c\u91cf 3000\uff0c\u6837\u672c\u5747\u503c\u975e\u5e38\u63a5\u8fd1\u7406\u8bba\u5747\u503c\uff0c\u56e0\u6b64\u843d\u5728\u4e86\u5bf9\u89d2\u7ebf\u4e0a\u3002)<\/p>\n<p>\u7b2c\u4e8c\u4e2a\u7edf\u8ba1\u5b66\u5bb6\uff0c\u7531\u4e8e\u53d7\u5230\u4e86\u9ad8\u7b49\u7684\u7edf\u8ba1\u8bad\u7ec3\uff0c\u77e5\u9053 R A Fisher \u7684 Analysis of Covariance (ANCOVA) \uff0c\u63d0\u51fa\u4e86\u66f4\u52a0\u590d\u6742\u7684\u65b9\u6cd5\u3002\u4ed6\u8ba4\u4e3a\uff0c\u6211\u4eec\u7684\u5206\u6790\u5e94\u8be5\u63a7\u5236\u5165\u5b66\u524d\u7684\u4f53\u91cd\uff0c\u505a\u5982\u4e0b\u7684\u7ebf\u6027\u56de\u5f52\uff1a<\/p>\n<p>Yi=\u03b20+\u03b2gGi+\u03b2xXi+\u03b5i.(\u2217)<\/p>\n<section><\/section>\n<section>\u4ed6\u8fdb\u4e00\u6b65\u8ba4\u4e3a\uff0c\u4e0a\u9762\u7ebf\u6027\u56de\u5f52\u7684\u7cfb\u6570\u00a0<span style=\"margin: 0px; padding: 1px 0px; outline: 0px; max-width: none; box-sizing: border-box !important; overflow-wrap: normal; display: inline-block; line-height: 0; font-size: 19.04px; float: none; direction: ltr; max-height: none; min-width: 0px; min-height: 0px; font-family: Optima, 'Lucida Sans', Calibri, Candara, Arial, source-han-serif-sc, 'Source Han Serif SC', 'Source Han Serif CN', 'Source Han Serif TC', 'Source Han Serif TW', 'Source Han Serif', 'Songti SC', 'Microsoft YaHei', sans-serif; border: 0px initial initial;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;msub&gt;&lt;mi&gt;&amp;#x03B2;&lt;\/mi&gt;&lt;mi&gt;g&lt;\/mi&gt;&lt;\/msub&gt;&lt;\/math&gt;\"><span aria-hidden=\"true\">\u03b2g<\/span><span role=\"presentation\">\u03b2g<\/span><\/span>\u00a0\u53cd\u5e94\u7684\u5c31\u662f\u7537\u5973\u7684\u5dee\u522b\u3002\u7528\u6700\u5c0f\u4e8c\u4e58\u6cd5\u62df\u5408\u4e0a\u9762\u7684\u56de\u5f52\u6a21\u578b\uff0c\u7b49\u4ef7\u4e8e\u5728\u7537\u5973\u5b66\u751f\u4e2d\u62df\u5408\u4e24\u6761\u5e73\u884c\u7684\u56de\u5f52\u76f4\u7ebf\u3002\u5982\u56fe\u6240\u793a\uff0c\u4e24\u6761\u76f4\u7ebf\u659c\u7387\u00a0<span style=\"margin: 0px; padding: 1px 0px; outline: 0px; max-width: none; box-sizing: border-box !important; overflow-wrap: normal; display: inline-block; line-height: 0; font-size: 19.04px; float: none; direction: ltr; max-height: none; min-width: 0px; min-height: 0px; font-family: Optima, 'Lucida Sans', Calibri, Candara, Arial, source-han-serif-sc, 'Source Han Serif SC', 'Source Han Serif CN', 'Source Han Serif TC', 'Source Han Serif TW', 'Source Han Serif', 'Songti SC', 'Microsoft YaHei', sans-serif; border: 0px initial initial;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;msub&gt;&lt;mi&gt;&amp;#x03B2;&lt;\/mi&gt;&lt;mi&gt;x&lt;\/mi&gt;&lt;\/msub&gt;&lt;\/math&gt;\"><span aria-hidden=\"true\">\u03b2x<\/span><span role=\"presentation\">\u03b2x<\/span><\/span>\u00a0\u76f8\u540c\uff0c\u4f46\u662f\u622a\u8ddd\u4e0d\u540c\uff0c\u622a\u8ddd\u4e4b\u5dee\u5c31\u662f\u56de\u5f52\u7cfb\u6570<span style=\"margin: 0px; padding: 1px 0px; outline: 0px; max-width: none; box-sizing: border-box !important; overflow-wrap: normal; display: inline-block; line-height: 0; font-size: 19.04px; float: none; direction: ltr; max-height: none; min-width: 0px; min-height: 0px; font-family: Optima, 'Lucida Sans', Calibri, Candara, Arial, source-han-serif-sc, 'Source Han Serif SC', 'Source Han Serif CN', 'Source Han Serif TC', 'Source Han Serif TW', 'Source Han Serif', 'Songti SC', 'Microsoft YaHei', sans-serif; border: 0px initial initial;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mover&gt;&lt;mi&gt;&amp;#x03B2;&lt;\/mi&gt;&lt;mo&gt;&amp;#x005E;&lt;\/mo&gt;&lt;\/mover&gt;&lt;\/mrow&gt;&lt;mi&gt;g&lt;\/mi&gt;&lt;\/msub&gt;&lt;mo&gt;=&lt;\/mo&gt;&lt;mn&gt;6.34&lt;\/mn&gt;&lt;\/math&gt;\"><span aria-hidden=\"true\">\u02c6\u03b2g=6.34<\/span><span role=\"presentation\">\u03b2^g=6.34<\/span><\/span>\u3002\u7ed3\u8bba\u662f\uff0c\u98df\u5802\u5bf9\u4e8e\u7537\u5973\u4f53\u91cd\u6709\u5dee\u522b\u6027\u7684\u5f71\u54cd\u3002<\/section>\n<section>\u8fd9\u4e24\u4f4d\u7edf\u8ba1\u5b66\u5bb6\u5f97\u5230\u4e86\u4e0d\u540c\u7684\u7ed3\u8bba\uff0c\u7a76\u7adf\u8c01\u5bf9\u8c01\u9519\u5462\uff1fLord \u79f0\u8fd9\u4e2a\u73b0\u8c61\u4e3a\u6096\u8bba\uff0c\u90a3\u4e48\u6096\u8bba\u7684\u6839\u6e90\u662f\u4ec0\u4e48\u5462\uff1f<\/section>\n<section><\/section>\n<section><\/section>\n<section><strong>\u4e8c\u3001\u6096\u8bba\u7684\u6839\u6e90\uff1a\u56e0\u679c\u63a8\u65ad\u89c6\u89d2\u4e0b\u7684\u89e3\u91ca<\/strong><\/section>\n<section><\/section>\n<section>\u8981\u60f3\u89e3\u91ca\u8fd9\u4e2a\u6096\u8bba\uff0c\u4f7f\u7528\u7ebf\u6027\u56de\u5f52\u6a21\u578b\u76ca\u5904\u4e0d\u5927\uff0c\u56e0\u4e3a\u7a76\u7adf\u80fd\u5426\u5c06\u56de\u5f52\u7cfb\u6570\u89e3\u91ca\u6210\u56e0\u679c\u4f5c\u7528\uff0c\u662f\u4e2a\u6839\u672c\u6027\u7684\u95ee\u9898\u3002\u5728\u4e0b\u9762\u7684\u8ba8\u8bba\u4e2d\uff0c\u6211\u4eec\u5047\u5b9a\u6570\u636e\u7684\u6837\u672c\u91cf\u8db3\u591f\u5927\uff0c\u56e0\u800c\u53ef\u4ee5\u5ffd\u7565\u5c0f\u6837\u672c\u5e26\u6765\u7684\u968f\u673a\u6027\uff1b\u4e5f\u53ef\u4ee5\u8ba4\u4e3a\u6574\u4e2a\u8ba8\u8bba\u90fd\u5728\u603b\u4f53\u4e0a\u8fdb\u884c\u3002\u548c\u524d\u9762\u4e00\u6837\uff0c\u6211\u4eec\u7528<code>Gi<\/code>\u8868\u793a\u4e2a\u4f53<code>i<\/code>\u7684\u6027\u522b\uff0c\u7537\u6027\u53d6\u503c\u4e3a 1\uff0c \u5973\u6027\u53d6\u503c\u4e3a 0\uff1b<code>Xi<\/code>\u662f\u4e2a\u4f53\u00a0<code>i<\/code>\u5728 1963 \u5e74 9 \u6708\u7684\u4f53\u91cd\u3002\u7531\u4e8e\u8fd9\u4e24\u4e2a\u53d8\u91cf\u90fd\u53d1\u751f\u5728\u63a5\u53d7\u5904\u7406\uff08\u5728\u98df\u5802\u8fdb\u9910\u4e0e\u5426\uff09\u4e4b\u524d\uff0c\u5b83\u4eec\u90fd\u53ef\u4ee5\u770b\u6210\u662f\u534f\u53d8\u91cf\uff0c\u4e0d\u53d7\u5904\u7406\u7684\u5f71\u54cd\u3002\u6211\u4eec\u91c7\u7528\u6f5c\u5728\u7ed3\u679c\u6a21\u578b\uff0c\u5b9a\u4e49\u00a0<code>{ Yi(1), Yi(0) }\u00a0<\/code>\u662f\u4e2a\u4f53 $i$ \u5728\u98df\u5802\u8fdb\u9910\u548c\u4e0d\u5728\u98df\u5802\u8fdb\u9910\u4e0b\u4e8e 1964 \u5e74\u516d\u6708\u4f53\u91cd\u7684\u6f5c\u5728\u7ed3\u679c\u3002<\/section>\n<section><\/section>\n<p>\u5982\u679c\u7528<code>T<\/code>\u8868\u793a\u5728\u98df\u5802\u8fdb\u9910\u4e0e\u5426\u7684\u53d8\u91cf\uff0c\u90a3\u4e48\u6bcf\u4e2a\u5b66\u751f\u90fd\u662f<code>T=1<\/code>\u3002\u5f53\u5199\u4e0b\u6f5c\u5728\u7ed3\u679c\u4e4b\u540e\uff0c\u6211\u4eec\u5c31\u53d1\u73b0\u95ee\u9898\u7684\u6839\u6e90\u4e4b\u4e00\uff0c\u662f\u6574\u4e2a\u7814\u7a76\u6839\u672c\u4e0d\u5b58\u5728\u5bf9\u7167\u7ec4\uff08\u5168\u4f53\u5b66\u751f\u5176\u5b9e\u90fd\u5728\u98df\u5802\u8fdb\u9910\uff09\uff0c\u6bcf\u4e2a\u4e2a\u4f53\u5728 1964 \u5e74 6 \u6708\u90fd\u53d6\u503c<code>Y(1)<\/code>(\u4e5f\u5c31\u662f\u524d\u9762\u7684\u8bb0\u53f7<code>Y<\/code>)\u3002<\/p>\n<p>\u0394g=E{Y(1)\u2013Y(0)\u2223G=g},g=1,0;<\/p>\n<section>\u0394g=E{Y(1)\u2013Y(0)\u2223G=g},g=1,0;<\/section>\n<section>\u98df\u5802\u5bf9\u4e8e\u7537\u5973\u5b66\u751f\u4f53\u91cd\u5e73\u5747\u56e0\u679c\u4f5c\u7528\u7684\u5dee\u662f\uff1a<\/section>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-659\" src=\"https:\/\/aif.amtbbs.org\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-42.png\" width=\"583\" height=\"136\" alt=\"\u56fe\u7247\" srcset=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-42.png 583w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-42-300x70.png 300w\" sizes=\"auto, (max-width: 583px) 100vw, 583px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>\u4e0a\u9762\u7684\u63a8\u5bfc\u867d\u7136\u7b80\u5355\uff0c\u4f46\u662f\u5c06\u00a0<span style=\"margin: 0px; padding: 1px 0px; outline: 0px; max-width: none; box-sizing: border-box !important; overflow-wrap: normal; display: inline-block; line-height: 0; word-spacing: normal; float: none; direction: ltr; max-height: none; min-width: 0px; min-height: 0px; border: 0px initial initial;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x0394;&lt;\/mi&gt;&lt;\/math&gt;\"><span aria-hidden=\"true\">\u0394<\/span><span role=\"presentation\">\u0394<\/span><\/span>\u00a0\u5206\u6210\u4e86\u4e24\u4e2a\u663e\u8457\u4e0d\u540c\u7684\u90e8\u5206\uff1a\u7b2c\u4e00\u4e2a\u65b9\u62ec\u53f7\u5185\u7684\u9879\u662f\u6211\u4eec\u80fd\u591f\u4ece\u89c2\u6d4b\u6570\u636e\u4e2d\u5f97\u5230\u7684\uff1b\u7b2c\u4e8c\u4e2a\u65b9\u62ec\u53f7\u4e2d\u7684\u9879\u662f\u6211\u4eec\u4e0d\u53ef\u89c2\u6d4b\u7684\uff0c\u56e0\u4e3a\u6ca1\u6709\u4efb\u4f55\u4e00\u4e2a\u5b66\u751f\u63a5\u53d7\u4e86\u98df\u5802\u4e4b\u5916\u7684\u5904\u7406\u3002<\/p>\n<p>\u5982\u679c\u6211\u4eec\u5047\u5b9a\u00a0<span style=\"margin: 0px; padding: 1px 0px; outline: 0px; max-width: none; box-sizing: border-box !important; overflow-wrap: normal; display: inline-block; line-height: 0; text-align: left; font-size: 19.04px; float: none; direction: ltr; max-height: none; min-width: 0px; min-height: 0px; border: 0px initial initial;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mi&gt;Y&lt;\/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;\/mo&gt;&lt;mn&gt;0&lt;\/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;\/mo&gt;&lt;mo&gt;=&lt;\/mo&gt;&lt;mi&gt;X&lt;\/mi&gt;&lt;\/math&gt;\"><span aria-hidden=\"true\">Y(0)=X<\/span><\/span><span style=\"margin: 0px; padding: 1px 0px; outline: 0px; max-width: none; box-sizing: border-box !important; overflow-wrap: normal; display: inline-block; line-height: 0; word-spacing: normal; float: none; direction: ltr; max-height: none; min-width: 0px; min-height: 0px; border: 0px initial initial;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mi&gt;Y&lt;\/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;\/mo&gt;&lt;mn&gt;0&lt;\/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;\/mo&gt;&lt;mo&gt;=&lt;\/mo&gt;&lt;mi&gt;X&lt;\/mi&gt;&lt;\/math&gt;\"><span role=\"presentation\">Y(0)=X<\/span><\/span>\uff0c\u4e5f\u5c31\u662f\u8bf4\u5982\u679c\u5b66\u751f\u4e0d\u6765\u98df\u5802\u8fdb\u9910\uff0c\u4ed6\u4eec\u7684\u4f53\u91cd\u5c06\u548c\u5165\u5b66\u524d\u4e00\u6837\uff0c\u90a3\u4e48<\/p>\n<p>\u0394g=E{Y(1)\u2013X\u2223G=g}=E(Y\u2212X\u2223G=g).