{"id":3428,"date":"2023-07-17T13:21:12","date_gmt":"2023-07-17T13:21:12","guid":{"rendered":"https:\/\/statorials.org\/cn\/t-%e6%a3%80%e9%aa%8c%e4%b8%8d%e7%ad%89%e6%a0%b7%e6%9c%ac%e9%87%8f\/"},"modified":"2023-07-17T13:21:12","modified_gmt":"2023-07-17T13:21:12","slug":"t-%e6%a3%80%e9%aa%8c%e4%b8%8d%e7%ad%89%e6%a0%b7%e6%9c%ac%e9%87%8f","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/t-%e6%a3%80%e9%aa%8c%e4%b8%8d%e7%ad%89%e6%a0%b7%e6%9c%ac%e9%87%8f\/","title":{"rendered":"\u5982\u4f55\u4f7f\u7528\u4e0d\u76f8\u7b49\u7684\u6837\u672c\u91cf\u6267\u884c t \u68c0\u9a8c"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">\u5f53\u8c08\u5230\u7edf\u8ba1\u65f6\uff0c\u5b66\u751f\u7ecf\u5e38\u95ee\u7684\u4e00\u4e2a\u95ee\u9898\u662f\uff1a<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong><em>\u5404\u7ec4\u6837\u672c\u91cf\u4e0d\u7b49\u65f6\u662f\u5426\u53ef\u4ee5\u8fdb\u884ct\u68c0\u9a8c\uff1f<\/em><\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u7b80\u77ed\u7684\u56de\u7b54\uff1a<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>\u662f\u7684\uff0c\u5f53\u6837\u672c\u91cf\u4e0d\u76f8\u7b49\u65f6\uff0c\u60a8\u53ef\u4ee5\u6267\u884c t \u68c0\u9a8c\u3002\u76f8\u540c\u7684\u6837\u672c\u91cf\u4e0d\u662f t \u68c0\u9a8c\u4e2d\u6240\u505a\u7684<a href=\"https:\/\/statorials.org\/cn\/t-\u68c0\u9a8c\u5047\u8bbe\/\" target=\"_blank\" rel=\"noopener\">\u5047\u8bbe\u4e4b\u4e00<\/a>\u3002<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u5f53\u4e24\u4e2a\u6837\u672c\u7684\u65b9\u5dee\u4e0d\u76f8\u7b49\u65f6\uff0c\u771f\u6b63\u7684\u95ee\u9898\u5c31\u4f1a\u51fa\u73b0\uff0c\u8fd9<em>\u662f<\/em>t \u68c0\u9a8c\u4e2d\u6240\u505a\u7684\u5047\u8bbe\u4e4b\u4e00\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u53d1\u751f\u8fd9\u79cd\u60c5\u51b5\u65f6\uff0c\u5efa\u8bae\u6539\u7528<a href=\"https:\/\/statorials.org\/cn\/\u97e6\u5c14\u5947t\u68c0\u9a8c\/\" target=\"_blank\" rel=\"noopener\">\u97e6\u5c14\u5947 t \u68c0\u9a8c<\/a>\uff0c\u8be5\u68c0\u9a8c\u4e0d\u5047\u8bbe\u65b9\u5dee\u76f8\u7b49\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u4ee5\u4e0b\u793a\u4f8b\u5c55\u793a\u4e86\u5f53\u65b9\u5dee\u76f8\u7b49\u548c\u4e0d\u76f8\u7b49\u65f6\u5982\u4f55\u4f7f\u7528\u4e0d\u76f8\u7b49\u7684\u6837\u672c\u91cf\u6267\u884c T \u68c0\u9a8c\u3002<\/span><\/p>\n<h2><span style=\"color: #000000;\"><strong>\u793a\u4f8b 1\uff1a\u6837\u672c\u91cf\u4e0d\u76f8\u7b49\u4e14\u65b9\u5dee\u76f8\u7b49<\/strong><\/span><\/h2>\n<p><span style=\"color: #000000;\">\u5047\u8bbe\u6211\u4eec\u7ba1\u7406\u4e24\u4e2a\u65e8\u5728\u5e2e\u52a9\u5b66\u751f\u5728\u67d0\u4e9b\u8003\u8bd5\u4e2d\u53d6\u5f97\u66f4\u597d\u6210\u7ee9\u7684\u8ba1\u5212\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u7ed3\u679c\u5982\u4e0b\uff1a<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>\u65b9\u6848\u4e00\uff1a<\/strong><\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>n<\/strong> \uff08\u6837\u672c\u91cf\uff09\uff1a500<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong><span style=\"border-top: 1px solid black;\">x<\/span><\/strong> \uff08\u6837\u672c\u5e73\u5747\u503c\uff09\uff1a80<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>s<\/strong> \uff08\u6837\u672c\u6807\u51c6\u5dee\uff09\uff1a5<\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000;\"><strong>\u65b9\u68482\uff1a<\/strong><\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>n<\/strong> \uff08\u6837\u672c\u91cf\uff09\uff1a20<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong><span