{"id":73780,"date":"2016-08-29T07:30:50","date_gmt":"2016-08-28T23:30:50","guid":{"rendered":"http:\/\/highscope.ch.ntu.edu.tw\/wordpress\/?p=73780"},"modified":"2021-10-06T16:03:57","modified_gmt":"2021-10-06T08:03:57","slug":"%e5%85%a9%e6%a8%a3%e6%9c%ac%e5%9d%87%e5%80%bc%e9%a1%af%e8%91%97%e6%80%a7%e6%aa%a2%e5%ae%9a%ef%bc%88%e4%b8%8b%ef%bc%89","status":"publish","type":"post","link":"http:\/\/localhost\/%e5%85%a9%e6%a8%a3%e6%9c%ac%e5%9d%87%e5%80%bc%e9%a1%af%e8%91%97%e6%80%a7%e6%aa%a2%e5%ae%9a%ef%bc%88%e4%b8%8b%ef%bc%89\/","title":{"rendered":"\u5169\u6a23\u672c\u5747\u503c\u986f\u8457\u6027\u6aa2\u5b9a\uff08\u4e0b\uff09"},"content":{"rendered":"

\u5169\u6a23\u672c\u5747\u503c\u986f\u8457\u6027\u6aa2\u5b9a\uff08\u4e0b\uff09(T Test for Two Sample Means (II))<\/strong><\/span>
\n\u570b\u7acb\u81fa\u7063\u5927\u5b78\u8fb2\u85dd\u5b78\u7cfb \u9ec3\u7e95\u6dc7<\/strong><\/span><\/p>\n

\u9023\u7d50\uff1a\u5169\u6a23\u672c\u5747\u503c\u986f\u8457\u6027\u6aa2\u5b9a\uff08\u4e0a\uff09<\/a><\/p>\n

2.\u5169\u6bcd\u7fa4\u9ad4\u70ba\u5e38\u614b\u5206\u5e03\u4e14\u6bcd\u9ad4\u8b8a\u7570\u6578\u672a\u77e5<\/span><\/strong><\/p>\n

\\(\\text{(II)}\\) \u5047\u8a2d\u5169\u6bcd\u7fa4\u9ad4\u8b8a\u7570\u6578\u4e0d\u76f8\u7b49\u6642\u00a0\\((\\sigma^2_1\\ne\\sigma^2_2)\\)<\/p>\n

\u5047\u82e5\u6211\u5011\u7372\u5f97\u5169\u7b46\u4e0d\u540c\u96a8\u6a5f\u7368\u7acb\u6a23\u672c\u8cc7\u6599\uff0c\u6b64\u5169\u7b46\u7368\u7acb\u6a23\u672c\u62bd\u6a23\u81ea\u5169\u6bcd\u7fa4\u9ad4\uff0c\u4e14\u5169\u6bcd\u7fa4\u9ad4\u90fd\u70ba\u5e38\u614b\u5206\u5e03\u4e14\u8b8a\u7570\u6578\u672a\u77e5\u4f46\u4e0d\u76f8\u540c\u6642\uff0c\u53ef\u63a1\u7528 Welch’s t \u6aa2\u5b9a\u6cd5\u3002<\/p>\n

Welch’s t \u6aa2\u5b9a\u7684\u7d71\u8a08\u91cf\u70ba\uff1a\\(\\displaystyle t’=\\frac{|\\overline{x}_1-\\overline{x}_2|}{\\sqrt{\\frac{S^2_1}{n_1}+\\frac{S^2_2}{n_2}}}~~~~~~~~~(3)\\)<\/p>\n

\\((3)\\)\u00a0\u5f0f\u4e2d\u7684 \\(\\overline{x}_1\\)\u3001\\(\\overline{x}_2\\) \u70ba\u6b64\u5169\u7b46\u6a23\u672c\u4e4b\u5e73\u5747\u503c\uff0c\u5169\u500b\u6a23\u672c\u8b8a\u7570\u6578\u70ba \\(S^2_1\\) \u8207 \\(S^2_2\\)\uff0c\\(n_1\\)\u3001\\(n_2\\) \u5247\u662f\u5169\u7d44\u6a23\u672c\u62bd\u6a23\u7684\u6a23\u672c\u6578\u3002\u4f46\u7531\u65bc\u5169\u6bcd\u7fa4\u9ad4\u8b8a\u7570\u6578\u4e0d\u76f8\u540c\uff0c\u6240\u4ee5\u7121\u6cd5\u76f4\u63a5\u5957\u7528 t \u5206\u5e03\uff0c\u56e0\u6b64\u9700\u8981\u5c0d t \u5206\u5e03\u7684\u81ea\u7531\u5ea6\u505a\u52a0\u6b0a\u5f8c\u624d\u53ef\u4ee5\u6aa2\u5b9a\uff0c\u52a0\u6b0a\u904e\u5f8c\u7684\u81ea\u7531\u5ea6\u70ba\uff1a<\/p>\n

