{"id":268,"date":"2022-08-14T19:59:18","date_gmt":"2022-08-14T10:59:18","guid":{"rendered":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/mann-whitney-u-test\/"},"modified":"2024-09-21T11:38:30","modified_gmt":"2024-09-21T02:38:30","slug":"mann-whitney-u-test","status":"publish","type":"post","link":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/mann-whitney-u-test\/","title":{"rendered":"\u30de\u30f3\u30db\u30a4\u30c3\u30c8\u30cb\u30fc\u306e U \u691c\u5b9a\u306b\u6700\u4f4e\u9650\u5fc5\u8981\u306a\u30b5\u30f3\u30d7\u30eb\u6570\u306f\u3044\u304f\u3064\u304b"},"content":{"rendered":"\n<p>\u30de\u30f3\u30db\u30a4\u30c3\u30c8\u30cb\u30fc\u306eU\u691c\u5b9a\u3092\u884c\u3046\u969b\u306b\u6700\u4f4e\u9650\u4f55\u4f8b\u3042\u308c\u3070\u3088\u3044\u304b\uff1f<\/p>\n\n\n\n<!--more-->\n\n\n\n<h2 class=\"wp-block-heading\" id=\"\u30de\u30f3\u30db\u30a4\u30c3\u30c8\u30cb\u30fc\u306eU\u691c\u5b9a\u306f\u3069\u3093\u306a\u8a08\u7b97\u3092\u3057\u3066\u3044\u308b\u304b\">\u30de\u30f3\u30db\u30a4\u30c3\u30c8\u30cb\u30fc\u306eU\u691c\u5b9a\u306f\u3069\u3093\u306a\u8a08\u7b97\u3092\u3057\u3066\u3044\u308b\u304b\uff1f<\/h2>\n\n\n\n<p>\u30de\u30f3\u30db\u30a4\u30c3\u30c8\u30cb\u30fc\u306eU\u691c\u5b9a\u306f\u305d\u3082\u305d\u3082\u3069\u3093\u306a\u8a08\u7b97\u3092\u3057\u3066\u3044\u308b\u304b\u3001\u3068\u3044\u3046\u70b9\u304b\u3089\u3001\u5404\u7fa4\u6700\u4f4e\u4f55\u4f8b\u5fc5\u8981\u304b\u3092\u8003\u3048\u305f\u3044\u3002<\/p>\n\n\n\n<p>\u6570\u5b66\u7684\u306b\u306f\u540c\u5024\u306b\u306a\u308b\u3001\u65b9\u6cd5\u304c2\u3064\u3042\u308b\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"\u65b9\u6cd5-1\">\u65b9\u6cd5 1<\/h3>\n\n\n\n<p>\u65b9\u6cd5\uff11\u306f\u3001\u6570\u5b57\u306e\u5927\u5c0f\u3067\u5927\u304d\u3044\u5834\u5408\u306f\uff11\uff0c\u5c0f\u3055\u3044\u5834\u5408\u306f\uff10\u3001\u540c\u3058\u5834\u5408\u306f1\/2\u3068\u30b9\u30b3\u30a2\u3092\u4ed8\u3051\u3066\u5408\u8a08\u3057\u3066\u3001\u691c\u5b9a\u7d71\u8a08\u91cf\u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5\u3060\u3002<\/p>\n\n\n\n<p>\u4f8b\u3048\u3070\u3001\u7fa4\uff58\u306e1.04\u306e\u5834\u5408\u3001\u7fa4\uff59\u306e1.15, 0.88, 0.90, 0.74, 1.21\u3068\u6bd4\u8f03\u3059\u308b\u3068\u30010\uff08\u5c0f\u3055\u3044\uff09\u3001\uff11\uff08\u5927\u304d\u3044\uff09\u3001\uff11\u3001\uff11\u3001\uff10\u3068\u3044\u3046\u3075\u3046\u306b\u30b9\u30b3\u30a2\u304c\u3064\u3051\u3089\u308c\u308b\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"527\" height=\"154\" src=\"https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2022\/08\/20220814192822.png\" alt=\"\" class=\"wp-image-1631\" title=\"\" srcset=\"https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2022\/08\/20220814192822.png 527w, https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2022\/08\/20220814192822-300x88.png 300w\" sizes=\"(max-width: 527px) 100vw, 