style=\"border-top: 1px solid black;\">x<\/span><\/strong> \uff08\u6837\u672c\u5e73\u5747\u503c\uff09\uff1a85<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>s<\/strong> \uff08\u6837\u672c\u6807\u51c6\u5dee\uff09\uff1a5<\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000;\">\u4ee5\u4e0b\u4ee3\u7801\u5c55\u793a\u4e86\u5982\u4f55\u5728 R \u4e2d\u521b\u5efa\u7bb1\u7ebf\u56fe\u4ee5\u53ef\u89c6\u5316\u6bcf\u4e2a\u7a0b\u5e8f\u7684\u8003\u8bd5\u5206\u6570\u5206\u5e03\uff1a<\/span> <\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#make this example reproducible\n<\/span>set. <span style=\"color: #3366ff;\">seeds<\/span> (1)\n\n<span style=\"color: #008080;\">#create vectors to hold exam scores\n<\/span>program1 &lt;- rnorm(500, mean=80, sd=5)\nprogram2 &lt;- rnorm(20, mean=85, sd=5)\n\n<span style=\"color: #008080;\">#create boxplots to visualize distribution of exam scores\n<\/span>boxplot(program1, program2, names=c(\" <span style=\"color: #ff0000;\">Program 1<\/span> \",\" <span style=\"color: #ff0000;\">Program 2<\/span> \"))\n<\/strong><\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-28705 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/inegal1.jpg\" alt=\"\" width=\"446\" height=\"399\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p><span style=\"color: #000000;\">\u9879\u76ee 2 \u7684\u5e73\u5747\u8003\u8bd5\u6210\u7ee9\u4f3c\u4e4e\u66f4\u9ad8\uff0c\u4f46\u4e24\u4e2a\u9879\u76ee\u4e4b\u95f4\u7684\u8003\u8bd5\u6210\u7ee9\u5dee\u5f02\u5927\u81f4\u76f8\u7b49\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u4ee5\u4e0b\u4ee3\u7801\u663e\u793a\u5982\u4f55\u4f7f\u7528 Welch t \u68c0\u9a8c\u6267\u884c\u72ec\u7acb\u6837\u672c t \u68c0\u9a8c\uff1a<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#perform independent samples t-test\n<\/span>t. <span style=\"color: #3366ff;\">test<\/span> (program1, program2, var. <span style=\"color: #3366ff;\">equal<\/span> = <span style=\"color: #008000;\">TRUE<\/span> )\n\n\tTwo Sample t-test\n\ndata: program1 and program2\nt = -3.3348, df = 518, p-value = 0.0009148\nalternative hypothesis: true difference in means is not equal to 0\n95 percent confidence interval:\n -6.111504 -1.580245\nsample estimates:\nmean of x mean of y \n 80.11322 83.95910\n\n<span style=\"color: #008080;\">#perform Welch's two sample t-test\n<\/span>t. <span style=\"color: #3366ff;\">test<\/span> (program1, program2, var. <span style=\"color: #3366ff;\">equal<\/span> = <span style=\"color: #008000;\">FALSE<\/span> )\n\n\tWelch Two Sample t-test\n\ndata: program1 and program2\nt = -3.3735, df = 20.589, p-value = 0.00293\nalternative hypothesis: true difference in means is not equal to 0\n95 percent confidence interval:\n -6.219551 -1.472199\nsample estimates:\nmean of x mean of y \n 80.11322 83.95910 \n<\/strong><\/pre>\n<p><span style=\"color: #000000;\">\u72ec\u7acb\u6837\u672c t \u68c0\u9a8c\u8fd4\u56de p \u503c\u4e3a<strong>0.0009<\/strong> \uff0c\u800c Welch t \u68c0\u9a8c\u8fd4\u56de p \u503c\u4e3a<strong>0.0029<\/strong> \u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u7531\u4e8e\u6bcf\u4e2a\u6d4b\u8bd5\u7684 p \u503c\u5c0f\u4e8e 0.05\uff0c\u56e0\u6b64\u6211\u4eec\u4f1a\u62d2\u7edd\u6bcf\u4e2a\u6d4b\u8bd5\u4e2d\u7684\u539f\u5047\u8bbe\uff0c\u5e76\u5f97\u51fa\u7ed3\u8bba\uff1a\u4e24\u4e2a\u9879\u76ee\u4e4b\u95f4\u7684\u5e73\u5747\u8003\u8bd5\u6210\u7ee9\u5b58\u5728\u7edf\u8ba1\u4e0a\u7684\u663e\u7740\u5dee\u5f02\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong><span