\\(\\displaystyle df’=\\frac{\\displaystyle\\left(\\frac{S^2_1}{n_1}+\\frac{S^2_2}{n_2}\\right)^2}{\\displaystyle\\frac{S^2_1\/n_1}{n_1-1}+\\frac{S^2_2\/n_2}{n_2-1}}\\)<\/p>\n

\u8209\u4f8b\u4f86\u8aaa\uff0c\u60f3\u8981\u4e86\u89e3\u75db\u98a8\u75c5\u60a3\u8207\u6b63\u5e38\u6210\u4eba\u8840\u4e2d\u5c3f\u9178\u91cf\u5747\u503c\u662f\u5426\u76f8\u540c\uff0c\u4e14\u5169\u6bcd\u7fa4\u9ad4\u8b8a\u7570\u6578\u672a\u77e5\u4f46\u4e0d\u76f8\u540c\uff0c\u96a8\u6a5f\u62bd\u53d6 10 \u4f4d\u75db\u98a8\u75c5\u60a3\u4ee5\u53ca 8 \u4f4d\u6b63\u5e38\u6210\u4eba\u4e26\u8a18\u9304\u5176\u8840\u4e2d\u5c3f\u9178\u91cf\uff0c\u96a8\u5f8c\u5404\u5225\u8a08\u7b97\u75db\u98a8\u75c5\u60a3\u8840\u4e2d\u5c3f\u9178\u91cf\u5e73\u5747\u503c\u53ca\u8b8a\u7570\u6578\u5206\u5225\u70ba 9.17 \\((\\overline{x}_1)\\)\u300110.6001 \\((S^2_1)\\)\uff0c\u800c\u6b63\u5e38\u6210\u4eba\u5247\u70ba 5.795 \\((\\overline{x}_2)\\)\u30011.145 \\((S^2_2)\\)\uff0c\u5247\u8a08\u7b97\u51fa\u4f86\u7684 t \u503c\u70ba\uff1a<\/p>\n

\\(\\displaystyle t’=\\frac{|9.17-5.795|}{\\sqrt{\\frac{10.6001}{10}+\\frac{1.145}{8}}}=3.076\\)<\/p>\n

\u52a0\u6b0a\u904e\u5f8c\u7684\u81ea\u7531\u5ea6\u70ba:<\/p>\n

\\(\\displaystyle df’=\\frac{\\displaystyle\\left(\\frac{10.6001}{10}+\\frac{1.145}{8}\\right)^2}{\\displaystyle\\frac{10.6001\/10}{10-1}+\\frac{1.145\/8}{8-1}}\\)<\/p>\n

\u8a08\u7b97\u51fa\u4f86\u7684 \\(t’\\) \u503c\u53ef\u4ee5\u8207\u81e8\u754c\u503c \\(t_{0.025,df’}\\) \u6bd4\u8f03\uff0c\u82e5 \\(t’\\) \u5c0f\u65bc\u9019\u500b\u81e8\u754c\u503c\uff0c\u6211\u5011\u5c31\u8a8d\u70ba\u5169\u6a23\u672c\u4e4b\u5747\u503c\u76f8\u540c\u3002\u5728\u6b64\u7bc4\u4f8b\u4e2d\uff0c\u7531\u65bc \\(t’=3.076>t_{0.025,df’=2.19}\\)\uff0c\u986f\u793a\u75db\u98a8\u75c5\u60a3\u8207\u6b63\u5e38\u6210\u4eba\u8840\u4e2d\u5c3f\u9178\u91cf\u5747\u503c\u5177\u6709\u986f\u8457\u5dee\u7570\u3002<\/p>\n

\u56db\u3001\u6210\u5c0d\u6a23\u672c\u4e0b\u5169\u6bcd\u7fa4\u9ad4\u5e73\u5747\u503c\u7684\u5047\u8a2d\u6aa2\u5b9a<\/span><\/strong><\/p>\n

