{"id":1691,"date":"2013-01-25T19:00:24","date_gmt":"2013-01-25T10:00:24","guid":{"rendered":"http:\/\/fujiitoshiki.com\/improvesociety\/?p=1691"},"modified":"2017-04-27T08:44:29","modified_gmt":"2017-04-26T23:44:29","slug":"%e3%83%94%e3%82%a2%e3%82%bd%e3%83%b3%e3%81%ae%e7%a9%8d%e7%8e%87%e7%9b%b8%e9%96%a2%e4%bf%82%e6%95%b0r%e3%81%a8%e3%81%9d%e3%82%8c%e3%81%ab%e5%af%be%e3%81%99%e3%82%8bt%e6%a4%9c%e5%ae%9a","status":"publish","type":"post","link":"https:\/\/www.fujiitoshiki.com\/improvesociety\/?p=1691","title":{"rendered":"\u30d4\u30a2\u30bd\u30f3\u306e\u7a4d\u7387\u76f8\u95a2\u4fc2\u6570 r \u3068\u305d\u308c\u306b\u5bfe\u3059\u308b t \u691c\u5b9a"},"content":{"rendered":"<div class=\"theContentWrap-ccc\"><p>\u3000<img src='https:\/\/s0.wp.com\/latex.php?latex=x&#038;bg=T&#038;fg=000000&#038;s=0' alt='x' title='x' class='latex' \/> \u3068 <img src='https:\/\/s0.wp.com\/latex.php?latex=y&#038;bg=T&#038;fg=000000&#038;s=0' alt='y' title='y' class='latex' \/> \u3068\u306e\u9593\u306e\u76f8\u95a2\u306e\u7a0b\u5ea6\u3092\u8868\u3059\u6307\u6a19\u3068\u3057\u3066\u30d4\u30a2\u30bd\u30f3\u306e\u7a4d\u7387\u76f8\u95a2\u4fc2\u6570 r \u304c\u3042\u308a\uff0c\u4e0b\u8a18\u306e\u5f0f\u3067\u8868\u73fe\u3057\u307e\u3059\uff0e\u76f8\u95a2\u4fc2\u6570 r \u306f -1 \u304b\u3089 1 \u306e\u7bc4\u56f2\u306b\u3042\u308a\u307e\u3059\uff0e<\/p>\n<p><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+r+%3D+%5Cfrac%7B%5Csum_%7Bi%3D1%7D%5En%28x_i-%5Cbar+x%29%28y_i+-+%5Cbar+y%29%7D%7B%5Csqrt%7B%5Csum_%7Bi%3D1%7D%5En%28x_i+-+%5Cbar+x%29%5E2%7D%5Csqrt%7B%5Csum_%7Bi%3D1%7D%5En%28y_i+-+%5Cbar+y%29%5E2%7D%7D&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle r = \\frac{\\sum_{i=1}^n(x_i-\\bar x)(y_i - \\bar y)}{\\sqrt{\\sum_{i=1}^n(x_i - \\bar x)^2}\\sqrt{\\sum_{i=1}^n(y_i - \\bar y)^2}}' title='\\displaystyle r = \\frac{\\sum_{i=1}^n(x_i-\\bar x)(y_i - \\bar y)}{\\sqrt{\\sum_{i=1}^n(x_i - \\bar x)^2}\\sqrt{\\sum_{i=1}^n(y_i - \\bar y)^2}}' class='latex' \/><\/p>\n<\/p>\n<p><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cbar+x&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\bar x' title='\\bar x' class='latex' \/> and <img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cbar+y&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\bar y' title='\\bar y' class='latex' \/> are average of <img src='https:\/\/s0.wp.com\/latex.php?latex=x&#038;bg=T&#038;fg=000000&#038;s=0' alt='x' title='x' class='latex' \/> and <img src='https:\/\/s0.wp.com\/latex.php?latex=y&#038;bg=T&#038;fg=000000&#038;s=0' alt='y' title='y' class='latex' \/>, respectively. i is number of sample (incremental variable). n is number of sample.