style=\"color: #000000;\">\u5c3d\u7ba1\u6837\u672c\u91cf\u4e0d\u76f8\u7b49\uff0c\u4f46\u72ec\u7acb\u6837\u672c t \u68c0\u9a8c\u548c Welch t \u68c0\u9a8c\u90fd\u8fd4\u56de\u76f8\u4f3c\u7684\u7ed3\u679c\uff0c\u56e0\u4e3a\u4e24\u4e2a\u6837\u672c\u5177\u6709\u76f8\u7b49\u7684\u65b9\u5dee\u3002<\/span><\/strong><\/span><\/p>\n<h2><span style=\"color: #000000;\"><strong>\u793a\u4f8b 2\uff1a\u4e0d\u7b49\u7684\u6837\u672c\u91cf\u548c\u4e0d\u7b49\u7684\u65b9\u5dee<\/strong><\/span><\/h2>\n<p><span style=\"color: #000000;\">\u5047\u8bbe\u6211\u4eec\u7ba1\u7406\u4e24\u4e2a\u65e8\u5728\u5e2e\u52a9\u5b66\u751f\u5728\u67d0\u4e9b\u8003\u8bd5\u4e2d\u53d6\u5f97\u66f4\u597d\u6210\u7ee9\u7684\u8ba1\u5212\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u7ed3\u679c\u5982\u4e0b\uff1a<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>\u65b9\u6848\u4e00\uff1a<\/strong><\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>n<\/strong> \uff08\u6837\u672c\u91cf\uff09\uff1a500<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong><span style=\"border-top: 1px solid black;\">x<\/span><\/strong> \uff08\u6837\u672c\u5e73\u5747\u503c\uff09\uff1a80<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>s<\/strong> \uff08\u6837\u672c\u6807\u51c6\u5dee\uff09\uff1a25<\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000;\"><strong>\u65b9\u68482\uff1a<\/strong><\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>n<\/strong> \uff08\u6837\u672c\u91cf\uff09\uff1a20<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong><span style=\"border-top: 1px solid black;\">x<\/span><\/strong> \uff08\u6837\u672c\u5e73\u5747\u503c\uff09\uff1a85<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>s<\/strong> \uff08\u6837\u672c\u6807\u51c6\u5dee\uff09\uff1a5<\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000;\">\u4ee5\u4e0b\u4ee3\u7801\u5c55\u793a\u4e86\u5982\u4f55\u5728 R \u4e2d\u521b\u5efa\u7bb1\u7ebf\u56fe\u4ee5\u53ef\u89c6\u5316\u6bcf\u4e2a\u7a0b\u5e8f\u7684\u8003\u8bd5\u5206\u6570\u5206\u5e03\uff1a<\/span> <\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#make this example reproducible\n<\/span>set. <span style=\"color: #3366ff;\">seeds<\/span> (1)\n\n<span style=\"color: #008080;\">#create vectors to hold exam scores\n<\/span>program1 &lt;- rnorm(500, mean=80, sd=25)\nprogram2 &lt;- rnorm(20, mean=85, sd=5)\n\n<span style=\"color: #008080;\">#create boxplots to visualize distribution of exam scores\n<\/span>boxplot(program1, program2, names=c(\" <span style=\"color: #ff0000;\">Program 1<\/span> \",\" <span style=\"color: #ff0000;\">Program 2<\/span> \"))\n<\/strong><\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-28706 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/inegal2.jpg\" alt=\"\" width=\"447\" height=\"404\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p><span style=\"color: #000000;\">\u9879\u76ee 2 \u7684\u5e73\u5747\u8003\u8bd5\u6210\u7ee9\u4f3c\u4e4e\u66f4\u9ad8\uff0c\u4f46\u9879\u76ee 1 \u7684\u8003\u8bd5\u6210\u7ee9\u65b9\u5dee\u8fdc\u9ad8\u4e8e\u9879\u76ee 2\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u4ee5\u4e0b\u4ee3\u7801\u663e\u793a\u5982\u4f55\u4f7f\u7528 Welch t \u68c0\u9a8c\u6267\u884c\u72ec\u7acb\u6837\u672c t \u68c0\u9a8c\uff1a<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#perform independent samples t-test\n<\/span>t. <span style=\"color: #3366ff;\">test<\/span> (program1, program2, var. <span