<\/p>\n<section><\/section>\n<section>\u6839\u636e\u4e0a\u9762\u7684\u56fe\u548c\u7edf\u8ba1\u5b66\u5bb6\u4e00\u7684\u63a8\u7406\u903b\u8f91\uff0c\u6211\u4eec\u77e5\u9053<span style=\"margin: 0px; padding: 1px 0px; outline: 0px; max-width: none; box-sizing: border-box !important; overflow-wrap: normal; display: inline-table; line-height: 0; text-align: left; font-size: 19.04px; float: none; direction: ltr; max-height: none; min-width: 0px; min-height: 0px; border: 0px initial initial;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;msub&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x0394;&lt;\/mi&gt;&lt;mi&gt;g&lt;\/mi&gt;&lt;\/msub&gt;&lt;mo&gt;=&lt;\/mo&gt;&lt;mn&gt;0&lt;\/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;\/mo&gt;&lt;mi&gt;g&lt;\/mi&gt;&lt;mo&gt;=&lt;\/mo&gt;&lt;mn&gt;0&lt;\/mn&gt;&lt;mo&gt;,&lt;\/mo&gt;&lt;mn&gt;1&lt;\/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;\/mo&gt;&lt;\/math&gt;\"><span aria-hidden=\"true\">\u0394g=0(g=0,1)<\/span><span role=\"presentation\">\u0394g=0(g=0,1)<\/span><\/span>\uff08\u7537\u5973\u5b66\u751f\u7684\u4f53\u91cd\u4e0d\u53d7\u5904\u7406\u5f71\u54cd\uff09\uff0c\u90a3\u4e48<span style=\"margin: 0px; padding: 1px 0px; outline: 0px; max-width: none; box-sizing: border-box !important; overflow-wrap: normal; display: inline-block; line-height: 0; text-align: left; font-size: 19.04px; float: none; direction: ltr; max-height: none; min-width: 0px; min-height: 0px; border: 0px initial initial;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x0394;&lt;\/mi&gt;&lt;mo&gt;=&lt;\/mo&gt;&lt;mn&gt;0&lt;\/mn&gt;&lt;\/math&gt;\"><span aria-hidden=\"true\">\u0394=0<\/span><span role=\"presentation\">\u0394=0<\/span><\/span>\uff08\u5904\u7406\u5bf9\u4e8e\u7537\u5973\u4f53\u91cd\u6ca1\u6709\u5dee\u5f02\u6027\u7684\u5f71\u54cd\uff09\u3002\u5728\u8fd9\u4e2a\u5047\u5b9a\u4e0b\uff0c\u7b2c\u4e00\u4e2a\u7edf\u8ba1\u5b66\u5bb6\u7684\u65ad\u8a00\u662f\u6b63\u786e\u7684\u3002<\/section>\n<section><\/section>\n<section>\u663e\u7136\uff0c\u5047\u5b9a<span style=\"margin: 0px; padding: 1px 0px; outline: 0px; max-width: none; box-sizing: border-box !important; overflow-wrap: normal; display: inline-block; line-height: 0; word-spacing: normal; float: none; direction: ltr; max-height: none; min-width: 0px; min-height: 0px; border: 0px initial initial;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mi&gt;Y&lt;\/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;\/mo&gt;&lt;mn&gt;0&lt;\/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;\/mo&gt;&lt;mo&gt;=&lt;\/mo&gt;&lt;mi&gt;X&lt;\/mi&gt;&lt;\/math&gt;\"><span aria-hidden=\"true\">\u00a0<span style=\"margin: 0px; padding: 1px 0px; outline: 0px; max-width: none; box-sizing: border-box !important; overflow-wrap: normal; display: inline-block; line-height: 0; text-align: left; font-size: 19.04px; float: none; direction: ltr; max-height: none; min-width: 0px; min-height: 0px; border: 0px initial initial;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mi&gt;Y&lt;\/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;\/mo&gt;&lt;mn&gt;0&lt;\/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;\/mo&gt;&lt;mo&gt;=&lt;\/mo&gt;&lt;mi&gt;X&lt;\/mi&gt;&lt;\/math&gt;\">Y(0)=X<\/span><\/span><span role=\"presentation\">Y(0)=X<\/span><\/span>\u662f\u65e0\u6cd5\u88ab\u6570\u636e\u8bc1\u660e\u6216\u8005\u8bc1\u4f2a\u7684\uff0c\u5b83\u53ea\u80fd\u4f9d\u8d56\u4e8e\u6211\u4eec\u7684\u5148\u9a8c\u77e5\u8bc6\u3002\u90a3\u4e48\u5728\u4ec0\u4e48\u5047\u5b9a\u4e0b\uff0c\u7b2c\u4e8c\u4e2a\u7edf\u8ba1\u5b66\u5bb6\u53c8\u662f\u5bf9\u7684\u5462\uff1f<\/section>\n<section><\/section>\n<section>\u6839\u636e\u7b2c\u4e8c\u4e2a\u7edf\u8ba1\u5b66\u5bb6\u505a ANCOVA \u7684\u903b\u8f91\uff0c\u4ed6\u53ef\u4ee5\u5047\u5b9a<\/section>\n<section><\/section>\n<p><img decoding=\"async\" class=\"rich_pages wxw-img img_loading\" src=\"data:image\/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVQImWNgYGBgAAAABQABh6FO1AAAAABJRU5ErkJggg==\" alt=\"\u56fe\u7247\" crossorigin=\"anonymous\" data-galleryid=\"\" data-ratio=\"0.15384615384615385\" data-s=\"300,640\" data-type=\"png\" data-w=\"338\" data-src=\"https:\/\/mmbiz.qpic.cn\/mmbiz_png\/wibWV1DB7tWIO90r3UsHjHlftibAW0QN6HxL3MLLjP7hjLRsoiaMeNDyCxSqkS7ZEeVibiaevrbNichHjF2hfzBStH1w\/640?wx_fmt=png\" \/><\/p>\n<p>\u5e76\u4e14\u628a<span style=\"margin: 0px; padding: 1px 0px; outline: 0px; max-width: none; box-sizing: border-box !important; overflow-wrap: normal; text-align: start; word-spacing: normal; display: inline-block; line-height: 0; font-size: 19.04px; float: none; direction: ltr; max-height: none; min-width: 0px; min-height: 0px; border: 0px initial initial;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mi&gt;&amp;#x03B4;&lt;\/mi&gt;&lt;mo&gt;=&lt;\/mo&gt;&lt;msub&gt;&lt;mi&gt;a&lt;\/mi&gt;&lt;mn&gt;1&lt;\/mn&gt;&lt;\/msub&gt;&lt;mo&gt;&amp;#x2013;&lt;\/mo&gt;&lt;msub&gt;&lt;mi&gt;a&lt;\/mi&gt;&lt;mn&gt;0&lt;\/mn&gt;&lt;\/msub&gt;&lt;\/math&gt;\"><span aria-hidden=\"true\">\u03b4=a1\u2013a0<\/span><span role=\"presentation\">\u03b4=a1\u2013a0<\/span><\/span><\/p>\n<section>\u5f53\u6210\u98df\u5802\u5bf9\u4e8e\u7537\u5973\u4f53\u91cd\u5dee\u5f02\u4f5c\u7528\u7684\u5ea6\u91cf\u3002<span style=\"margin: 0px; padding: 1px 0px; outline: 0px; max-width: none; box-sizing: border-box !important; overflow-wrap: normal; display: inline-block; line-height: 0; word-spacing: normal; float: none; direction: ltr; max-height: none; min-width: 0px; min-height: 0px; border: 0px initial initial;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mi&gt;&amp;#x03B4;&lt;\/mi&gt;&lt;\/math&gt;\"><span aria-hidden=\"true\">\u03b4<\/span><span role=\"presentation\">\u03b4<\/span><\/span>\u00a0\u5176\u5b9e\u5c31\u662f\u4e0a\u9762\u7684\u7ebf\u6027\u56de\u5f52\u6a21\u578b(\u2217)\u7684\u56de\u5f52\u7cfb\u6570\u00a0\u03b2g\u3002\u5982\u679c\u6211\u4eec\u5047\u5b9a\u00a0<\/section>\n<p><span style=\"margin: 0px; padding: 1px 0px; outline: 0px; max-width: none; box-sizing: border-box !important; overflow-wrap: normal; text-align: start; word-spacing: normal; display: inline-block; line-height: 0; font-size: 19.04px; float: none; direction: ltr; max-height: none; min-width: 0px; min-height: 0px; border: 0px initial initial;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mi&gt;Y&lt;\/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;\/mo&gt;&lt;mn&gt;0&lt;\/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;\/mo&gt;&lt;mo&gt;=&lt;\/mo&gt;&lt;mi&gt;&amp;#x03B1;&lt;\/mi&gt;&lt;mo&gt;+&lt;\/mo&gt;&lt;mi&gt;b&lt;\/mi&gt;&lt;mi&gt;X&lt;\/mi&gt;&lt;\/math&gt;\"><span aria-hidden=\"true\">Y(0)=\u03b1+bX<\/span><\/span><span style=\"margin: 0px; padding: 1px 0px; outline: 0px; max-width: none; box-sizing: border-box !important; overflow-wrap: normal; display: inline-block; line-height: 0; word-spacing: normal; float: none; direction: ltr; max-height: none; min-width: 0px; min-height: 0px; border: 0px initial initial;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mi&gt;Y&lt;\/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;\/mo&gt;&lt;mn&gt;0&lt;\/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;\/mo&gt;&lt;mo&gt;=&lt;\/mo&gt;&lt;mi&gt;&amp;#x03B1;&lt;\/mi&gt;&lt;mo&gt;+&lt;\/mo&gt;&lt;mi&gt;b&lt;\/mi&gt;&lt;mi&gt;X&lt;\/mi&gt;&lt;\/math&gt;\"><span role=\"presentation\">Y(0)=\u03b1+bX<\/span><\/span>\uff0c\u90a3\u4e48\u4e0d\u53bb\u98df\u5802\u8fdb\u9910\u65f6\u7684\u6f5c\u5728\u4f53\u91cdY(0)\u662f\u5165\u5b66\u524d\u4f53\u91cd\u00a0<span