\u7576\u6211\u5011\u5f97\u5230\u4e00\u7d44\u7531 n \u500b\u914d\u5c0d\u6240\u69cb\u6210\u7684 n \u500b \\(d_i\\) \u96a8\u6a5f\u6a23\u672c\uff0c\u6b64\u914d\u5c0d\u6a23\u672c\u7684\u5dee\u503c\u4f86\u81ea\u4e00\u500b\u5e38\u614b\u6bcd\u7fa4\u9ad4\u6642\uff0c\u5176\u5e73\u5747\u503c \\(u_D\\)\uff0c\u8b8a\u7570\u6578\u5247\u70ba \\(\\sigma^2_D\\)\uff0c\u4f46\u7531\u65bc \\(\\sigma^2_D\\) \u672a\u77e5\uff0c\u56e0\u6b64\u53ef\u4ee5\u5229\u7528 \\(S^2_D\\) \u4f86\u4f30\u8a08\uff0c\u800c \\(u_D\\) \u5247\u70ba\u9ede\u4f30\u8a08 \\(\\overline{D}\\) \u4f86\u4f30\u8a08\uff0c\\(\\overline{D}\\) \u53ca \\(S^2_D\\) \u8a08\u7b97\u516c\u5f0f\u5982\u4e0b:<\/p>\n

\\(\\displaystyle \\overline{D}=\\frac{\\sum^n_{i=1}d_i}{n},~~~S^2_D=\\frac{\\sum^n_{i=1}(d_i-\\overline{D})^2}{n-1}~~~~~~~~~(4)\\)<\/p>\n

\\(d_i\\) \u70ba\u540c\u4e00\u8a66\u9a57\u55ae\u4f4d\u65bc\u4e0d\u540c\u74b0\u5883\u4e0b\u6240\u7372\u5f97\u89c0\u6e2c\u503c\u4e4b\u5dee\u503c\uff0c\u7372\u5f97 \\(\\overline{D}\\) \u53ca \\(S^2_D\\) \u5c31\u53ef\u4ee5\u6aa2\u5b9a \\(u_D\\) \u662f\u5426\u70ba 0\uff0c\u5176\u63a1\u7528\u7684\u6aa2\u5b9a\u7d71\u8a08\u91cf\u70ba\uff1a<\/p>\n

\\(\\displaystyle t=\\frac{\\overline{D}}{\\sqrt{\\frac{S^2_D}{n}}}\\)<\/p>\n

\u4f8b\u5982\uff1a\u7814\u7a76\u8005\u60f3\u8981\u4e86\u89e3\uff0c\u80a5\u80d6\u570b\u4e2d\u7537\u6027\u904b\u52d5\u534a\u5e74\u5f8c\uff0c\u5176\u9ad4\u91cd\u904b\u52d5\u524d\u5f8c\u5dee\u503c\u4e4b\u5747\u503c\u662f\u5426\u6709\u5dee\u7570\uff0c\u56e0\u6b64\u5f9e\u53c3\u52a0\u6b64\u8a08\u756b\u7684\u80a5\u80d6\u570b\u4e2d\u7537\u6027\u96a8\u6a5f\u62bd\u53d6 9 \u4f4d\uff0c\u5206\u5225\u6e2c\u91cf\u5176\u904b\u52d5\u524d\u5f8c\u9ad4\u91cd\uff0c\u7d50\u679c\u5982\u8868\u4e00\uff1a<\/p>\n

\\(\\displaystyle \\overline{D}=\\frac{\\sum^n_{i=1}d_i}{n}=(11+7+…+9)\/9=8.67\\)<\/p>\n

\\(\\displaystyle S^2_D=\\frac{\\sum^n_{i=1}(d_i-\\overline{D})^2}{n-1}=[(11-8.67)^2+…+(9-8.67)^2]\/8=5.75\\)<\/p>\n

\u8868\u4e00\u3001\u570b\u4e2d\u7537\u6027\u904b\u52d5\u534a\u5e74\u5f8c\u9ad4\u91cd\u5dee\u503c\u7d71\u8a08\u8868\u3002\uff08\u672c\u6587\u4f5c\u8005\u9ec3\u7e95\u6dc7\u88fd\u4f5c\uff09<\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n
\u7de8\u865f<\/td>\n\u904b\u52d5\u524d<\/td>\n\u904b\u52d5\u5f8c<\/td>\n\u5dee\u503c<\/td>\n<\/tr>\n
1<\/td>\n72<\/td>\n61<\/td>\n11<\/td>\n<\/tr>\n
2<\/td>\n70<\/td>\n63<\/td>\n7<\/td>\n<\/tr>\n
3<\/td>\n84<\/td>\n72<\/td>\n12<\/td>\n<\/tr>\n
4<\/td>\n81<\/td>\n70<\/td>\n11<\/td>\n<\/tr>\n
5<\/td>\n75<\/td>\n70<\/td>\n5<\/td>\n<\/tr>\n
6<\/td>\n72<\/td>\n63<\/td>\n9<\/td>\n<\/tr>\n
7<\/td>\n90<\/td>\n84<\/td>\n6<\/td>\n<\/tr>\n
8<\/td>\n68<\/td>\n60<\/td>\n8<\/td>\n<\/tr>\n
9<\/td>\n87<\/td>\n78<\/td>\n9<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\u5f97\u5230 \\(\\overline{D}\\) \u53ca \\(S^2_D\\) \u5c31\u53ef\u4ee5\u8a08\u7b97 t \u503c\uff0c\u5176\u70ba\uff1a<\/p>\n