527px\" \/><\/figure>\n\n\n\n<p><span itemscope=\"\" itemtype=\"http:\/\/schema.org\/Photograph\"><\/span><\/p>\n\n\n\n<p>\u3053\u308c\u3092\u3059\u3079\u3066\u306e\u5024\u306b\u3064\u3044\u3066\u3001\u30b9\u30b3\u30a2\u3092\u4ed8\u3051\u3066\u5408\u8a08\u3059\u308b\u3002<\/p>\n\n\n\n<p>\u4ee5\u4e0b\u306e\uff32\u30b9\u30af\u30ea\u30d7\u30c8\u3067Method One\u3068\u66f8\u3044\u3066\u3042\u308b\u3068\u3053\u308d\u304c\u3001\u30b9\u30b3\u30a2\u3092\u5408\u8a08\u3057\u3066\u3044\u308b\u3068\u3053\u308d\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<p>Ux1\u3001Uy1\u304cMethod One\u3067\u8a08\u7b97\u3057\u305f\u7d50\u679c\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code><span class=\"synComment\"># wilcoxon rank sum test and mann-whitney U test<\/span>\nx <span class=\"synStatement\">&lt;-<\/span> <span class=\"synIdentifier\">c(0.80,<\/span> <span class=\"synConstant\">0.83,<\/span> <span class=\"synConstant\">1.89,<\/span> <span class=\"synConstant\">1.04,<\/span> <span class=\"synConstant\">1.45,<\/span> <span class=\"synConstant\">2.01)<\/span>\ny <span class=\"synStatement\">&lt;-<\/span> <span class=\"synIdentifier\">c(1.15,<\/span> <span class=\"synConstant\">0.88,<\/span> <span class=\"synConstant\">0.90,<\/span> <span class=\"synConstant\">0.74,<\/span> <span class=\"synConstant\">1.21)<\/span>\n<span class=\"synIdentifier\">wilcox.test(<\/span>x<span class=\"synSpecial\">,<\/span> y<span class=\"synSpecial\">)<\/span>\n\n<span class=\"synComment\">#Method One:<\/span>\nUx1 <span class=\"synStatement\">&lt;-<\/span> <span class=\"synIdentifier\">sum(<\/span>\n<span class=\"synIdentifier\">c(0,0,0,1,0),<\/span>\n<span class=\"synIdentifier\">c(0,0,0,1,0),<\/span>\n<span class=\"synIdentifier\">c(1,1,1,1,1),<\/span>\n<span class=\"synIdentifier\">c(0,1,1,1,0),<\/span>\n<span class=\"synIdentifier\">c(1,1,1,1,1),<\/span>\n<span class=\"synIdentifier\">c(1,1,1,1,1)<\/span>\n<span class=\"synSpecial\">)<\/span>\nUy1 <span class=\"synStatement\">&lt;-<\/span> <span class=\"synIdentifier\">sum(<\/span>\n<span class=\"synIdentifier\">c(1,1,0,1,0,0),<\/span>\n<span class=\"synIdentifier\">c(1,1,0,0,0,0),<\/span>\n<span class=\"synIdentifier\">c(1,1,0,0,0,0),<\/span>\n<span class=\"synIdentifier\">c(0,0,0,0,0,0),<\/span>\n<span class=\"synIdentifier\">c(1,1,0,1,0,0)<\/span>\n<span class=\"synSpecial\">)<\/span>\n\n<span class=\"synComment\">#Method Two:<\/span>\nx.rank <span class=\"synStatement\">&lt;-<\/span> <span class=\"synIdentifier\">c(2,3,10,6,9,11)<\/span>\ny.rank <span class=\"synStatement\">&lt;-<\/span> <span class=\"synIdentifier\">c(7,4,5,1,8)<\/span>\nRx <span class=\"synStatement\">&lt;-<\/span> <span class=\"synIdentifier\">sum(<\/span>x.rank<span class=\"synSpecial\">)<\/span>\nRy <span class=\"synStatement\">&lt;-<\/span> <span class=\"synIdentifier\">sum(<\/span>y.rank<span class=\"synSpecial\">)<\/span>\nnx <span class=\"synStatement\">&lt;-<\/span> <span class=\"synIdentifier\">length(<\/span>x<span class=\"synSpecial\">)<\/span>\nny <span class=\"synStatement\">&lt;-<\/span> <span class=\"synIdentifier\">length(<\/span>y<span class=\"synSpecial\">)<\/span>\nUx2 <span class=\"synStatement\">&lt;-<\/span> Rx<span class=\"synStatement\">-<\/span>nx<span class=\"synStatement\">*(<\/span>nx<span class=\"synStatement\">+1)\/2<\/span>\nUy2 <span class=\"synStatement\">&lt;-<\/span> Ry<span class=\"synStatement\">-<\/span>ny<span class=\"synStatement\">*(<\/span>ny<span class=\"synStatement\">+1)\/2<\/span>\n<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"\u65b9\u6cd5-2\">\u65b9\u6cd5 2<\/h3>\n\n\n\n<p>\u65b9\u6cd5\uff12\uff08Method Two\uff09\u306f\u3001\u4e21\u7fa4\u306e\u5024\u3092\u5c0f\u3055\u3044\u9806\u306b\u4e26\u3079\u3066\u3001\u901a\u3057\u3067\u9806\u4f4d\u3092\u3064\u3051\u3066\u3001\u7fa4\u3054\u3068\u306b\u5408\u8a08\u3059\u308b\u3002<\/p>\n\n\n\n<p>\u3068\u3082\u306b\u7fa4\u3054\u3068\u306b\uff11\u304b\u3089\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\uff08\u4eca\u56de\u306f\uff16\u3068\uff15\uff09\u307e\u3067\u306e\u5408\u8a08\uff08nx*(nx+1)\/2, ny*(ny+1)\/2 \u306e\u3068\u3053\u308d\uff09\u3092\u5f15\u304f\u3068\u3001Ux2, Uy2\u306b\u306a\u308b\u3002<\/p>\n\n\n\n<p>\u7d50\u679c\u3068\u3057\u3066\u3001Ux1, Ux2\u306f\u540c\u3058\u5024\u306b\u306a\u308b\u3057\u3001Uy1, Uy2\u3082\u540c\u3058\u5024\u306b\u306a\u308b\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"460\" height=\"318\" src=\"https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2022\/08\/20220814193803.png\" alt=\"\" class=\"wp-image-1633\" title=\"\" srcset=\"https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2022\/08\/20220814193803.png 460w, https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2022\/08\/20220814193803-300x207.png 300w\" sizes=\"(max-width: 460px) 100vw, 460px\" \/><\/figure>\n\n\n\n<p><span itemscope=\"\" itemtype=\"http:\/\/schema.org\/Photograph\"><\/span><\/p>\n\n\n\n<p>\u8981\u3059\u308b\u306b\u3001Method One\u306e\u7d50\u679c\u3068\u3001Method Two\u306e\u7d50\u679c\u304c\u4e00\u81f4\u3057\u3066\u3044\u308b\u306e\u304c\u308f\u304b\u308b\u3002<\/p>\n\n\n\n<p>\u3044\u305a\u308c\u306e\u65b9\u6cd5\u3067\u3082\u7d50\u679c\u306f\u540c\u3058\u3068\u3044\u3046\u3053\u3068\u3060\u304c\u3001\u3064\u307e\u308a\u306f\u30de\u30f3\u30db\u30a4\u30c3\u30c8\u30cb\u30fc\u306eU\u691c\u5b9a\u306f\u3053\u306e\u3088\u3046\u306a\u8a08\u7b97\u3092\u3057\u3066\u691c\u5b9a\u3057\u3066\u3044\u308b\u3068\u3044\u3046\u3053\u3068\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<p>\u539f\u8457\u8ad6\u6587\u306e\u6570\u5024\u8868\u3092\u78ba\u8a8d\u3059\u308b\u3068\u3001\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u304c\u5927\u304d\u3044\u7fa4\u304cn=6\u3001\u5c0f\u3055\u3044\u7fa4\u304cn=5\u306a\u306e\u3067\u3001n=6\u306e\u8868\u3092\u898b\u308b\u3053\u3068\u306b\u306a\u308b\u3002<\/p>\n\n\n\n<p>m=5\u3067\u3001U\u304c10\uff08\u4e0a\u8a18\u3067\u306fUy1\u3084Uy2\u304c10\u3067\u3042\u3063\u305f\uff09\u3092\u898b\u308b\u3068 .214 \u3068\u3042\u308b\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"383\" height=\"625\" src=\"https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2022\/08\/20220814155003.png\" alt=\"\" class=\"wp-image-1634\" title=\"\" srcset=\"https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2022\/08\/20220814155003.png 383w, https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2022\/08\/20220814155003-184x300.png 184w\" sizes=\"(max-width: 383px) 100vw, 383px\" \/><\/figure>\n\n\n\n<p><span itemscope=\"\" itemtype=\"http:\/\/schema.org\/Photograph\"><\/span><\/p>\n\n\n\n<p>\u3053\u306e\u78ba\u7387\u306f\u7247\u5074\u306a\u306e\u3067\u3001\u901a\u5e38\u306e\u4e21\u5074\u691c\u5b9a\u3068\u3059\u308b\u3068\u305d\u306e\u500d\u306e 0.428 \u304c\u6c42\u3081\u308b\u3079\u304d\u6709\u610f\u78ba\u7387\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<p>R \u306e\u95a2\u6570\u306e wilcox.test() \u3067\u8a08\u7b97\u3059\u308b\u3068\u4ee5\u4e0b\u306e\u901a\u308a\u3068\u306a\u308a\u3001\u307b\u307c\u540c\u3058\u6709\u610f\u78ba\u7387 0.4286 \u304c\u5f97\u3089\u308c\u308b\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"793\" height=\"306\" src=\"https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2022\/08\/20220814153716.png\" alt=\"\" class=\"wp-image-1635\" title=\"\" srcset=\"https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2022\/08\/20220814153716.png 793w, https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2022\/08\/20220814153716-300x116.png 300w, https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2022\/08\/20220814153716-768x296.png 768w\" sizes=\"(max-width: 793px) 100vw, 793px\" \/><\/figure>\n\n\n\n<p><span itemscope=\"\" itemtype=\"http:\/\/schema.org\/Photograph\"><\/span><\/p>\n\n\n\n<p>W=20\u304c\u691c\u5b9a\u7d71\u8a08\u91cf\u3067\u3042\u308b\u304c\u3001Ux1, Ux2\u306e20\u306e\u307b\u3046\u3092\u4f7f\u3063\u3066\u3044\u308b\u3002<\/p>\n\n\n\n<p>\u5c0f\u3055\u3044\u307b\u3046\u3092\u4f7f\u3046\u306e\u304c\u3082\u3068\u3082\u3068\u306e\u65b9\u6cd5\u3067\u3042\u308b\u304c\u3001R \u3067\u306f\u3001\u5927\u304d\u3044\u307b\u3046\u3092\u4f7f\u3063\u3066\u8a08\u7b97\u3057\u3066\u3044\u308b\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"\u30de\u30f3\u30db\u30a4\u30c3\u30c8\u30cb\u30fc\u306eU\u691c\u5b9a\u306f\u5404\u7fa4\u6700\u4f4e\u4f55\u4f8b\u5fc5\u8981\u304b\">\u30de\u30f3\u30db\u30a4\u30c3\u30c8\u30cb\u30fc\u306eU\u691c\u5b9a\u306f\u5404\u7fa4\u6700\u4f4e\u4f55\u4f8b\u5fc5\u8981\u304b\uff1f<\/h2>\n\n\n\n<p>\u4e0a\u8a18\u306e\u901a\u308a\u3001\u30de\u30f3\u30db\u30a4\u30c3\u30c8\u30cb\u30fc\u306eU\u306f\u5927\u304d\u3044\u5834\u5408\u306f\uff11\u3001\u540c\u3058\u5834\u5408\u306f0.5\u3092\u8db3\u3057\u5408\u308f\u305b\u3066\u3044\u304f\u3001\u3082\u3057\u304f\u306f\u9806\u4f4d\u3092\u8db3\u3057\u5408\u308f\u305b\u3066\u3044\u304f\u3060\u3051\u306a\u306e\u3067\u3001\u6975\u7aef\u306a\u8a71 