style=\"margin: 0px; padding: 1px 0px; outline: 0px; max-width: none; box-sizing: border-box !important; overflow-wrap: normal; display: inline-block; line-height: 0; word-spacing: normal; float: none; direction: ltr; max-height: none; min-width: 0px; min-height: 0px; border: 0px initial initial;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mi&gt;X&lt;\/mi&gt;&lt;\/math&gt;\"><span aria-hidden=\"true\">X<\/span><span role=\"presentation\">X<\/span><\/span>\u00a0\u7684\u7ebf\u6027\u51fd\u6570\u4e14\u622a\u8ddd\u662f\u00a0<span style=\"margin: 0px; padding: 1px 0px; outline: 0px; max-width: none; box-sizing: border-box !important; overflow-wrap: normal; display: inline-block; line-height: 0; word-spacing: normal; float: none; direction: ltr; max-height: none; min-width: 0px; min-height: 0px; border: 0px initial initial;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mi&gt;b&lt;\/mi&gt;&lt;\/math&gt;\"><span aria-hidden=\"true\">b<\/span><span role=\"presentation\">b<\/span><\/span>\uff1b\u8fd9\u8868\u660e<span style=\"margin: 0px; padding: 1px 0px; outline: 0px; max-width: none; box-sizing: border-box !important; overflow-wrap: normal; text-align: start; word-spacing: normal; display: inline-block; line-height: 0; font-size: 19.04px; float: none; direction: ltr; max-height: none; min-width: 0px; min-height: 0px; border: 0px initial initial;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mi&gt;Y&lt;\/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;\/mo&gt;&lt;mn&gt;1&lt;\/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;\/mo&gt;&lt;\/math&gt;\"><span aria-hidden=\"true\">Y(1)<\/span><span role=\"presentation\">Y(1)<\/span><\/span>\u00a0\u548c\u00a0<span style=\"margin: 0px; padding: 1px 0px; outline: 0px; max-width: none; box-sizing: border-box !important; overflow-wrap: normal; text-align: start; word-spacing: normal; display: inline-block; line-height: 0; font-size: 19.04px; float: none; direction: ltr; max-height: none; min-width: 0px; min-height: 0px; border: 0px initial initial;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mi&gt;Y&lt;\/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;\/mo&gt;&lt;mn&gt;0&lt;\/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;\/mo&gt;&lt;\/math&gt;\"><span aria-hidden=\"true\">Y(0)<\/span><\/span>\u00a0\u5173\u4e8e\u00a0<span style=\"margin: 0px; padding: 1px 0px; outline: 0px; max-width: none; box-sizing: border-box !important; overflow-wrap: normal; display: inline-block; line-height: 0; word-spacing: normal; float: none; direction: ltr; max-height: none; min-width: 0px; min-height: 0px; border: 0px initial initial;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mi&gt;X&lt;\/mi&gt;&lt;\/math&gt;\"><span aria-hidden=\"true\">X<\/span><span role=\"presentation\">X<\/span><\/span>\u00a0\u7684\u6a21\u578b\uff0c\u4ec5\u4ec5\u622a\u8ddd\u4e0d\u540c\uff0c\u659c\u7387\u76f8\u540c\u3002\u8fd9\u4e2a\u5047\u5b9a\u5e76\u975e\u4e0d\u53ef\u80fd\u3002\u6b64\u65f6\uff0c<\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"margin: 0px; padding: 1px 0px; outline: 0px; max-width: none; box-sizing: border-box !important; overflow-wrap: normal; display: inline-block; line-height: 0; font-size: 19.04px; word-spacing: normal; float: none; direction: ltr; max-height: none; min-width: 0px; min-height: 0px; border: 0px initial initial;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot; display=&quot;block&quot;&gt;&lt;mtable columnalign=&quot;right center left&quot; rowspacing=&quot;3pt&quot; columnspacing=&quot;0 thickmathspace&quot; displaystyle=&quot;true&quot;&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x0394;&lt;\/mi&gt;&lt;\/mtd&gt;&lt;mtd&gt;&lt;mi&gt;&lt;\/mi&gt;&lt;mo&gt;=&lt;\/mo&gt;&lt;\/mtd&gt;&lt;mtd&gt;&lt;mi&gt;E&lt;\/mi&gt;&lt;mo fence=&quot;false&quot; stretchy=&quot;false&quot;&gt;{&lt;\/mo&gt;&lt;mi&gt;Y&lt;\/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;\/mo&gt;&lt;mn&gt;1&lt;\/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;\/mo&gt;&lt;mo&gt;&amp;#x2013;&lt;\/mo&gt;&lt;mi&gt;Y&lt;\/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;\/mo&gt;&lt;mn&gt;0&lt;\/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;\/mo&gt;&lt;mo&gt;&amp;#x2223;&lt;\/mo&gt;&lt;mi&gt;G&lt;\/mi&gt;&lt;mo&gt;=&lt;\/mo&gt;&lt;mn&gt;1&lt;\/mn&gt;&lt;mo fence=&quot;false&quot; stretchy=&quot;false&quot;&gt;}&lt;\/mo&gt;&lt;mo&gt;&amp;#x2013;&lt;\/mo&gt;&lt;mi&gt;E&lt;\/mi&gt;&lt;mo fence=&quot;false&quot; stretchy=&quot;false&quot;&gt;{&lt;\/mo&gt;&lt;mi&gt;Y&lt;\/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;\/mo&gt;&lt;mn&gt;1&lt;\/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;\/mo&gt;&lt;mo&gt;&amp;#x2013;&lt;\/mo&gt;&lt;mi&gt;Y&lt;\/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;\/mo&gt;&lt;mn&gt;0&lt;\/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;\/mo&gt;&lt;mo&gt;&amp;#x2223;&lt;\/mo&gt;&lt;mi&gt;G&lt;\/mi&gt;&lt;mo&gt;=&lt;\/mo&gt;&lt;mn&gt;0&lt;\/mn&gt;&lt;mo fence=&quot;false&quot; stretchy=&quot;false&quot;&gt;}&lt;\/mo&gt;&lt;\/mtd&gt;&lt;\/mtr&gt;&lt;mtr&gt;&lt;mtd &gt;&lt;\/mtd&gt;&lt;mtd&gt;&lt;mi&gt;&lt;\/mi&gt;&lt;mo&gt;=&lt;\/mo&gt;&lt;\/mtd&gt;&lt;mtd&gt;&lt;mi&gt;E&lt;\/mi&gt;&lt;mo fence=&quot;false&quot; stretchy=&quot;false&quot;&gt;{&lt;\/mo&gt;&lt;mi&gt;Y&lt;\/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;\/mo&gt;&lt;mn&gt;1&lt;\/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;\/mo&gt;&lt;mo&gt;&amp;#x2013;&lt;\/mo&gt;&lt;mi&gt;&amp;#x03B1;&lt;\/mi&gt;&lt;mo&gt;&amp;#x2013;&lt;\/mo&gt;&lt;mi&gt;b&lt;\/mi&gt;&lt;mi&gt;X&lt;\/mi&gt;&lt;mo&gt;&amp;#x2223;&lt;\/mo&gt;&lt;mi&gt;G&lt;\/mi&gt;&lt;mo&gt;=&lt;\/mo&gt;&lt;mn&gt;1&lt;\/mn&gt;&lt;mo fence=&quot;false&quot; stretchy=&quot;false&quot;&gt;}&lt;\/mo&gt;&lt;mo&gt;&amp;#x2013;&lt;\/mo&gt;&lt;mi&gt;E&lt;\/mi&gt;&lt;mo fence=&quot;false&quot; stretchy=&quot;false&quot;&gt;{&lt;\/mo&gt;&lt;mi&gt;Y&lt;\/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;\/mo&gt;&lt;mn&gt;1&lt;\/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;\/mo&gt;&lt;mo&gt;&amp;#x2013;&lt;\/mo&gt;&lt;mi&gt;&amp;#x03B1;&lt;\/mi&gt;&lt;mo&gt;&amp;#x2013;&lt;\/mo&gt;&lt;mi&gt;b&lt;\/mi&gt;&lt;mi&gt;X&lt;\/mi&gt;&lt;mo&gt;&amp;#x2223;&lt;\/mo&gt;&lt;mi&gt;G&lt;\/mi&gt;&lt;mo&gt;=&lt;\/mo&gt;&lt;mn&gt;0&lt;\/mn&gt;&lt;mo fence=&quot;false&quot; stretchy=&quot;false&quot;&gt;}&lt;\/mo&gt;&lt;\/mtd&gt;&lt;\/mtr&gt;&lt;mtr&gt;&lt;mtd &gt;&lt;\/mtd&gt;&lt;mtd&gt;&lt;mi&gt;&lt;\/mi&gt;&lt;mo&gt;=&lt;\/mo&gt;&lt;\/mtd&gt;&lt;mtd&gt;&lt;mrow&gt;&lt;mo&gt;[&lt;\/mo&gt;&lt;mrow&gt;&lt;mi&gt;E&lt;\/mi&gt;&lt;mo fence=&quot;false&quot; stretchy=&quot;false&quot;&gt;{&lt;\/mo&gt;&lt;mi&gt;Y&lt;\/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;\/mo&gt;&lt;mn&gt;1&lt;\/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;\/mo&gt;&lt;mo&gt;&amp;#x2223;&lt;\/mo&gt;&lt;mi&gt;G&lt;\/mi&gt;&lt;mo&gt;=&lt;\/mo&gt;&lt;mn&gt;1&lt;\/mn&gt;&lt;mo fence=&quot;false&quot; stretchy=&quot;false&quot;&gt;}&lt;\/mo&gt;&lt;mo&gt;&amp;#x2013;&lt;\/mo&gt;&lt;mi&gt;b&lt;\/mi&gt;&lt;mi&gt;E&lt;\/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;\/mo&gt;&lt;mi&gt;X&lt;\/mi&gt;&lt;mo&gt;&amp;#x2223;&lt;\/mo&gt;&lt;mi&gt;G&lt;\/mi&gt;&lt;mo&gt;=&lt;\/mo&gt;&lt;mn&gt;1&lt;\/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;\/mo&gt;&lt;\/mrow&gt;&lt;mo&gt;]&lt;\/mo&gt;&lt;\/mrow&gt;&lt;\/mtd&gt;&lt;\/mtr&gt;&lt;mtr&gt;&lt;mtd &gt;&lt;\/mtd&gt;&lt;mtd &gt;&lt;\/mtd&gt;&lt;mtd&gt;&lt;mi&gt;&lt;\/mi&gt;&lt;mo&gt;&amp;#x2212;&lt;\/mo&gt;&lt;mrow&gt;&lt;mo&gt;[&lt;\/mo&gt;&lt;mrow&gt;&lt;mi&gt;E&lt;\/mi&gt;&lt;mo fence=&quot;false&quot; stretchy=&quot;false&quot;&gt;{&lt;\/mo&gt;&lt;mi&gt;Y&lt;\/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;\/mo&gt;&lt;mn&gt;1&lt;\/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;\/mo&gt;&lt;mo&gt;&amp;#x2223;&lt;\/mo&gt;&lt;mi&gt;G&lt;\/mi&gt;&lt;mo&gt;=&lt;\/mo&gt;&lt;mn&gt;0&lt;\/mn&gt;&lt;mo fence=&quot;false&quot; stretchy=&quot;false&quot;&gt;}&lt;\/mo&gt;&lt;mo&gt;&amp;#x2013;&lt;\/mo&gt;&lt;mi&gt;b&lt;\/mi&gt;&lt;mi&gt;E&lt;\/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;\/mo&gt;&lt;mi&gt;X&lt;\/mi&gt;&lt;mo&gt;&amp;#x2223;&lt;\/mo&gt;&lt;mi&gt;G&lt;\/mi&gt;&lt;mo&gt;=&lt;\/mo&gt;&lt;mn&gt;0&lt;\/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;\/mo&gt;&lt;\/mrow&gt;&lt;mo&gt;]&lt;\/mo&gt;&lt;\/mrow&gt;&lt;\/mtd&gt;&lt;\/mtr&gt;&lt;mtr&gt;&lt;mtd &gt;&lt;\/mtd&gt;&lt;mtd&gt;&lt;mi&gt;&lt;\/mi&gt;&lt;mo&gt;=&lt;\/mo&gt;&lt;\/mtd&gt;&lt;mtd&gt;&lt;msub&gt;&lt;mi&gt;a&lt;\/mi&gt;&lt;mn&gt;1&lt;\/mn&gt;&lt;\/msub&gt;&lt;mo&gt;&amp;#x2013;&lt;\/mo&gt;&lt;msub&gt;&lt;mi&gt;a&lt;\/mi&gt;&lt;mn&gt;0&lt;\/mn&gt;&lt;\/msub&gt;&lt;mo&gt;=&lt;\/mo&gt;&lt;mi&gt;&amp;#x03B4;&lt;\/mi&gt;&lt;mo&gt;.