{"id":257,"date":"2022-09-02T21:31:41","date_gmt":"2022-09-02T12:31:41","guid":{"rendered":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/requirement-for-kruskal-wallis-test\/"},"modified":"2024-09-21T08:26:07","modified_gmt":"2024-09-20T23:26:07","slug":"requirement-for-kruskal-wallis-test","status":"publish","type":"post","link":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/requirement-for-kruskal-wallis-test\/","title":{"rendered":"\u30af\u30e9\u30b9\u30ab\u30eb\u30a6\u30a9\u30ea\u30b9\u691c\u5b9a\u306e\u5404\u7fa4\u30b5\u30f3\u30d7\u30eb\u6570\u6761\u4ef6\u3068\u30bf\u30a4\u30c7\u30fc\u30bf\u306e\u5f71\u97ff"},"content":{"rendered":"\n

\u30af\u30e9\u30b9\u30ab\u30eb\u30a6\u30a9\u30ea\u30b9\u691c\u5b9a\u3092\u3001\u539f\u8457\u306b\u7acb\u3061\u8fd4\u3063\u3066\u3001\u308f\u304b\u308a\u3084\u3059\u304f\u89e3\u8aac\u3002<\/p>\n\n\n\n

\u5404\u7fa4\u306e\u30b5\u30f3\u30d7\u30eb\u6570\u304c\u504f\u3063\u3066\u306f\u3044\u3051\u306a\u3044\u306a\u3069\u306e\u6761\u4ef6\u304c\u3042\u308b\u306e\u304b\u3069\u3046\u304b\u3001\u307e\u305f\u3001\u30bf\u30a4\u30c7\u30fc\u30bf\uff08\u540c\u9806\u4f4d\u30c7\u30fc\u30bf\uff09\u306e\u5f71\u97ff\u306b\u3064\u3044\u3066\u3002<\/p>\n\n\n\n\n\n\n\n

\u30af\u30e9\u30b9\u30ab\u30eb\u30a6\u30a9\u30ea\u30b9\u691c\u5b9a\u3068\u306f\uff1f<\/h2>\n\n\n\n

\u30af\u30e9\u30b9\u30ab\u30eb\u30a6\u30a9\u30ea\u30b9\u691c\u5b9a\u3068\u306f\u3001\uff13\u7fa4\u4ee5\u4e0a\u306e\u7fa4\u304c\u3042\u3063\u305f\u3068\u304d\u306e\u9806\u4f4d\u3092\u7528\u3044\u305f\u30ce\u30f3\u30d1\u30e9\u30e1\u30c8\u30ea\u30c3\u30af\u306a\u5206\u6563\u5206\u6790\u3068\u8003\u3048\u308c\u3070\u3088\u3044\u3002<\/p>\n\n\n\n

\u5404\u7fa4\u306e\u5e73\u5747\u9806\u4f4d\u3092\u6bd4\u8f03\u3057\u3066\u3044\u308b\u3068\u7406\u89e3\u3059\u308c\u3070OK\u3067\u3042\u308b\u3002<\/p>\n\n\n\n

\u4ee5\u4e0b\u3082\u53c2\u7167\u306e\u3053\u3068\u3002<\/p>\n\n\n

\t\t\t
\n\t\t\t\t
\n\t\t\t\t\t\u3042\u308f\u305b\u3066\u8aad\u307f\u305f\u3044<\/span>\n\t\t\t\t\t
\"\"<\/figure><\/div>\t\t\t\t\t
\n\t\t\t\t\t\t\u30af\u30e9\u30b9\u30ab\u30eb\u30a6\u30a9\u30ea\u30b9\u691c\u5b9a\u3068\u30de\u30f3\u30db\u30a4\u30c3\u30c8\u30cb\u30fc\u306e U \u691c\u5b9a\u306f\u4f55\u3092\u691c\u5b9a\u3057\u3066\u3044\u308b\u304b<\/a>\n\t\t\t\t\t\t\u30ce\u30f3\u30d1\u30e9\u30e1\u30c8\u30ea\u30c3\u30af\u691c\u5b9a\u306e\u5834\u5408\u3001\u5e73\u5747\u5024\u306e\u5dee\u3092\u4f7f\u3063\u3066\u3044\u308b\u308f\u3051\u3067\u306f\u306a\u3044\u304c\u3001\u3067\u306f\u4f55\u306e\u691c\u5b9a\u306a\u306e\u304b\uff1f \u30af\u30e9\u30b9\u30ab\u30eb\u30a6\u30a9\u30ea\u30b9\u691c\u5b9a\u306f\u4f55\u306e\u5dee\u3092\u898b\u3066\u3044\u308b\u306e\u304b\uff1f \u30af\u30e9\u30b9\u30ab\u30eb\u30a6\u30a9\u30ea\u30b9\u691c…<\/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

\u691c\u5b9a\u7d71\u8a08\u91cf H \u3092\u8a08\u7b97\u3057\u3066\u3001\u6709\u610f\u78ba\u7387\u3092\u6c42\u3081\u308b\u3053\u3068\u306b\u306a\u308b\u3002<\/p>\n\n\n\n