\\(\\displaystyle t=\\frac{8.67-0}{\\sqrt{\\frac{5.75}{9}}}=10.85\\)<\/p>\n

\u60f3\u8981\u77e5\u9053\u5728\u6b64\u689d\u4ef6\u4e0b\uff0c8.67 \u5c0f\u6642\u7684\u5dee\u7570\u5920\u4e0d\u5920\u986f\u8457\uff1f\u53ef\u4ee5\u4f7f\u7528\u4e00\u500b\u5408\u7406\u7684\u81e8\u754c\u503c\uff0c\u5982\u679c\u6b64\u914d\u5c0d\u6a23\u672c\u5dee\u503c\u5c0f\u65bc\u9019\u500b\u81e8\u754c\u503c\uff0c\u6211\u5011\u5c31\u8a8d\u5b9a\u914d\u5c0d\u6a23\u672c\u5dee\u503c\u4e4b\u5747\u503c\u76f8\u540c\u3002\u6b64\u81e8\u754c\u503c\u901a\u5e38\u9078\u5b9a\u70ba \\(t_{0.025,n-1}\\)\u3002\u5728\u80a5\u80d6\u570b\u4e2d\u7537\u6027\u904b\u52d5\u524d\u5f8c\u9ad4\u91cd\u5dee\u503c\u4e4b\u5747\u503c\u4f8b\u5b50\u4e2d\uff0c\u7531\u65bc \\(t = 10.85 >t_{0.025,8}= 2.306\\)\uff0c\u986f\u793a\u904b\u52d5\u5c0d\u65bc\u6e1b\u91cd\u662f\u6709\u6548\u7684\uff0c\u56e0\u70ba\u904b\u52d5\u524d\u5f8c\u9ad4\u91cd\u5dee\u503c\u4e4b\u5747\u503c\u5177\u6709\u986f\u8457\u7684\u5dee\u7570\u3002<\/p>\n

\"73780_p1\"<\/a>

\u5716\u4e00\u3001\u6210\u5c0d\u6a23\u672c\u4e0b\u5169\u6bcd\u7fa4\u9ad4\u5e73\u5747\u503c\u7684\u5047\u8a2d\u6aa2\u5b9a\u3002\uff08\u672c\u6587\u4f5c\u8005\u9ec3\u7e95\u6dc7\u88fd\u4f5c\uff09<\/p><\/div>\n

\n

\u53c3\u8003\u6587\u737b<\/strong><\/p>\n

    \n
  1. \u6c88\u660e\u4f86 (2014)\u3002\u751f\u7269\u7d71\u8a08\u5b78\u5165\u9580\u3002\u4e5d\u5dde\u3002<\/li>\n
  2. \u90ed\u5bf6\u931a\u3001\u9673\u7389\u654f (2011)\u3002\u751f\u7269\u7d71\u8a08\u5b78\u3002\u4e94\u5357\u3002<\/li>\n<\/ol>\n<\/div>","protected":false},"excerpt":{"rendered":"

    \u5169\u6a23\u672c\u5747\u503c\u986f\u8457\u6027\u6aa2\u5b9a\uff08\u4e0b\uff09(T Test for Two Sample Means (II)) \u570b\u7acb\u81fa\u7063\u5927\u5b78\u8fb2…<\/p>\n","protected":false},"author":50,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[111,230,229],"tags":[10581,10463,10582,10027,10462,11064,10580],"class_list":["post-73780","post","type-post","status-publish","format-standard","hentry","category-mathematics00","category-math06-01","category-math06","tag-independent-sample","tag-paired-sample","tag-sd","tag-standard-deviation","tag-10462","tag-11064","tag-10580","loop-entry","cat-111","cat-230","cat-229","no-thumbnail"],"views":9922,"_links":{"self":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/73780","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/users\/50"}],"replies":[{"embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/comments?post=73780"}],"version-history":[{"count":1,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/73780\/revisions"}],"predecessor-version":[{"id":85990,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/73780\/revisions\/85990"}],"wp:attachment":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/media?parent=73780"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/categories?post=73780"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/tags?post=73780"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}