&lt;\/mo&gt;&lt;\/mtd&gt;&lt;\/mtr&gt;&lt;\/mtable&gt;&lt;\/math&gt;\"><span aria-hidden=\"true\">\u0394=E{Y(1)\u2013Y(0)\u2223G=1}\u2013E{Y(1)\u2013Y(0)\u2223G=0}=E{Y(1)\u2013\u03b1\u2013bX\u2223G=1}\u2013E{Y(1)\u2013\u03b1\u2013bX\u2223G=0}=[E{Y(1)\u2223G=1}\u2013bE(X\u2223G=1)]\u2212[E{Y(1)\u2223G=0}\u2013bE(X\u2223G=0)]=a1\u2013a0=\u03b4.<\/span><\/span><\/p>\n<section>\u6700\u540e\u4e00\u884c\u7b49\u4e8e\u00a0<span style=\"margin: 0px; padding: 1px 0px; outline: 0px; max-width: none; box-sizing: border-box !important; overflow-wrap: normal; display: inline-block; line-height: 0; font-size: 19.04px; float: none; direction: ltr; max-height: none; min-width: 0px; min-height: 0px; border: 0px initial initial;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mi&gt;&amp;#x03B4;&lt;\/mi&gt;&lt;\/math&gt;\"><span aria-hidden=\"true\">\u03b4<\/span><span role=\"presentation\">\u03b4<\/span><\/span>\uff0c\u56e0\u4e3a\u6839\u636e\u6761\u4ef6\u671f\u671b\u7684\u6027\u8d28\uff0c\u65b9\u62ec\u53f7\u4e2d\u7684\u4e24\u9879\u5206\u522b\u662f\u00a0<span style=\"margin: 0px; padding: 1px 0px; outline: 0px; max-width: none; box-sizing: border-box !important; overflow-wrap: normal; display: inline-block; line-height: 0; font-size: 19.04px; float: none; direction: ltr; max-height: none; min-width: 0px; min-height: 0px; border: 0px initial initial;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;msub&gt;&lt;mi&gt;a&lt;\/mi&gt;&lt;mn&gt;1&lt;\/mn&gt;&lt;\/msub&gt;&lt;\/math&gt;\"><span aria-hidden=\"true\">a1<\/span><span role=\"presentation\">a1<\/span><\/span>\u00a0\u548c\u00a0<span style=\"margin: 0px; padding: 1px 0px; outline: 0px; max-width: none; box-sizing: border-box !important; overflow-wrap: normal; display: inline-block; line-height: 0; font-size: 19.04px; float: none; direction: ltr; max-height: none; min-width: 0px; min-height: 0px; border: 0px initial initial;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;msub&gt;&lt;mi&gt;a&lt;\/mi&gt;&lt;mn&gt;0&lt;\/mn&gt;&lt;\/msub&gt;&lt;\/math&gt;\"><span aria-hidden=\"true\">a0<\/span><span role=\"presentation\">a0<\/span><\/span>\uff1a<span style=\"margin: 0px; padding: 0.475em 0.007em 0.265em 0px; outline: 0px; max-width: none; box-sizing: content-box !important; overflow-wrap: normal; line-height: 0; text-align: left; float: none; direction: ltr; max-height: none; min-width: 0px; min-height: 0px; white-space: pre-wrap; display: block; font-family: MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw; border: 0px initial initial;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mi&gt;&amp;#x03B4;&lt;\/mi&gt;&lt;\/math&gt;\"><br \/>\n<\/span><\/section>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-660\" src=\"https:\/\/aif.amtbbs.org\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-43.png\" width=\"584\" height=\"138\" alt=\"\u56fe\u7247\" srcset=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-43.png 584w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-43-300x71.png 300w\" sizes=\"auto, (max-width: 584px) 100vw, 584px\" \/><\/p>\n<section><\/section>\n<section>\u8fd9\u6837\u4e00\u6765\uff0c\u7b2c\u4e8c\u4e2a\u7edf\u8ba1\u5b66\u5bb6\u7684\u7ed3\u8bba\u5c31\u662f\u6b63\u786e\u7684\u3002<\/section>\n<section><\/section>\n<section><strong>\u4e09\u3001\u7ed3\u8bba<\/strong><\/section>\n<section><\/section>\n<section>\u6839\u636e\u4e0a\u9762\u7684\u8ba8\u8bba\uff0c\u5173\u4e8e Lord\u2019s Paradox\uff0c\u6211\u4eec\u6709\u5982\u4e0b\u7684\u7ed3\u8bba\uff1a<\/section>\n<section>\uff081\uff09Lord\u2019s Paradox \u7684\u6839\u6e90\u5728\u4e8e\uff0c\u6574\u4e2a\u7814\u7a76\u6ca1\u6709\u5bf9\u7167\u7ec4\uff1b\u6211\u4eec\u751a\u81f3\u4e0d\u77e5\u9053\u4ec0\u4e48\u662f\u5bf9\u7167\u7ec4\uff0c\u4e0d\u5728\u98df\u5802\u8fdb\u9910\uff0c\u662f\u5728\u5bb6\u91cc\u8fdb\u9910\uff0c\u8fd8\u662f\u5916\u9762\u7684\u53c2\u89c2\u8fdb\u9910\uff0c\u8fd8\u662f\u5176\u4ed6\uff1f\u8fd9\u5176\u5b9e\u5bfc\u81f4 $Y(0)$ \u5e76\u975e\u5b8c\u597d\u5b9a\u4e49\u3002\u4e0a\u9762\u7684\u8ba8\u8bba\u5219\u662f\u5047\u5b9a<span style=\"margin: 0px; padding: 1px 0px; outline: 0px; max-width: none; box-sizing: border-box !important; overflow-wrap: normal; display: inline-block; line-height: 0; word-spacing: normal; float: none; direction: ltr; max-height: none; min-width: 0px; min-height: 0px; border: 0px initial initial;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mi&gt;Y&lt;\/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;\/mo&gt;&lt;mn&gt;0&lt;\/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;\/mo&gt;&lt;\/math&gt;\"><span aria-hidden=\"true\">\u00a0<span style=\"margin: 0px; padding: 1px 0px; outline: 0px; max-width: none; box-sizing: border-box !important; overflow-wrap: normal; display: inline-block; line-height: 0; text-align: left; font-size: 19.04px; float: none; direction: ltr; max-height: none; min-width: 0px; min-height: 0px; font-family: Optima, 'Lucida Sans', Calibri, Candara, Arial, source-han-serif-sc, 'Source Han Serif SC', 'Source Han Serif CN', 'Source Han Serif TC', 'Source Han Serif TW', 'Source Han Serif', 'Songti SC', 'Microsoft YaHei', sans-serif; border: 0px initial initial;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mi&gt;Y&lt;\/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;\/mo&gt;&lt;mn&gt;0&lt;\/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;\/mo&gt;&lt;\/math&gt;\">Y(0)<\/span><\/span><span role=\"presentation\">Y(0)<\/span><\/span>\u662f\u826f\u597d\u5b9a\u4e49\u7684\u3002<\/section>\n<section>\uff082\uff09\u56de\u5f52\u6216\u8005\u534f\u65b9\u5dee\u5206\u6790\u7b49\u7edf\u8ba1\u5de5\u5177\uff0c\u5e76\u4e0d\u80fd\u6e05\u695a\u7684\u56de\u7b54\u56e0\u679c\u7684\u95ee\u9898\u3002\u8fd9\u4e2a\u95ee\u9898\u4e2d\uff0c<span style=\"margin: 0px; padding: 1px 0px; outline: 0px; max-width: none; box-sizing: border-box !important; overflow-wrap: normal; display: inline-block; line-height: 0; word-spacing: normal; float: none; direction: ltr; max-height: none; min-width: 0px; min-height: 0px; border: 0px initial initial;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x0394;&lt;\/mi&gt;&lt;\/math&gt;\"><span aria-hidden=\"true\">\u0394<\/span><span role=\"presentation\">\u0394<\/span><\/span>\u662f\u4e00\u4e2a\u6211\u4eec\u5173\u5fc3\u7684\u56e0\u679c\u5ea6\u91cf\uff0c\u79bb\u5f00\u6f5c\u5728\u7ed3\u679c\uff0c\u662f\u5f88\u96be\u5b9a\u4e49\u7684\u3002\u6839\u636e\u4e0a\u9762\u7684\u8ba8\u8bba\uff0c\u4e24\u4f4d\u7edf\u8ba1\u5b66\u5bb6\u4e0d\u91c7\u7528\u6f5c\u5728\u7ed3\u679c\u6a21\u578b\uff0c\u751a\u81f3\u6ca1\u6709\u610f\u8bc6\u5230\uff0c\u8fd9\u4e2a\u7814\u7a76\u6839\u672c\u7684\u95ee\u9898\u5728\u4e8e\u7f3a\u5c11\u5bf9\u7167\u3002\u5f53\u7136\uff0c\u5982\u679c\u6211\u4eec\u80fd\u591f\u505a\u4e00\u4e2a\u968f\u673a\u5316\u7684\u5b9e\u9a8c\uff0c\u6709\u5904\u7406\u548c\u5bf9\u7167\u7ec4\uff0c\u90a3\u4e48\u56de\u5f52\u5206\u6790\u4e5f\u53ef\u80fd\u5f97\u5230\u5408\u7406\u7684\u7b54\u6848\u3002<\/section>\n<section>\uff083\uff09\u7edf\u8ba1\u5b66\u5bb6\u4e00\u548c\u4e8c\uff0c\u90fd\u53ef\u4ee5\u662f\u5bf9\u7684\u3002\u4ed6\u4eec\u7ed3\u8bba\u7684\u6b63\u786e\u6027\uff0c\u4f9d\u8d56\u4e8e\u4e0d\u540c\u7684\u5047\u5b9a\uff1b\u800c\u8fd9\u4e9b\u5047\u5b9a\u672c\u8eab\u662f\u4e0d\u53ef\u80fd\u88ab\u68c0\u9a8c\u7684\u3002<\/section>\n<section>\uff084\uff09\u5047\u5b9a\u00a0<span style=\"margin: 0px; padding: 1px 0px; outline: 0px; max-width: none; box-sizing: border-box !important; overflow-wrap: normal; display: inline-block; line-height: 0; text-align: left; font-size: 19.04px; float: none; direction: ltr; max-height: none; min-width: 0px; min-height: 0px; border: 0px initial initial;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mi&gt;Y&lt;\/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;\/mo&gt;&lt;mn&gt;0&lt;\/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;\/mo&gt;&lt;mo&gt;=&lt;\/mo&gt;&lt;mi&gt;X&lt;\/mi&gt;&lt;\/math&gt;\"><span aria-hidden=\"true\">Y(0)=X<\/span><span role=\"presentation\">Y(0)=X<\/span><\/span>\u00a0\u53ef\u4ee5\u51cf\u5f31\u5230\u00a0<span style=\"margin: 0px; padding: 1px 0px; outline: 0px; max-width: none; box-sizing: border-box !important; overflow-wrap: normal; display: inline-block; line-height: 0; text-align: left; font-size: 19.04px; float: none; direction: ltr; max-height: none; min-width: 0px; min-height: 0px; border: 0px initial