n=1 \u3067\u3082\u8a08\u7b97\u3067\u304d\u308b\u3002<\/p>\n\n\n\n<p>\u4e8b\u5b9f\u3001\u30de\u30f3\u30db\u30a4\u30c3\u30c8\u30cb\u30fc\u306e\u539f\u8457\u8ad6\u6587\u3092\u898b\u308b\u3068\u3001\u6700\u5c0f\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u306f\u3001n=3, m=1\u3001\u3064\u307e\u308a\u3001\u7fa4\uff11\u306f\uff13\u4f8b\u3001\u7fa4\uff12\u306f\uff11\u4f8b\u3068\u3044\u3046\u72b6\u6cc1\u3067\u691c\u5b9a\u7d71\u8a08\u91cfU\u306e\u6709\u610f\u78ba\u7387\u3092\u793a\u3057\u3066\u3044\u308b\u3002<\/p>\n\n\n\n<p>\u7406\u8ad6\u7684\u306b\u306f\u30013\u4f8b\u30681\u4f8b\u306e\u5408\u8a084\u4f8b\u3067\u89e3\u6790\u3067\u304d\u308b\u3068\u3044\u3046\u3053\u3068\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"788\" height=\"519\" src=\"https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2022\/08\/20220814195612.png\" alt=\"\" class=\"wp-image-1636\" title=\"\" srcset=\"https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2022\/08\/20220814195612.png 788w, https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2022\/08\/20220814195612-300x198.png 300w, https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2022\/08\/20220814195612-768x506.png 768w\" sizes=\"(max-width: 788px) 100vw, 788px\" \/><\/figure>\n\n\n\n<p><span itemscope=\"\" itemtype=\"http:\/\/schema.org\/Photograph\"><\/span><\/p>\n\n\n\n<div id=\"biost-95685643\" class=\"biost- biost-entity-placement\"><p style=\"text-align: center;\"><span style=\"font-size: 20px;\"><strong><a href=\"https:\/\/best-biostatistics.com\/kmhl\">\uff1e\uff1e\u3082\u3046\u7d71\u8a08\u3067\u60a9\u3080\u306e\u306f\u7d42\u308f\u308a\u306b\u3057\u307e\u305b\u3093\u304b\uff1f\u00a0<\/a><\/strong><\/span><\/p>\r\n<a href=\"https:\/\/best-biostatistics.com\/kmhl\"><img class=\"aligncenter wp-image-2794 size-full\" src=\"https:\/\/best-biostatistics.com\/wp\/wp-content\/uploads\/2023\/11\/bn_r_03.png\" alt=\"\" width=\"500\" height=\"327\" \/><\/a>\r\n<p style=\"text-align: center;\"><span style=\"color: #ff0000; font-size: 20px;\"><strong><span 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id=\"\u95a2\u9023\u8a18\u4e8b\">\u95a2\u9023\u8a18\u4e8b<\/h2>\n\n\n\n<p>\u30b5\u30f3\u30d7\u30eb\u6570\u8a08\u7b97\u306b\u3064\u3044\u3066\u306f\u3001\u904e\u53bb\u8a18\u4e8b\u53c2\u7167\u3002<\/p>\n\n\n<div class=\"swell-block-postLink\">\t\t\t<div class=\"p-blogCard -internal\" data-type=\"type1\" data-onclick=\"clickLink\">\n\t\t\t\t<div class=\"p-blogCard__inner\">\n\t\t\t\t\t<span class=\"p-blogCard__caption\">\u3042\u308f\u305b\u3066\u8aad\u307f\u305f\u3044<\/span>\n\t\t\t\t\t<div class=\"p-blogCard__thumb