style=\"color: #3366ff;\">equal<\/span> = <span style=\"color: #008000;\">TRUE<\/span> )\n\n\tTwo Sample t-test\n\ndata: program1 and program2\nt = -0.5988, df = 518, p-value = 0.5496\nalternative hypothesis: true difference in means is not equal to 0\n95 percent confidence interval:\n -14.52474 7.73875\nsample estimates:\nmean of x mean of y \n  80.5661 83.9591\n\n<span style=\"color: #008080;\">#perform Welch's two sample t-test\n<\/span>t. <span style=\"color: #3366ff;\">test<\/span> (program1, program2, var. <span style=\"color: #3366ff;\">equal<\/span> = <span style=\"color: #008000;\">FALSE<\/span> )\n\n\tWelch Two Sample t-test\n\ndata: program1 and program2\nt = -2.1338, df = 74.934, p-value = 0.03613\nalternative hypothesis: true difference in means is not equal to 0\n95 percent confidence interval:\n -6.560690 -0.225296\nsample estimates:\nmean of x mean of y \n  80.5661 83.9591 \n<\/strong><\/pre>\n<p><span style=\"color: #000000;\">\u72ec\u7acb\u6837\u672c t \u68c0\u9a8c\u8fd4\u56de\u7684 p \u503c\u4e3a<strong>0.5496<\/strong> \uff0c\u800c Welch t \u68c0\u9a8c\u8fd4\u56de\u7684 p \u503c\u4e3a<strong>0.0361<\/strong> \u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u72ec\u7acb\u6837\u672c t \u68c0\u9a8c\u65e0\u6cd5\u68c0\u6d4b\u5e73\u5747\u8003\u8bd5\u6210\u7ee9\u7684\u5dee\u5f02\uff0c\u4f46\u97e6\u5c14\u5947 t \u68c0\u9a8c\u80fd\u591f\u68c0\u6d4b\u7edf\u8ba1\u663e\u7740\u6027\u5dee\u5f02\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\"><b>\u7531\u4e8e\u4e24\u4e2a\u6837\u672c\u7684\u65b9\u5dee\u4e0d\u76f8\u7b49\uff0c\u56e0\u6b64\u53ea\u6709\u97e6\u5c14\u5947 t \u68c0\u9a8c\u80fd\u591f\u68c0\u6d4b\u5e73\u5747\u8003\u8bd5\u6210\u7ee9\u7684\u7edf\u8ba1\u663e\u7740\u6027\u5dee\u5f02\uff0c\u56e0\u4e3a\u8be5\u68c0\u9a8c\u4e0d\u5047\u8bbe\u6837\u672c\u4e4b\u95f4\u7684\u65b9\u5dee<\/b><span style=\"color: #000000;\"><b>\u76f8\u7b49<\/b><\/span><b>\u3002<\/b><\/span><\/p>\n<h2><span style=\"color: #000000;\"><strong>\u5176\u4ed6\u8d44\u6e90<\/strong><\/span><\/h2>\n<p><span style=\"color: #000000;\">\u4ee5\u4e0b\u6559\u7a0b\u63d0\u4f9b\u6709\u5173 t \u68c0\u9a8c\u7684\u5176\u4ed6\u4fe1\u606f\uff1a<\/span><\/p>\n<p><a href=\"https:\/\/statorials.org\/cn\/\u6837\u672c-t-\u68c0\u9a8c\/\" target=\"_blank\" rel=\"noopener\">\u5355\u6837\u672c t \u68c0\u9a8c\u7b80\u4ecb<\/a><br \/><a href=\"https:\/\/statorials.org\/cn\/\u6d4b\u8bd5\u4f60\u7684\u4e24\u4e2a\u6837\u672c\/\" target=\"_blank\" rel=\"noopener\">\u53cc\u6837\u672c t \u68c0\u9a8c\u7b80\u4ecb<\/a><br \/><a href=\"https:\/\/statorials.org\/cn\/\u914d\u5bf9\u6837\u672ct\u68c0\u9a8c\/\" target=\"_blank\" rel=\"noopener\">\u914d\u5bf9\u6837\u672c t \u68c0\u9a8c\u7b80\u4ecb<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5f53\u8c08\u5230\u7edf\u8ba1\u65f6\uff0c\u5b66\u751f\u7ecf\u5e38\u95ee\u7684\u4e00\u4e2a\u95ee\u9898\u662f\uff1a \u5404\u7ec4\u6837\u672c\u91cf\u4e0d\u7b49\u65f6\u662f\u5426\u53ef\u4ee5\u8fdb\u884ct\u68c0\u9a8c\uff1f \u7b80\u77ed\u7684\u56de\u7b54\uff1a \u662f\u7684\uff0c\u5f53\u6837\u672c\u91cf\u4e0d\u76f8 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11],"tags":[],"class_list":["post-3428","post","type-post","status-publish","format-standard","hentry","category-11"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u5982\u4f55\u4f7f\u7528\u4e0d\u76f8\u7b49\u7684\u6837\u672c\u91cf\u6267\u884c T \u68c0\u9a8c - Statorials<\/title>\n<meta name=\"description\" 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