initial;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mi&gt;Y&lt;\/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;\/mo&gt;&lt;mn&gt;0&lt;\/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;\/mo&gt;&lt;mo&gt;=&lt;\/mo&gt;&lt;mi&gt;X&lt;\/mi&gt;&lt;mo&gt;+&lt;\/mo&gt;&lt;mi&gt;u&lt;\/mi&gt;&lt;mo&gt;,&lt;\/mo&gt;&lt;mi&gt;E&lt;\/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;\/mo&gt;&lt;mi&gt;u&lt;\/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;\/mo&gt;&lt;mo&gt;=&lt;\/mo&gt;&lt;mn&gt;0&lt;\/mn&gt;&lt;mo&gt;,&lt;\/mo&gt;&lt;mi&gt;u&lt;\/mi&gt;&lt;mo&gt;&amp;#x22A5;&lt;\/mo&gt;&lt;mi&gt;G&lt;\/mi&gt;&lt;\/math&gt;\"><span aria-hidden=\"true\">Y(0)=X+u,E(u)=0,u\u22a5G<\/span><span role=\"presentation\">Y(0)=X+u,E(u)=0,u\u22a5G<\/span><\/span>\uff1b\u5047\u5b9a<span style=\"margin: 0px; padding: 1px 0px; outline: 0px; max-width: none; box-sizing: border-box !important; overflow-wrap: normal; display: inline-block; line-height: 0; word-spacing: normal; float: none; direction: ltr; max-height: none; min-width: 0px; min-height: 0px; border: 0px initial initial;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mi&gt;Y&lt;\/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;\/mo&gt;&lt;mn&gt;0&lt;\/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;\/mo&gt;&lt;mo&gt;=&lt;\/mo&gt;&lt;mi&gt;&amp;#x03B1;&lt;\/mi&gt;&lt;mo&gt;+&lt;\/mo&gt;&lt;mi&gt;b&lt;\/mi&gt;&lt;mi&gt;X&lt;\/mi&gt;&lt;\/math&gt;\"><span aria-hidden=\"true\"><span style=\"margin: 0px; padding: 1px 0px; outline: 0px; max-width: none; box-sizing: border-box !important; overflow-wrap: normal; display: inline-table; line-height: 0; text-align: left; font-size: 19.04px; float: none; direction: ltr; max-height: none; min-width: 0px; min-height: 0px; border: 0px initial initial;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mi&gt;Y&lt;\/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;\/mo&gt;&lt;mn&gt;0&lt;\/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;\/mo&gt;&lt;mo&gt;=&lt;\/mo&gt;&lt;mi&gt;&amp;#x03B1;&lt;\/mi&gt;&lt;mo&gt;+&lt;\/mo&gt;&lt;mi&gt;b&lt;\/mi&gt;&lt;mi&gt;X&lt;\/mi&gt;&lt;\/math&gt;\">Y(0)=\u03b1+bX<span role=\"presentation\">Y(0)=\u03b1+bX<\/span><\/span>\u00a0<\/span><span role=\"presentation\">Y(0)=\u03b1+bX<\/span><\/span>\u53ef\u4ee5\u51cf\u5f31\u5230<span style=\"margin: 0px; padding: 1px 0px; outline: 0px; max-width: none; box-sizing: border-box !important; overflow-wrap: normal; display: inline-block; line-height: 0; text-align: left; font-size: 19.04px; float: none; direction: ltr; max-height: none; min-width: 0px; min-height: 0px; border: 0px initial initial;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mi&gt;Y&lt;\/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;\/mo&gt;&lt;mn&gt;0&lt;\/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;\/mo&gt;&lt;mo&gt;=&lt;\/mo&gt;&lt;mi&gt;&amp;#x03B1;&lt;\/mi&gt;&lt;mo&gt;+&lt;\/mo&gt;&lt;mi&gt;b&lt;\/mi&gt;&lt;mi&gt;X&lt;\/mi&gt;&lt;mo&gt;+&lt;\/mo&gt;&lt;mi&gt;v&lt;\/mi&gt;&lt;mo&gt;,&lt;\/mo&gt;&lt;mi&gt;E&lt;\/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;\/mo&gt;&lt;mi&gt;v&lt;\/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;\/mo&gt;&lt;mo&gt;=&lt;\/mo&gt;&lt;mn&gt;0&lt;\/mn&gt;&lt;mo&gt;,&lt;\/mo&gt;&lt;mi&gt;v&lt;\/mi&gt;&lt;mo&gt;&amp;#x22A5;&lt;\/mo&gt;&lt;mi&gt;G&lt;\/mi&gt;&lt;\/math&gt;\"><span aria-hidden=\"true\">Y(0)=\u03b1+bX+v,E(v)=0,v\u22a5G<\/span><span role=\"presentation\">Y(0)=\u03b1+bX+v,E(v)=0,v\u22a5G<\/span><\/span>\u3002\u5f53\u7136\uff0c\u8fd9\u90fd\u662f\u7ec6\u679d\u672b\u8282\u7684\u95ee\u9898\u3002<\/section>\n<section>\uff085\uff09\u7edf\u8ba1\u5b66\u5bb6\u4e00\u548c\u4e8c\uff0c\u90fd\u662f\u9519\u7684\u3002\u4ed6\u4eec\u6709\u7ed3\u8bba\uff0c\u4f46\u662f\u5374\u4ece\u672a\u6e05\u695a\u5730\u9648\u8ff0\u7ed3\u8bba\u56de\u7b54\u7684\u662f\u4ec0\u4e48\u95ee\u9898\u3002<\/section>\n<section>\uff086\uff09R A Fisher \u5728\u5b9e\u9a8c\u8bbe\u8ba1\u4e2d\u63d0\u51fa\u4e86 ANCOVA\uff0c\u4f46\u662f\u8fd9\u4e2a\u65b9\u6cd5\u4e0d\u662f\u4e07\u80fd\u7684\u3002\u4e8b\u5b9e\u4e0a\uff0c\u8fd9\u4e2a\u65b9\u6cd5\u5bfc\u81f4\u7684\u95ee\u9898\uff0c\u6bd4\u5b83\u5e26\u6765\u7684\u529f\u7528\u66f4\u4e25\u91cd\uff1b\u8fd9\u70b9\u4ee5\u540e\u518d\u8bf4\u3002<\/section>\n<section><\/section>\n<section>\n<section>\n<section>\n<section>\n<section><\/section>\n<section><\/section>\n<section>\n<section><\/section>\n<\/section>\n<\/section>\n<section><strong>8. \u56e0\u679c\u63a8\u65ad\u7b80\u4ecb\u4e4b\u516b\uff1a<\/strong><\/p>\n<p><strong>\u5438\u70df\u662f\u5426\u5bfc\u81f4\u80ba\u764c\uff1fFisher versus Cornfield<\/strong><\/p>\n<\/section>\n<section>\n<section><\/section>\n<section><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<p>\u8fd9\u4e00\u8282\u4ecb\u7ecd\u4e00\u4e2a\u6709\u8da3\u7684\u5386\u53f2\u6027\u4f8b\u5b50\uff1a\u5438\u70df\u662f\u5426\u5bfc\u81f4\u80ba\u764c\uff1f\u4e3b\u8981\u6d89\u53ca\u7684\u4eba\u7269\u662f R A Fisher \u548c J Cornfield\u3002\u524d\u8005\u4f30\u8ba1\u4e0a\u8fd9\u4e2a\u7f51\u7ad9\u7684\u4eba\u90fd\u542c\u8fc7\uff0c\u540e\u8005\u5c31\u663e\u5f97\u6bd4\u8f83\u964c\u751f\u4e86\u3002\u4e8b\u5b9e\u4e0a\uff0cCornfield \u5728\u7edf\u8ba1\u3001\u751f\u7269\u7edf\u8ba1\u548c\u6d41\u884c\u75c5\u5b66\u90fd\u6709\u7740\u975e\u5e38\u91cd\u8981\u7684\u8d21\u732e\u3002\u6765\u81ea Wikipedia \u7684\u4e00\u53e5\u4ecb\u7ecd\uff1a\u201cHe was the R. A. Fisher Lecturer in 1973 and President of the American Statistical Association in 1974.\u201d \u867d\u7136 Cornfield \u548c Fisher \u5b66\u672f\u89c2\u70b9\u4e0d\u540c\uff08\u672c\u8282\u4ecb\u7ecd\uff09\uff0c\u4f46\u662f Cornfield \u8fd8\u662f\u5728 1973 \u5e74\u7ed9\u4e86 Fisher Lecture\u3002<\/p>\n<p>\u4e0b\u9762\u6211\u4eec\u5148\u4ecb\u7ecd Fisher \u548c Cornfield \u5173\u4e8e\u89c2\u5bdf\u6027\u7814\u7a76\u4e2d\u56e0\u679c\u63a8\u65ad\u7684\u4e24\u79cd\u89c2\u70b9\uff0c\u518d\u7ed9\u51fa\u6280\u672f\u6027\u7684\u7ec6\u8282\u3002<\/p>\n<h1><strong>\u4e00\u3001Cornfield \u6761\u4ef6\u6216\u8005 Cornfield \u4e0d\u7b49\u5f0f<\/strong><\/h1>\n<p><img decoding=\"async\" class=\"rich_pages wxw-img img_loading\" src=\"data:image\/gif;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAADUlEQVQImWNgYGBgAAAABQABh6FO1AAAAABJRU5ErkJggg==\" alt=\"\u56fe\u7247\" crossorigin=\"anonymous\" data-galleryid=\"\" data-ratio=\"1.0261282660332542\" data-type=\"jpeg\" data-w=\"421\" data-src=\"https:\/\/mmbiz.qpic.cn\/mmbiz_png\/wibWV1DB7tWIO90r3UsHjHlftibAW0QN6Hh0qmvnJrTOj8pHKlp0ib5gD5KaUkn2v4wCckMM5pFngBx3FzQYMKKng\/640?wx_fmt=jpeg\" \/><\/p>\n<section>\uff08\u56fe\u6ce8\uff1aR A Fisher\uff09<\/section>\n<section><\/section>\n<section>\u6211\u5148\u9648\u8ff0 Fisher \u7684\u89c2\u70b9\u3002\u7531\u4e8e Yule-Simpson Paradox \u7684\u5b58\u5728\uff0c\u5373\u4f7f\u6211\u4eec\u89c2\u6d4b\u5230\u5438\u70df\u548c\u80ba\u764c\u4e4b\u95f4\u7684\u6b63\u76f8\u5173\u5173\u7cfb\uff0c\u4e5f\u4e0d\u80fd\u65ad\u5b9a\u5b83\u4eec\u4e4b\u95f4\u6709\u56e0\u679c\u6027\u3002\u53ef\u80fd\u5b58\u5728\u4e00\u4e2a\u672a\u89c2\u6d4b\u7684\u57fa\u56e0\uff0c\u5b83\u65e2\u4f7f\u5f97\u67d0\u4e9b\u4eba\u66f4\u53ef\u80fd\u5438\u70df\uff0c\u53c8\u4f7f\u5f97\u8fd9\u4e9b\u4eba\u66f4\u53ef\u80fd\u60a3\u80ba\u764c\u3002\u56e0\u6b64\uff0c\u5373\u4f7f\u5438\u70df\u548c\u80ba\u764c\u6ca1\u6709\u56e0\u679c\u5173\u7cfb\uff0c\u8fd9\u4e2a\u672a\u89c2\u6d4b\u7684\u57fa\u56e0\u4e5f\u53ef\u80fd\u5bfc\u81f4\u5438\u70df\u548c\u80ba\u764c\u662f\u6b63\u76f8\u5173\u7684\u3002\u5173\u4e8e Yule-Simpson Paradox\uff0c\u8fd9\u4e00\u7cfb\u5217\u7684\u7b2c\u4e00\u7bc7\u6709\u4ecb\u7ecd\u3002Fisher \u7684\u89c2\u70b9\u53ef\u4ee5\u7528\u4e00\u4e2a\u6709\u5411\u65e0\u73af\u56fe\u00a0\uff08DAG\uff09\u00a0\u6765\u8868\u793a\uff1a<\/section>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-661\" src=\"https:\/\/aif.amtbbs.org\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-20.jpg\" width=\"303\" height=\"191\" alt=\"\u56fe\u7247\" srcset=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-20.jpg 303w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-20-300x189.jpg 300w\" sizes=\"auto, (max-width: 303px) 100vw, 303px\" \/><\/p>\n<section>\u56fe\u4e2d\uff0c\u5438\u70df\u5230\u80ba\u764c\u6ca1\u6709\u76f4\u63a5\u7684\u8fb9\uff0c\u56e0\u6b64\u5438\u70df\u5bf9\u80ba\u764c\u7684\u56e0\u679c\u4f5c\u7528\u662f\u00a0<span tabindex=\"0\" role=\"presentation\">0<\/span>\u3002\u4f46\u662f\u7531\u4e8e\u5b83\u4eec\u4e4b\u95f4\u5b58\u5728\u4e00\u4e2a\u5171\u540c\u539f\u56e0 \u201chidden gene\u201d\uff0c\u5b83\u4eec\u662f\u76f8\u5173\u7684\u3002\u6211\u4eec\u7528\u00a0<span tabindex=\"0\" role=\"presentation\">E<\/span>\u00a0\u8868\u793a\u662f\u5426\u5438\u70df\u00a0(<span tabindex=\"0\" role=\"presentation\">1=<\/span>\u00a0\u662f\uff0c<span tabindex=\"0\" role=\"presentation\">0=<\/span>\u5426)\uff1b<span