c-postThumb\"><figure class=\"c-postThumb__figure\"><img decoding=\"async\" src=\"https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2024\/08\/1920x1080-video-Excel-300x169.jpg\" alt=\"\" class=\"c-postThumb__img u-obf-cover\" width=\"320\" height=\"180\"><\/figure><\/div>\t\t\t\t\t<div class=\"p-blogCard__body\">\n\t\t\t\t\t\t<a class=\"p-blogCard__title\" href=\"https:\/\/best-biostatistics.com\/toukei-er\/entry\/sample-size-determination-non-parametric-test\/\">R \u3067\u30de\u30f3\u30db\u30a4\u30c3\u30c8\u30cb\u30fc\u306e U \u691c\u5b9a\u306b\u5fc5\u8981\u306a\u30b5\u30f3\u30d7\u30eb\u6570\u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5<\/a>\n\t\t\t\t\t\t<span class=\"p-blogCard__excerpt\">\u30de\u30f3\u30db\u30a4\u30c3\u30c8\u30cb\u30fc U \u691c\u5b9a\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97\u306e\u65b9\u6cd5 \u30de\u30f3\u30db\u30a4\u30c3\u30c8\u30cb\u30fc\u306e U \u691c\u5b9a \u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97 R \u306e\u201dsamplesize&#8221;\u3068\u3044\u3046\u30d1\u30c3\u30b1\u30fc\u30b8\u3067\u3001\u30de\u30f3\u30db\u30a4\u30c3\u30c8\u30cb\u30fc\u306e U \u691c\u5b9a&#8230;<\/span>\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/div>\n\n\n\n\n\n\n<h2 class=\"wp-block-heading\" id=\"\u53c2\u8003\u6587\u732e\">\u53c2\u8003\u6587\u732e<\/h2>\n\n\n\n<p>\u30de\u30f3\u30db\u30a4\u30c3\u30c8\u30cb\u30fc\u306e\u539f\u8457\u8ad6\u6587<\/p>\n\n\n\n<p><a href=\"https:\/\/projecteuclid.org\/journals\/annals-of-mathematical-statistics\/volume-18\/issue-1\/On-a-Test-of-Whether-one-of-Two-Random-Variables\/10.1214\/aoms\/1177730491.full\">On a Test of Whether one of Two Random Variables is Stochastically Larger than the Other<\/a><\/p>\n\n\n\n\n","protected":false},"excerpt":{"rendered":"<p>\u30de\u30f3\u30db\u30a4\u30c3\u30c8\u30cb\u30fc\u306eU\u691c\u5b9a\u3092\u884c\u3046\u969b\u306b\u6700\u4f4e\u9650\u4f55\u4f8b\u3042\u308c\u3070\u3088\u3044\u304b\uff1f<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"swell_btn_cv_data":"","_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[19,41],"tags":[],"class_list":["post-268","post","type-post","status-publish","format-standard","hentry","category-19","category-u"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/posts\/268","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/comments?post=268"}],"version-history":[{"count":2,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/posts\/268\/revisions"}],"predecessor-version":[{"id":1638,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/posts\/268\/revisions\/1638"}],"wp:attachment":[{"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/media?parent=268"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/categories?post=268"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/tags?post=268"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}