<\/p>\n<p>\u3000\u6bcd\u96c6\u56e3\u304b\u3089\u7121\u4f5c\u70ba\u306b\u62bd\u51fa\u3057\u305f\u30b5\u30f3\u30d7\u30eb\u306e2\u7a2e\u985e\u306e\u5909\u6570\u306e\u9593\u306e\u76f8\u95a2\u4fc2\u6570 r \u306f t \u5206\u5e03\u306b\u5f93\u3044\u307e\u3059\u306e\u3067\u6709\u610f\u5dee\u691c\u5b9a\u3092\u884c\u3046\u3053\u3068\u304c\u3067\u304d\u307e\u3059\uff0e<\/p>\n<p>\u3000\u76f8\u95a2\u4fc2\u6570 r \u306b\u5bfe\u3059\u308b t \u7d71\u8a08\u5024\u306f\u4e0b\u8a18\u306e\u5f0f\u3067\u6c42\u307e\u308a\uff0c\u30b5\u30f3\u30d7\u30eb\u6570 n \u3068\u3059\u308b\u3068\u81ea\u7531\u5ea6 n-2 \u306e t \u5206\u5e03\u306b\u5f93\u3044\u307e\u3059\uff0e\u6bcd\u96c6\u56e3\u306e\u76f8\u95a2\u4fc2\u6570\u3092 <img src='https:\/\/s0.wp.com\/latex.php?latex=%5Crho&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\rho' title='\\rho' class='latex' \/> \u3068\u3057\u3066\u5e30\u7121\u4eee\u8aac\u3092\u300e\u76f8\u95a2\u4fc2\u6570 <img src='https:\/\/s0.wp.com\/latex.php?latex=%5Crho+%3D+0&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\rho = 0' title='\\rho = 0' class='latex' \/> \u3067\u3042\u308b\u300f\u3068\u3057\u307e\u3059\uff0e\u30b5\u30f3\u30d7\u30eb\u6570 n, \u76f8\u95a2\u4fc2\u6570 r \u304b\u3089\u8a08\u7b97\u3057\u305f t \u7d71\u8a08\u5024\u304c\uff0c\u6709\u610f\u6c34\u6e96 <img src='https:\/\/s0.wp.com\/latex.php?latex=%5Calpha&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\alpha' title='\\alpha' class='latex' \/> \u306b\u5bfe\u5fdc\u3059\u308b t \u7d71\u8a08\u5024\u3092\u8d8a\u3048\u308c\u3070\u5e30\u7121\u4eee\u8aac\u3092\u68c4\u5374\u3057\u307e\u3059\uff0e<\/p>\n<p><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+t+%3D+r%5Csqrt%7B%5Cfrac%7Bn+-+2%7D%7B1+-+r%5E2%7D%7D&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle t = r\\sqrt{\\frac{n - 2}{1 - r^2}}' title='\\displaystyle t = r\\sqrt{\\frac{n - 2}{1 - r^2}}' class='latex' \/><\/p>\n<\/p>\n<p>\u3000\u30d4\u30a2\u30bd\u30f3\u306e\u7a4d\u7387\u76f8\u95a2\u4fc2\u6570 r \u306e\u6709\u610f\u5dee\u691c\u5b9a\u306b\u3064\u3044\u3066\u4ee5\u524d\u8cea\u554f\u3092\u3044\u305f\u3060\u304d\u307e\u3057\u305f\u304c\uff0c\u53c2\u8003\u6587\u732e\u3092\u5165\u624b\u3057\u307e\u3057\u305f\u306e\u3067\u8ffd\u8a18\u3057\u307e\u3059\uff0e\u5b9f\u306f\u8a3c\u660e\u306a\u3069\u671f\u5f85\u3057\u3066\u3044\u305f\u306e\u3067\u3059\u304c\uff0c\u671f\u5f85\u306f\u305a\u308c\u3067\u3057\u305f\uff0e<img src='https:\/\/s0.wp.com\/latex.php?latex=%5Crho&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\rho' title='\\rho' class='latex' \/> \u306b\u3064\u3044\u3066\u306e\u5e30\u7121\u4eee\u8aac\u3092\u7c21\u5358\u306b\u691c\u5b9a\u3067\u304d\u308b\u6b63\u78ba\u306a\u65b9\u6cd5\u306f\u5b58\u5728\u3057\u306a\u3044\uff0c\u3068\u66f8\u3044\u3066\u3042\u308a\u307e\u3057\u305f\uff0e\u305d\u306e\u3088\u3046\u306a\u5e30\u7121\u4eee\u8aac\u306b\u5bfe\u3057\u3066 