tabindex=\"0\" role=\"presentation\">D\u00a0<\/span>\u8868\u793a\u662f\u5426\u60a3\u80ba\u764c\u00a0(<span tabindex=\"0\" role=\"presentation\">1=<\/span>\u662f\uff0c<span tabindex=\"0\" role=\"presentation\">0=<\/span>\u5426)\uff1b<span tabindex=\"0\" role=\"presentation\">U<\/span>\u00a0\u8868\u793a\u662f\u5426\u6709\u67d0\u79cd\u57fa\u56e0\u00a0(<span tabindex=\"0\" role=\"presentation\">1=<\/span>\u00a0\u662f\uff0c<span tabindex=\"0\" role=\"presentation\">0=<\/span>\u00a0\u5426)\u3002\u8fd9\u4e2a\u7b26\u53f7\u7cfb\u7edf\u5728\u6d41\u884c\u75c5\u5b66\u6bd4\u8f83\u5e38\u7528\uff0c\u56e0\u4e3a\u00a0<span tabindex=\"0\" role=\"presentation\">E<\/span>\u00a0\u8868\u793a\u66b4\u9732\u4e0e\u5426\u00a0\uff08exposure\uff09\uff0c<span tabindex=\"0\" role=\"presentation\">D<\/span>\u8868\u793a\u75be\u75c5\u00a0\uff08disease\uff09\uff0c<span tabindex=\"0\" role=\"presentation\">U<\/span>\u8868\u793a\u672a\u89c2\u6d4b\u7684\u6df7\u6742\u56e0\u7d20\u00a0\uff08unobservable confounder\uff09\u3002\u5728 Fisher \u7684\u65f6\u4ee3\uff0c\u7814\u7a76\u8005\u901a\u8fc7\u6536\u96c6\u7684\u5927\u91cf\u6570\u636e\uff0c\u5f97\u5230\u5438\u70df\u5bf9\u4e8e\u80ba\u764c\u7684\u76f8\u5bf9\u98ce\u9669\uff08relative risk\uff1b\u6216\u79f0\u98ce\u9669\u6bd4\uff0crisk ratio\uff1b\u90fd\u7b80\u5199\u6210\u00a0<span tabindex=\"0\" role=\"presentation\">RR<\/span>\uff09\u662f<\/section>\n<section><\/section>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-662\" src=\"https:\/\/aif.amtbbs.org\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-44.png\" width=\"473\" height=\"88\" alt=\"\u56fe\u7247\" srcset=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-44.png 473w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-44-300x56.png 300w\" sizes=\"auto, (max-width: 473px) 100vw, 473px\" \/><\/p>\n<section>\u6d41\u884c\u75c5\u5b66\u5bb6\u5173\u5fc3\u8fd9\u4e2a\u00a0<span tabindex=\"0\" role=\"presentation\">RRED<\/span>\u00a0\u662f\u5426\u8868\u660e\u4e86\u5438\u70df\u548c\u80ba\u764c\u7684\u56e0\u679c\u5173\u7cfb\u3002Fisher \u8868\u793a\u5426\u5b9a\u3002\u4ece\u4e00\u4e2a\u60b2\u89c2\u7684\u89d2\u5ea6\u6765\u8bb2\uff0c\u6211\u4eec\u786e\u5b9e\u4e0d\u80fd\u4ece\u76f8\u5173\u5173\u7cfb\u5f97\u5230\u56e0\u679c\u6027\uff1bFisher \u5982\u679c\u8868\u793a\u6000\u7591\uff0c\u5047\u5b9a\u6709\u4e00\u4e2a\u672a\u89c2\u6d4b\u7684\u57fa\u56e0\uff0c\u4e5f\u662f\u65e0\u53ef\u53cd\u9a73\u7684\u3002Fisher \u7684\u8fd9\u4e2a\u8bf4\u6cd5\u6709\u65f6\u4e5f\u88ab\u79f0\u4e3a \u201c\u5171\u540c\u539f\u56e0\u201d \u5047\u8bf4\u3002Cornfield \u5219\u91c7\u53d6\u4e86\u4e00\u4e2a\u4e0d\u592a\u60b2\u89c2\u7684\u89d2\u5ea6\u3002\u4ed6\u95ee\uff1a\u5982\u679c Fisher \u7684 \u201c\u5171\u540c\u539f\u56e0\u201d \u5047\u8bf4\u662f\u5bf9\u7684\uff0c\u90a3\u4e48\u00a0<span tabindex=\"0\" role=\"presentation\">E<\/span>\u00a0\u548c\u00a0<span tabindex=\"0\" role=\"presentation\">U<\/span>\u00a0\u4e4b\u95f4\u7684\u76f8\u5173\u5173\u7cfb\u9700\u8981\u591a\u5f3a\uff0c\u624d\u80fd\u5bfc\u81f4\u00a0<span tabindex=\"0\" role=\"presentation\">RRED=9<\/span>\uff0c\u5373 \u201c\u5438\u70df\u60a3\u80ba\u764c\u201d \u662f\u201c\u4e0d\u5438\u70df\u60a3\u80ba\u764c\u201d\u7684\u98ce\u9669\u7684\u00a0<span tabindex=\"0\" role=\"presentation\">99<\/span>\u00a0\u500d\u5462\uff1f\u5982\u679c\u00a0<span tabindex=\"0\" role=\"presentation\">E<\/span>\u548c\u00a0<span tabindex=\"0\" role=\"presentation\">U<\/span>\u4e4b\u95f4\u7684\u76f8\u5173\u5173\u7cfb\u5f3a\u5230\u4e0d\u5177\u6709\u751f\u7269\u5b66\u610f\u4e49\uff08<span tabindex=\"0\" role=\"presentation\">E<\/span>\u4e0e\u00a0<span tabindex=\"0\" role=\"presentation\">U<\/span>\u00a0\u7684\u76f8\u5bf9\u98ce\u9669\u503c\u5927\u5f97\u5728\u73b0\u5b9e\u4e2d\u4e0d\u592a\u53ef\u80fd\uff09\uff0c\u90a3\u4e48 Fisher \u7684 \u201c\u5171\u540c\u539f\u56e0\u201d \u5047\u8bf4\u5c31\u4e0d\u6210\u7acb\uff0c\u66f4\u5927\u7684\u53ef\u80fd\u6027\u662f\u5438\u70df\u00a0<span tabindex=\"0\" role=\"presentation\">E\u00a0<\/span>\u5bf9\u80ba\u764c\u00a0<span tabindex=\"0\" role=\"presentation\">D<\/span>\u00a0\u6709\u56e0\u679c\u4f5c\u7528\u3002<\/section>\n<section><\/section>\n<p>\u90a3\u4e48 Cornfield \u662f\u5982\u4f55\u6709\u529b\u53cd\u9a73 Fisher \u7684\u89c2\u70b9\u7684\u5462\uff1f<\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-663\" src=\"https:\/\/aif.amtbbs.org\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-21.jpg\" width=\"184\" height=\"273\" alt=\"\u56fe\u7247\" \/><\/p>\n<section>\uff08\u56fe\u6ce8\uff1aJ Cornfield\uff09<\/section>\n<section>Cornfield \u901a\u8fc7\u7b80\u5355\u7684\u6570\u5b66\u8bc1\u660e\uff0c\u5f97\u5230\u4e86\u5982\u4e0b\u7684\u4e0d\u7b49\u5f0f\uff0c\u6587\u732e\u4e2d\u4e5f\u79f0\u4e3a Cornfield \u4e0d\u7b49\u5f0f\uff1a<\/section>\n<section><\/section>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-664\" src=\"https:\/\/aif.amtbbs.org\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-45.png\" width=\"209\" height=\"41\" alt=\"\u56fe\u7247\" \/><\/p>\n<section><\/section>\n<p>\u4e5f\u5c31\u662f\u8bf4\uff0c\u5982\u679c Fisher \u7684 \u201c\u5171\u540c\u539f\u56e0\u201d \u5047\u8bf4\u6210\u7acb\uff0c\u90a3\u4e48\u00a0<span tabindex=\"0\" role=\"presentation\">E<\/span>\u00a0\u548c\u00a0<span tabindex=\"0\" role=\"presentation\">U<\/span>\u00a0\u4e4b\u95f4\u7684\u00a0<span tabindex=\"0\" role=\"presentation\">RR<\/span>\u00a0\u5fc5\u5c06\u5927\u4e8e\u00a0<span tabindex=\"0\" role=\"presentation\">E<\/span>\u00a0\u548c\u00a0<span tabindex=\"0\" role=\"presentation\">D<\/span>\u00a0\u4e4b\u95f4\u7684\u00a0<span tabindex=\"0\" role=\"presentation\">RR<\/span>\u3002\u5728\u5438\u70df\u548c\u80ba\u764c\u7684\u4f8b\u5b50\u4e2d\uff0c<span tabindex=\"0\" role=\"presentation\">RREU\u22659<\/span>\u3002<span tabindex=\"0\" role=\"presentation\">RREU\u22659<\/span>\uff0c\u5373\u00a0<span tabindex=\"0\" role=\"presentation\">P(U=1|E=1)\/P(U=1|E=0)\u22659<\/span>\uff0c\u76f4\u89c2\u89e3\u91ca\u5c31\u662f \u201c\u5438\u70df\u65f6\u6709\u67d0\u4e2a\u57fa\u56e0\u00a0<span tabindex=\"0\" role=\"presentation\">U<\/span>\u00a0\u5b58\u5728\u201d \u7684\u6982\u7387\u662f \u201c\u4e0d\u5438\u70df\u65f6\u6709\u67d0\u4e2a\u57fa\u56e0\u00a0<span tabindex=\"0\" role=\"presentation\">U<\/span>\u00a0\u5b58\u5728\u201d \u7684\u6982\u7387\u7684\u00a0<span tabindex=\"0\" role=\"presentation\">9<\/span>\u00a0\u500d\u591a\u3002\u6839\u636e Cornfield \u8fdb\u4e00\u6b65\u7684\u903b\u8f91\uff0c\u7531\u4e8e\u5438\u70df\u66f4\u591a\u7684\u662f\u4e00\u4e2a\u793e\u4f1a\u6027\u7684\u884c\u4e3a\uff0c\u5f88\u96be\u60f3\u8c61\u5438\u70df\u7684\u884c\u4e3a\u80fd\u591f\u5bf9\u4e8e\u67d0\u4e2a\u57fa\u56e0\u7684\u5b58\u5728\u4e0e\u5426\u6709\u7740\u00a0<span tabindex=\"0\" role=\"presentation\">9<\/span>\u00a0\u500d\u7684\u9884\u6d4b\u80fd\u529b\u3002\u6211\u524d\u6bb5\u65f6\u95f4\u95ee\u8eab\u8fb9\u4e00\u4e2a\u751f\u7269\u7684 PhD\uff0c\u4f60\u89c9\u5f97\u00a0<span tabindex=\"0\" role=\"presentation\">RREU\u22659<\/span>\u00a0\u53ef\u80fd\u5417\uff1f\u4ed6\u7684\u56de\u7b54\u662f\u4e0d\u592a\u53ef\u80fd\uff0c\u7406\u7531\u4e5f\u662f\u8bf4\uff0c\u5438\u70df\u66f4\u591a\u7684\u51b3\u5b9a\u4e8e\u793e\u4f1a\u7ecf\u6d4e\u5730\u4f4d\u3001\u5bb6\u5ead\u80cc\u666f\u7b49\u53d8\u91cf\uff0c\u548c\u57fa\u56e0\u4e5f\u8bb8\u6709\u5173\u7cfb\uff0c\u4f46\u662f\u4e0d\u4f1a\u5f3a\u5230\u00a0<span tabindex=\"0\" role=\"presentation\">RREU\u22659<\/span>\u00a0\u7684\u7a0b\u5ea6\u3002Cornfield et al. (1959) \u7684\u539f\u8bdd\u662f\uff1a<\/p>\n<blockquote><p>\u2026 if cigarette smokers have 9 times the risk of nonsmokers for developing lung cancer, and this is not because cigarette smoke is a causal agent, but only because cigarette smokers produce hormone X, then the proportion of hormone-X producers among cigarette smokers must be at least 9 times greater than nonsmokers. If the relative prevalence of hormone-X-producers is considerably less than ninefold, then hormone-X cannot account for the magnitude of the apparent effect.<\/p><\/blockquote>\n<section>\u5982\u679c\u6211\u4eec\u76f8\u4fe1 Cornfield \u7684\u903b\u8f91\uff0c\u00a0<span tabindex=\"0\" role=\"presentation\">RREU\u22659<\/span>\u00a0\u00a0\u5728\u751f\u7269\u5b66\u610f\u4e49\u4e0a\u4e0d\u592a\u53ef\u80fd\uff0c\u90a3\u4e48 Fisher \u7684 \u201c\u5171\u540c\u539f\u56e0\u201d \u5047\u8bf4\u5c31\u4e0d\u6210\u7acb\uff0c\u5438\u70df\u5bf9\u80ba\u764c\u7684\u786e\u5b58\u5728\u56e0\u679c\u4f5c\u7528\uff1b\u53cd\u6620\u5230\u4e0a\u9762\u7684DAG \u4e0a\uff0c\u5438\u70df\u00a0<span style=\"margin: 0px; padding: 1px 0px; outline: 0px; max-width: none; box-sizing: border-box !important; overflow-wrap: normal; display: inline-block; line-height: 0; word-spacing: normal; float: none; direction: ltr; max-height: none; min-width: 0px; min-height: 0px; border: 0px initial initial;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mi&gt;E&lt;\/mi&gt;&lt;\/math&gt;\"><span aria-hidden=\"true\">E<\/span><span role=\"presentation\">E<\/span><\/span>\u00a0\u5230\u80ba\u764c\u00a0<span style=\"margin: 0px; padding: 1px 0px; outline: 0px; max-width: none; box-sizing: border-box !important; overflow-wrap: normal; display: inline-block; line-height: 0; word-spacing: normal; float: none; direction: ltr; max-height: none; min-width: 0px; min-height: 0px; border: 0px initial initial;\" tabindex=\"0\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mi&gt;D&lt;\/mi&gt;&lt;\/math&gt;\"><span aria-hidden=\"true\">D<\/span><span role=\"presentation\">D<\/span><\/span>\u00a0\u6709\u4e00\u6761\u76f4\u63a5\u7684\u8fb9\u3002<\/section>\n<section><\/section>\n<section>Cornfield \u7684\u8fd9\u9879\u7b80\u5355\u7814\u7a76\uff0c\u5f00\u59cb\u4e86\u6d41\u884c\u75c5\u5b66\u548c\u7edf\u8ba1\u5b66\u4e2d\u654f\u611f\u6027\u5206\u6790\u7684\u7814\u7a76\uff1b\u6bd4\u5982 Rubin \u548c Rosenbaum \u5f88\u591a\u5de5\u4f5c\u90fd\u662f\u5728 Cornfield \u7684\u542f\u53d1\u4e0b\u505a\u51fa\u6765\u7684\u3002\u7b80\u5355\u5730\u8bf4\uff0c\u654f\u611f\u6027\u5206\u6790\uff0c\u5c31\u662f\u5728\u671d\u7740 Yule-Simpson Paradox \u7684\u53cd\u65b9\u5411\u8fdb\u884c\u7684\uff1a\u590d\u6742\u867d\u7136\u603b\u662f\u5b58\u5728\uff0c\u4f46\u662f\u6211\u4eec\u76f8\u4fe1\u8fd9\u4e2a\u4e16\u754c\u5e76\u4e0d\u662f\u75af\u72c2\u7684\u590d\u6742\u3002<\/section>\n<section><\/section>\n<p><strong>\u4e8c\u3001\u6280\u672f\u7ec6\u8282<\/strong><\/p>\n<section>\u8fd9\u4e00\u90e8\u5206\u6211\u4eec\u7ed9\u51fa Cornfield \u4e0d\u7b49\u5f0f\u7684\u8bc1\u660e\u3002\u867d\u7136\u8bc1\u660e\u4e0d\u96be\uff0c\u4f46\u662f\u60f3\u60f3 Cornfield \u4e8e 1959 \u5e74\u7528\u8fd9\u6837\u4e00\u4e2a\u7b80\u5355\u7684\u4e0d\u7b49\u5f0f\u6765\u53cd\u9a73 Fisher\uff0c\u5c31\u89c9\u5f97\u5b83\u7684\u5386\u53f2\u610f\u4e49\u8fd8\u662f\u4e0d\u5c0f\u7684\u3002\u5f53\u7136\u4e0d\u5173\u5fc3\u6280\u672f\u7ec6\u8282\u7684\u8bfb\u8005\uff0c\u53ef\u4ee5\u76f4\u63a5\u5ffd\u7565\u672c\u8282\u3002\u5173\u5fc3\u6280\u672f\u7ec6\u8282\u7684\u8bfb\u8005\uff0c\u4e0b\u9762\u7684\u8bc1\u660e\u867d\u7136\u5197\u957f\uff0c\u4f46\u662f\u53ea\u7528\u5230\u975e\u5e38\u521d\u7b49\u7684\u6570\u5b66\uff08\u4e5f\u8bb8\u5b83\u53ef\u4ee5\u4f5c\u4e3a\u4e00\u9053\u521d\u7b49\u6982\u7387\u8bba\u7684\u4e60\u9898\uff09\u3002<\/section>\n<section>\u4e3a\u4e86\u7b80\u5316\u8bc1\u660e\uff0c\u6211\u4eec\u5f15\u8fdb\u4e00\u4e9b\u8bb0\u53f7\uff1a<\/section>\n<section><\/section>\n<section><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-665\" src=\"https:\/\/aif.amtbbs.org\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-46.png\" width=\"753\" height=\"117\" alt=\"\u56fe\u7247\" srcset=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-46.png 753w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-46-300x47.png 300w\" sizes=\"auto, (max-width: 753px) 100vw, 753px\" \/><\/section>\n<p>\u4e0d\u59a8\u5047\u8bbe\u00a0<span tabindex=\"0\" role=\"presentation\">RRED\u22651<\/span>\u00a0\u5e76\u4e14\u00a0<span tabindex=\"0\" role=\"presentation\">RREU\u22651<\/span>\uff1b\u82e5\u4e0d\u6210\u7acb\uff0c\u6211\u4eec\u603b\u53ef\u4ee5\u91cd\u65b0\u5bf9\u8fd9\u4e9b\u4e8c\u503c\u53d8\u91cf\u7684\u00a0<span tabindex=\"0\" role=\"presentation\">0<\/span>\u00a0\u548c\u00a0<span tabindex=\"0\" role=\"presentation\">1<\/span>\u00a0\u7c7b\u8fdb\u884c\u91cd\u65b0\u5b9a\u4e49\u3002\u9996\u5148\uff0c\u6211\u4eec\u5728\u6761\u4ef6\u72ec\u7acb\u6027\u00a0<span tabindex=\"0\" role=\"presentation\">E\u22a5D|U<\/span>\u00a0\u4e0b\u5f97\u5230\u00a0<span tabindex=\"0\" role=\"presentation\">RRED<\/span>\u7684\u7b49\u4ef7\u8868\u793a\uff1a<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-666\" src=\"https:\/\/aif.amtbbs.org\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-47.png\" width=\"849\" height=\"342\" alt=\"\u56fe\u7247\" srcset=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-47.png 849w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-47-300x121.png 300w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-47-768x309.png 768w\" sizes=\"auto, (max-width: 849px) 100vw, 849px\" \/><\/p>\n<p>\u6761\u4ef6\u00a0<span tabindex=\"0\" role=\"presentation\">RREU\u22651<\/span>\u7b49\u4ef7\u4e8e\u00a0<span tabindex=\"0\" role=\"presentation\">f1\u2265f0<\/span>\uff0c\u56e0\u6b64\uff0c\u4e0a\u9762\u00a0<span tabindex=\"0\" role=\"presentation\">RRED<\/span>\u662f\u5173\u4e8e\u00a0<span tabindex=\"0\" role=\"presentation\">RRUD<\/span>\u7684\u5355\u8c03\u9012\u589e\u51fd\u6570\u3002\u8fdb\u4e00\u6b65\uff0c<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-667\" src=\"https:\/\/aif.amtbbs.org\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-48.png\" width=\"628\" height=\"74\" alt=\"\u56fe\u7247\" srcset=\"https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-48.png 628w, https:\/\/aiforumimage.oss-cn-shanghai.aliyuncs.com\/wp-content\/uploads\/2021\/09\/4ffce04d92a4d6cb21c1494cdfcd6dc1-48-300x35.png 300w\" sizes=\"auto, (max-width: 628px) 100vw, 628px\" \/><\/p>\n<section>\u7531\u6b64\uff0cCornfield \u4e0d\u7b49\u5f0f\u5f97\u8bc1\u3002<\/section>\n<section><\/section>\n<section>\n<section>\n<section><strong>\u53c2\u8003\u6587\u732e<\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n<section>\n<section>\n<section>\n<section>\n<section><\/section>\n<ol class=\"list-paddingleft-2\">\n<li>\n<section>Bickel, P. J. and Hammel, E. A. and O\u2019Connell, J. W. (1975) Sex bias in graduate admissions: Data from Berkeley. Science, 187, 398-404.<\/section>\n<\/li>\n<li>\n<section>Pearl, J. (2000) Causality: models, reasoning, and inference. Cambridge University Press\u3002<\/section>\n<\/li>\n<li>\n<section>Rosenbaum, P.R. and Rubin, D.B. (1983) The central role of the propensity score in observational studies for causal effects. Biometrika, 70, 41-55.<\/section>\n<\/li>\n<li>\n<section>Rothman, K., Greenland, S. and Lash, T. L. \u00a0(2008) Modern Epidemiology. Lippincott Williams &amp; Wilkins.<\/section>\n<\/li>\n<li>\n<section>Neyman, J. (1923) On the application of probability theory to agricultural experiments. Essay on principles. Section 9. reprint in Statistical Science. 5, 465-472.<\/section>\n<\/li>\n<li>\n<section>Pearl, J. (1995) Causal diagrams for empirical research. Biometrika, 82, 669-688.<\/section>\n<\/li>\n<li>\n<section>Pearl, J. (2000) Causality: models, reasoning, and inference. Cambridge University Press\u3002<\/section>\n<\/li>\n<li>\n<section>Rubin, D.B. (1978) Bayesian inference for causal effects: The role of randomization. The Annals of Statistics, 6, 34-58.<\/section>\n<\/li>\n<li>\n<section>Neyman, J. (1923) On the application of probability theory to agricultural experiments. Essay on principles. Section 9. reprint in Statistical Science. 5, 465-472. with discussion by Donald Rubin.<\/section>\n<\/li>\n<li>\n<section>Rosenbaum, P. R. and Rubin, D. B. (1983) The central role of the propensity score in observational studies for causal effects. Biometrika, 70, 41-55.<\/section>\n<\/li>\n<li>\n<section>Rubin, D. B. (1976) Inference and\u00a0missing data (with discussion). Biometrika, 63, 581-592.<\/section>\n<\/li>\n<li>\n<section>Rubin, D. B. (1978) Bayesian inference for causal effects: The role of randomization. The Annals of Statistics, 6, 34-58.<\/section>\n<\/li>\n<li>\n<section>Wooldridge, J. M. (2002) Econometric analysis of cross section and panel data. The MIT press.<\/section>\n<\/li>\n<li>\n<section>Lord FM. A paradox in the interpretation of group comparisons. Psychol Bull. 1967;68:304\u20135. doi: 10.1037\/h0025105.<\/section>\n<\/li>\n<li>\n<section>Holland, P.W., Rubin, D.B. (1983). On Lord\u2019s paradox. In: Wainer, H., Messick, S. (Eds.), Principals of Modern Psychological Measurement. Lawrence Erlbaum Associates, Hillsdale, NJ, pp. 3\u201325.<\/section>\n<\/li>\n<li>\n<section>Cornfield \u6700\u65e9\u7684\u8bba\u6587\u53d1\u8868\u4e8e 1959 \u5e74\uff1b\u7531\u4e8e\u5b83\u7684\u91cd\u8981\u6027\uff0c\u8fd9\u7bc7\u6587\u7ae0\u53c8\u5728 2009 \u5e74\u91cd\u5370\u4e86\u4e00\u6b21\uff0850 \u5468\u5e74\u7eaa\u5ff5\uff09\u3002\u4e8e\u662f\u53c2\u8003\u6587\u732e\u6709\u4e24\u7bc7\uff0c\u5b83\u4eec\u662f\u4e00\u6837\u7684\uff1b\u4e0d\u8fc7\u540e\u8005\u591a\u4e86\u5f88\u591a\u540d\u4eba\u7684\u8ba8\u8bba\u3002<\/section>\n<section>Cornfield J et al. Smoking and lung cancer: recent evidence and a discussion of some questions. JNCI 1959;22:173-203.<\/section>\n<section>Cornfield J et al. Smoking and lung cancer: recent evidence and a discussion of some questions. Int J Epidemiol 2009;38:1175-91.