Fisher \u304c\u8fd1\u4f3c\u7684\u306a\u65b9\u6cd5\u3092\u63d0\u4f9b\u3057\u3066\u3044\u308b\u3068\u66f8\u304b\u308c\u3066\u3044\u307e\u3057\u305f\u304c\uff0c\u305d\u308c\u4ee5\u4e0a\u306e\u8a18\u8ff0\u306f\u3042\u308a\u307e\u305b\u3093\u3067\u3057\u305f\uff0e\u4ee5\u4e0b\u62d9\u8a33\u3067\u3059\uff0e<\/p>\n<blockquote>\n<p>\u3000\u5e30\u7121\u4eee\u8aac H (&rho; = 0) \u306f\u6b21\u306e\u5e30\u7121\u4eee\u8aac\u3068\u540c\u7b49\u3067\u3042\u308b\uff0eH (&beta;<sub>1<\/sub> = 0) \u307e\u305f\u306f H (&beta;<sub>2<\/sub> = 0)\uff0e\u305d\u3053\u3067\u4eee\u306b x, y \u304c\u5171\u540c\u4e8c\u5909\u91cf\u6b63\u898f\u5206\u5e03\u3092\u53d6\u308b\u5834\u5408\uff0c\u4eee\u306b\u691c\u5b9a\u5bfe\u8c61\u306e\u5e30\u7121\u4eee\u8aac\u304c\u771f\u3067\u3042\u308b\u3068\u3059\u308b\u3068\uff0c\u5e30\u7121\u4eee\u8aac H (&rho; = 0) \u306e\u305f\u3081\u306e\u691c\u5b9a\u304c\u5f97\u3089\u308c\u308b\uff0e<\/p>\n<p><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+F+%3D+%5Cfrac%7B%28n-2%29Z%5E2%7D%7BXY-Z%5E2%7D+%3D+%5Cfrac%7B%28n-2%29r%5E2%7D%7B1-r%5E2%7D%5Cvspace%7B0.1in%7D%5C%5C+X+%3D+%5Csum%28x+-+%5Cbar%7Bx%7D%29%5E2%5Cvspace%7B0.1in%7D%5C%5C+Y+%3D+%5Csum%28y+-+%5Cbar%7By%7D%29%5E2%5Cvspace%7B0.1in%7D%5C%5C+Z+%3D+%5Csum%28x+-+%5Cbar%7Bx%7D%29%28y+-+%5Cbar%7By%7D%29%5Cvspace%7B0.1in%7D%5C%5C+r%5E2+%3D+%5Cfrac%7BZ%5E2%7D%7BXY%7D&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle F = \\frac{(n-2)Z^2}{XY-Z^2} = \\frac{(n-2)r^2}{1-r^2}\\vspace{0.1in}\\\\ X = \\sum(x - \\bar{x})^2\\vspace{0.1in}\\\\ Y = \\sum(y - \\bar{y})^2\\vspace{0.1in}\\\\ Z = \\sum(x - \\bar{x})(y - \\bar{y})\\vspace{0.1in}\\\\ r^2 = \\frac{Z^2}{XY}' title='\\displaystyle F = \\frac{(n-2)Z^2}{XY-Z^2} = \\frac{(n-2)r^2}{1-r^2}\\vspace{0.1in}\\\\ X = \\sum(x - \\bar{x})^2\\vspace{0.1in}\\\\ Y = \\sum(y - \\bar{y})^2\\vspace{0.1in}\\\\ Z = \\sum(x - \\bar{x})(y - \\bar{y})\\vspace{0.1in}\\\\ r^2 = \\frac{Z^2}{XY}' class='latex' \/><\/p>\n<\/p>\n<p>\u3000\u4e0a\u8a18\u306e F \u306f\u81ea\u7531\u5ea6 n-2 \u306e F \u5206\u5e03\u306b\u5f93\u3046\uff0e\u540c\u7b49\u306e\u6709\u610f\u5dee\u691c\u5b9a\u3068\u3057\u3066\uff0c\u4eee\u306b\u5e30\u7121\u4eee\u8aac\u304c\u771f\u3060\u3068\u3059\u308b\u3068\u4ee5\u4e0b\u306e\u5f0f\u306f\u81ea\u7531\u5ea6 n-2 \u306e Student&#8217;s-t \u5206\u5e03\u306b\u5f93\u3046\uff0e<\/p>\n<p><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+t+%3D+%5Cfrac%7Br%5Csqrt%7Bn+-+2%7D%7D%7B%5Csqrt%7B1+-+r%5E2%7D%7D&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle t = \\frac{r\\sqrt{n - 2}}{\\sqrt{1 - r^2}}' title='\\displaystyle t = \\frac{r\\sqrt{n - 2}}{\\sqrt{1 - r^2}}' class='latex' \/><\/p>\n<\/p>\n<p>\u3000&rho; \u306b\u3064\u3044\u3066\u306e\u3044\u304b\u306a\u308b\u5e30\u7121\u4eee\u8aac\u3067\u3082\u76f8\u95a2\u4fc2\u6570 &rho; \u3068\u56de\u5e30\u4fc2\u6570 &beta;<sub>1<\/sub> \u304a\u3088\u3073 &beta;<sub>2<\/sub> \u3068\u306e\u9593\u306b\u5e73\u884c\u6027\u306f\u5b58\u5728\u3057\u306a\u3044\uff0e\u4e8b\u5b9f &rho; \u306b\u3064\u3044\u3066\u306e\u5e30\u7121\u4eee\u8aac\u3092\u7c21\u5358\u306b\u691c\u5b9a\u3067\u304d\u308b\u6b63\u78ba\u306a\u65b9\u6cd5\u306f\u5b58\u5728\u3057\u306a\u3044\uff0e\u305d\u306e\u3088\u3046\u306a\u5e30\u7121\u4eee\u8aac\u306b\u5bfe\u3057\u3066 Fisher \u304c\u8fd1\u4f3c\u7684\u306a\u65b9\u6cd5\u3092\u63d0\u4f9b\u3057\u3066\u3044\u308b\u304c\uff0c\u3053\u3053\u3067\u306f\u53d6\u308a\u6271\u308f\u306a\u3044\uff0e<\/p>\n<\/blockquote>\n<p><iframe src=\"\/\/rcm-fe.amazon-adsystem.com\/e\/cm?lt1=_blank&#038;bc1=000000&#038;IS2=1&#038;bg1=FFFFFF&#038;fc1=000000&#038;lc1=0000FF&#038;t=fujiitoshiki-22&#038;o=9&#038;p=8&#038;l=as4&#038;m=amazon&#038;f=ifr&#038;ref=ss_til&#038;asins=0852640684\" style=\"width:120px;height:240px;\" scrolling=\"no\" marginwidth=\"0\" marginheight=\"0\" frameborder=\"0\"><\/iframe><\/p>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>\u3000 \u3068 \u3068\u306e\u9593\u306e\u76f8\u95a2\u306e\u7a0b\u5ea6\u3092\u8868\u3059\u6307\u6a19\u3068\u3057\u3066\u30d4\u30a2\u30bd\u30f3\u306e\u7a4d\u7387\u76f8\u95a2\u4fc2\u6570 r \u304c\u3042\u308a\uff0c\u4e0b\u8a18\u306e\u5f0f\u3067\u8868\u73fe\u3057\u307e\u3059\uff0e\u76f8\u95a2\u4fc2\u6570 r \u306f -1 \u304b\u3089 1 \u306e\u7bc4\u56f2\u306b\u3042\u308a\u307e\u3059\uff0e and are average of and , respecti &hellip; <a href=\"https:\/\/www.fujiitoshiki.com\/improvesociety\/?p=1691\" class=\"more-link\"><span class=\"screen-reader-text\">&#8220;\u30d4\u30a2\u30bd\u30f3\u306e\u7a4d\u7387\u76f8\u95a2\u4fc2\u6570 r \u3068\u305d\u308c\u306b\u5bfe\u3059\u308b t \u691c\u5b9a&#8221; \u306e<\/span>\u7d9a\u304d\u3092\u8aad\u3080<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_crdt_document":"","_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"categories":[7],"tags":[],"class_list":["post-1691","post","type-post","status-publish","format-standard","hentry","category-statistics"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/posts\/1691","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1691"}],"version-history":[{"count":66,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/posts\/1691\/revisions"}],"predecessor-version":[{"id":7663,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/posts\/1691\/revisions\/7663"}],"wp:attachment":[{"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1691"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1691"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1691"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}