\uff08\u672c\u6587\u9080\u8bf7\u4e86 David R Cox \u548c Joel B Greenhouse \u7b49\u4eba\u8ba8\u8bba\u3002\uff09<\/section>\n<\/li>\n<li>\n<section>\u6700\u8fd1 Ding and VanderWeele \u91cd\u65b0\u56de\u8bbf\u4e86\u8fd9\u4e2a\u7ecf\u5178\u95ee\u9898\uff0c\u7ed9\u51fa\u4e86\u66f4\u52a0\u5e7f\u6cdb\u7684\u7ed3\u679c\u3002<\/section>\n<section>Ding, Peng and Vanderweele, Tyler J. (2014). Generalized Cornfield conditions for the risk difference, Biometrika, 101:4, 971-977.\u00a0https:\/\/doi.org\/10.1093\/biomet\/asu030<\/section>\n<\/li>\n<\/ol>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<section>\n<section>\uff08\u53c2\u8003\u6587\u732e\u53ef<strong>\u4e0a\u4e0b\u6ed1\u52a8<\/strong>\u67e5\u770b\uff09<\/p>\n<\/section>\n<\/section>\n<section><\/section>\n<div class=\"pvc_clear\"><\/div>\n<p id=\"pvc_stats_617\" class=\"pvc_stats total_only  \" data-element-id=\"617\" style=\"\"><i class=\"pvc-stats-icon medium\" aria-hidden=\"true\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" version=\"1.0\" viewBox=\"0 0 502 315\" preserveAspectRatio=\"xMidYMid meet\"><g transform=\"translate(0,332) scale(0.1,-0.1)\" fill=\"\" stroke=\"none\"><path d=\"M2394 3279 l-29 -30 -3 -207 c-2 -182 0 -211 15 -242 39 -76 157 -76 196 0 15 31 17 60 15 243 l-3 209 -33 29 c-26 23 -41 29 -80 29 -41 0 -53 -5 -78 -31z\"\/><path d=\"M3085 3251 c-45 -19 -58 -50 -96 -229 -47 -217 -49 -260 -13 -295 52 -53 146 -42 177 20 16 31 87 366 87 410 0 70 -86 122 -155 94z\"\/><path d=\"M1751 3234 c-13 -9 -29 -31 -37 -50 -12 -29 -10 -49 21 -204 19 -94 39 -189 45 -210 14 -50 54 -80 110 -80 34 0 48 6 76 34 21 21 34 44 34 59 0 14 -18 113 -40 219 -37 178 -43 195 -70 221 -36 32 -101 37 -139 11z\"\/><path d=\"M1163 3073 c-36 -7 -73 -59 -73 -102 0 -56 133 -378 171 -413 34 -32 83 -37 129 -13 70 36 67 87 -16 290 -86 209 -89 214 -129 231 -35 14 -42 15 -82 7z\"\/><path d=\"M3689 3066 c-15 -9 -33 -30 -42 -48 -48 -103 -147 -355 -147 -375 0 -98 131 -148 192 -74 13 15 57 108 97 206 80 196 84 226 37 273 -30 30 -99 39 -137 18z\"\/><path d=\"M583 2784 c-38 -19 -67 -74 -58 -113 9 -42 211 -354 242 -373 16 -10 45 -18 66 -18 51 0 107 52 107 100 0 39 -1 41 -124 234 -80 126 -108 162 -133 173 -41 17 -61 16 -100 -3z\"\/><path d=\"M4250 2784 c-14 -9 -74 -91 -133 -183 -95 -150 -107 -173 -107 -213 0 -55 33 -94 87 -104 67 -13 90 8 211 198 130 202 137 225 78 284 -27 27 -42 34 -72 34 -22 0 -50 -8 -64 -16z\"\/><path d=\"M2275 2693 c-553 -48 -1095 -270 -1585 -649 -135 -104 -459 -423 -483 -476 -23 -49 -22 -139 2 -186 73 -142 361 -457 571 -626 285 -228 642 -407 990 -497 242 -63 336 -73 660 -74 310 0 370 5 595 52 535 111 1045 392 1455 803 122 121 250 273 275 326 19 41 19 137 0 174 -41 79 -309 363 -465 492 -447 370 -946 591 -1479 653 -113 14 -422 18 -536 8z m395 -428 c171 -34 330 -124 456 -258 112 -119 167 -219 211 -378 27 -96 24 -300 -5 -401 -72 -255 -236 -447 -474 -557 -132 -62 -201 -76 -368 -76 -167 0 -236 14 -368 76 -213 98 -373 271 -451 485 -162 444 86 934 547 1084 153 49 292 57 452 25z m909 -232 c222 -123 408 -262 593 -441 76 -74 138 -139 138 -144 0 -16 -233 -242 -330 -319 -155 -123 -309 -223 -461 -299 l-81 -41 32 46 c18 26 49 83 70 128 143 306 141 649 -6 957 -25 52 -61 116 -79 142 l-34 47 45 -20 c26 -10 76 -36 113 -56z m-2057 25 c-40 -58 -105 -190 -130 -263 -110 -324 -59 -707 132 -981 25 -35 42 -64 37 -64 -19 0 -241 119 -326 174 -188 122 -406 314 -532 468 l-58 71 108 103 c185 178 428 349 672 473 66 33 121 60 123 61 2 0 -10 -19 -26 -42z\"\/><path d=\"M2375 1950 c-198 -44 -350 -190 -395 -379 -18 -76 -8 -221 19 -290 114 -284 457 -406 731 -260 98 52 188 154 231 260 27 69 37 214 19 290 -38 163 -166 304 -326 360 -67 23 -215 33 -279 19z\"\/><\/g><\/svg><\/i> <img loading=\"lazy\" decoding=\"async\" width=\"16\" height=\"16\" alt=\"Loading\" src=\"https:\/\/aif.amtbbs.org\/wp-content\/plugins\/page-views-count\/ajax-loader-2x.gif\" border=0 \/><\/p>\n<div class=\"pvc_clear\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u5bfc\u8bed \u63a8\u65ad\u56e0\u679c\u5173\u7cfb\uff0c\u662f\u4eba\u7c7b\u601d\u60f3\u53f2\u4e0e\u79d1\u5b66\u53f2\u4e0a\u7684\u91cd\u8981\u4e3b\u9898\u3002\u73b0\u4ee3\u56e0\u679c\u63a8\u65ad\u7684\u7814\u7a76\uff0c\u59cb\u4e8e\u7ea6\u5c14-\u8f9b\u666e\u68ee\u6096\u8bba\uff0c\u7ecf\u7531\u9c81\u5bbe\u56e0\u679c\u6a21 [&hellip;]<\/p>\n<div class=\"pvc_clear\"><\/div>\n<p id=\"pvc_stats_617\" class=\"pvc_stats total_only  \" data-element-id=\"617\" style=\"\"><i class=\"pvc-stats-icon medium\" aria-hidden=\"true\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" version=\"1.0\" viewBox=\"0 0 502 315\" preserveAspectRatio=\"xMidYMid meet\"><g transform=\"translate(0,332) scale(0.1,-0.1)\" fill=\"\" stroke=\"none\"><path d=\"M2394 3279 l-29 -30 -3 -207 c-2 -182 0 -211 15 -242 39 -76 157 -76 196 0 15 31 17 60 15 243 l-3 209 -33 29 c-26 23 -41 29 -80 29 -41 0 -53 -5 -78 -31z\"\/><path d=\"M3085 3251 c-45 -19 -58 -50 -96 -229 -47 -217 -49 -260 -13 -295 52 -53 146 -42 177 20 16 31 87 366 87 410 0 70 -86 122 -155 94z\"\/><path d=\"M1751 3234 c-13 -9 -29 -31 -37 -50 -12 -29 -10 -49 21 -204 19 -94 39 -189 45 -210 14 -50 54 -80 110 -80 34 0 48 6 76 34 21 21 34 44 34 59 0 14 -18 113 -40 219 -37 178 -43 195 -70 221 -36 32 -101 37 -139 11z\"\/><path d=\"M1163 3073 c-36 -7 -73 -59 -73 -102 0 -56 133 -378 171 -413 34 -32 83 -37 129 -13 70 36 67 87 -16 290 -86 209 -89 214 -129 231 -35 14 -42 15 -82 7z\"\/><path d=\"M3689 3066 c-15 -9 -33 -30 -42 -48 -48 -103 -147 -355 -147 -375 0 -98 131 -148 192 -74 13 15 57 108 97 206 80 196 84 226 37 273 -30 30 -99 39 -137 18z\"\/><path d=\"M583 2784 c-38 -19 -67 -74 -58 -113 9 -42 211 -354 242 -373 16 -10 45 -18 66 -18 51 0 107 52 107 100 0 39 -1 41 -124 234 -80 126 -108 162 -133 173 -41 17 -61 16 -100 -3z\"\/><path d=\"M4250 2784 c-14 -9 -74 -91 -133 -183 -95 -150 -107 -173 -107 -213 0 -55 33 -94 87 -104 67 -13 90 8 211 198 130 202 137 225 78 284 -27 27 -42 34 -72 34 -22 0 -50 -8 -64 -16z\"\/><path d=\"M2275 2693 c-553 -48 -1095 -270 -1585 -649 -135 -104 -459 -423 -483 -476 -23 -49 -22 -139 2 -186 73 -142 361 -457 571 -626 285 -228 642 -407 990 -497 242 -63 336 -73 660 -74 310 0 370 5 595 52 535 111 1045 392 1455 803 122 121 250 273 275 326 19 41 19 137 0 174 -41 79 -309 363 -465 492 -447 370 -946 591 -1479 653 -113 14 -422 18 -536 8z m395 -428 c171 -34 330 -124 456 -258 112 -119 167 -219 211 -378 27 -96 24 -300 -5 -401 -72 -255 -236 -447 -474 -557 -132 -62 -201 -76 -368 -76 -167 0 -236 14 -368 76 -213 98 -373 271 -451 485 -162 444 86 934 547 1084 153 49 292 57 452 25z m909 -232 c222 -123 408 -262 593 -441 76 -74 138 -139 138 -144 0 -16 -233 -242 -330 -319 -155 -123 -309 -223 -461 -299 l-81 -41 32 46 c18 26 49 83 70 128 143 306 141 649 -6 957 -25 52 -61 116 -79 142 l-34 47 45 -20 c26 -10 76 -36 113 -56z m-2057 25 c-40 -58 -105 -190 -130 -263 -110 -324 -59 -707 132 -981 25 -35 42 -64 37 -64 -19 0 -241 119 -326 174 -188 122 -406 314 -532 468 l-58 71 108 103 c185 178 428 349 672 473 66 33 121 60 123 61 2 0 -10 -19 -26 -42z\"\/><path d=\"M2375 1950 c-198 -44 -350 -190 -395 -379 -18 -76 -8 -221 19 -290 114 -284 457 -406 731 -260 98 52 188 154 231 260 27 69 37 214 19 290 -38 163 -166 304 -326 360 -67 23 -215 33 -279 19z\"\/><\/g><\/svg><\/i> <img loading=\"lazy\" decoding=\"async\" width=\"16\" height=\"16\" alt=\"Loading\" src=\"https:\/\/aif.amtbbs.org\/wp-content\/plugins\/page-views-count\/ajax-loader-2x.gif\" border=0 \/><\/p>\n<div class=\"pvc_clear\"><\/div>\n","protected":false},"author":1,"featured_media":618,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[],"class_list":["post-617","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-ai"],"_links":{"self":[{"href":"https:\/\/aif.amtbbs.org\/index.php\/wp-json\/wp\/v2\/posts\/617","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/aif.amtbbs.org\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/aif.amtbbs.org\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/aif.amtbbs.org\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/aif.amtbbs.org\/index.php\/wp-json\/wp\/v2\/comments?post=617"}],"version-history":[{"count":1,"href":"https:\/\/aif.amtbbs.org\/index.php\/wp-json\/wp\/v2\/posts\/617\/revisions"}],"predecessor-version":[{"id":668,"href":"https:\/\/aif.amtbbs.org\/index.php\/wp-json\/wp\/v2\/posts\/617\/revisions\/668"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/aif.amtbbs.org\/index.php\/wp-json\/wp\/v2\/media\/618"}],"wp:attachment":[{"href":"https:\/\/aif.amtbbs.org\/index.php\/wp-json\/wp\/v2\/media?parent=617"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/aif.amtbbs.org\/index.php\/wp-json\/wp\/v2\/categories?post=617"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/aif.amtbbs.org\/index.php\/wp-json\/wp\/v2\/tags?post=617"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}