\\begin{equation}
H = \\frac{12}{N(N+1)} \\sum \\frac{R^2}{n} – 3(N+1)
\\end{equation}<\/p>\n\n\n\n

\u3053\u3053\u3067\u3001N \u306f\u5168\u7fa4\u3092\u5408\u308f\u305b\u305f\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u3001$ R^2 $ \u306f\u5404\u7fa4\u306e\u9806\u4f4d\u306e\u5408\u8a08\u306e\uff12\u4e57\u3001n \u306f\u5404\u7fa4\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u3001$ \\sum $ \u306f\u6dfb\u3048\u5b57\u3092\u7701\u7565\u3057\u3066\u3044\u308b\u304c\u3001\u5404\u7fa4\u306e\u5024\u304c\u8a08\u7b97\u3055\u308c\u305f\u3089\u3001\u5168\u7fa4\u3092\u5408\u8a08\u3059\u308b\u610f\u5473\u3067\u3042\u308b\u3002<\/p>\n\n\n\n

\u3053\u306e\u691c\u5b9a\u7d71\u8a08\u91cf\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u3082\u66f8\u3051\u308b\u3002<\/p>\n\n\n\n

\\begin{equation}
H = \\frac{N-1}{N} \\sum \\frac{n (\\bar{R} – \\frac{1}{2} (N + 1))^2}{(N^2-1)\/12}
\\end{equation}<\/p>\n\n\n\n

\u3053\u3053\u3067\u3001\u4e0a\u306e\u5f0f\u3068\u540c\u3058\u8a18\u53f7\u306f\u540c\u3058\u3082\u306e\u3092\u6307\u3057\u3066\u3044\u3066\u3001\u4e0a\u306b\u306f\u767b\u5834\u3057\u306a\u304b\u3063\u305f $ \\bar{R} $ \u306f\u5404\u7fa4\u306e\u5e73\u5747\u9806\u4f4d\u3092\u8868\u3057\u3066\u3044\u308b\u3002<\/p>\n\n\n\n

$ \\frac{1}{2} (N + 1) $ \u306f\u3001N \u500b\u306e\u9806\u4f4d\u306e\u5e73\u5747\u9806\u4f4d\u306e\u516c\u5f0f\u3067\u3042\u308b\u3002<\/p>\n\n\n\n

\u306a\u306e\u3067\u3001$ (\\bar{R} – \\frac{1}{2} (N + 1))^2 $ \u306e\u90e8\u5206\u306f\u3001\u5404\u7fa4\u306e\u5e73\u5747\u9806\u4f4d\u3068\u5168\u4f53\u306e\u5e73\u5747\u9806\u4f4d\u306e\u5dee\u306e2\u4e57\u3092\u8a08\u7b97\u3057\u3066\u3044\u308b\u3053\u3068\u304c\u308f\u304b\u308b\u3002<\/p>\n\n\n\n

\u307e\u3055\u306b\u3053\u306e\u90e8\u5206\u304c\u5e73\u5747\u9806\u4f4d\u3092\u4f7f\u3063\u305f\u7fa4\u9593\u6bd4\u8f03\u3068\u3044\u3046\u5f62\u306e\u5206\u6563\u5206\u6790\u3068\u7406\u89e3\u3067\u304d\u308b\u3086\u3048\u3093\u3067\u3042\u308b\u3002<\/p>\n\n\n\n

\u3053\u306e\u5f0f\u306b\u3059\u308b\u3068\u3001\u5404\u7fa4\u306e\u5e73\u5747\u9806\u4f4d\u3092\u6bd4\u3079\u3066\u3044\u308b\u3053\u3068\u304c\u826f\u304f\u308f\u304b\u308b\u3002<\/p>\n\n\n\n

\u305d\u3057\u3066\u3001\u3053\u306e\u691c\u5b9a\u7d71\u8a08\u91cf\u304c \u81ea\u7531\u5ea6 \u7fa4\u306e\u6570\u30fc\uff11 \uff08\u4f8b\u3048\u3070\u5168\uff13\u7fa4\u3067\u3042\u308c\u3070\uff12\uff09\u306e $ \\chi^2 $ \u5206\u5e03\u306b\u5f93\u3046\u3068\u3044\u3046\u6027\u8cea\u3092\u4f7f\u3063\u3066\u6709\u610f\u78ba\u7387\u3092\u6c42\u3081\u308b\u3002<\/p>\n\n\n\n

\u6709\u610f\u6c34\u6e96\uff08\u4f8b\u3048\u3070\uff15\uff05\uff09\u3088\u308a\u3082\u6709\u610f\u78ba\u7387\u304c\u5c0f\u3055\u3051\u308c\u3070\u3001\u6bd4\u8f03\u3057\u305f\u7fa4\u305f\u3061\u306f\u3001\u7d71\u8a08\u5b66\u7684\u6709\u610f\u306b\u7570\u306a\u308b\u3068\u8a00\u3048\u308b\u3002<\/p>\n\n\n\n

\u30af\u30e9\u30b9\u30ab\u30eb\u30a6\u30a9\u30ea\u30b9\u691c\u5b9a\u306f\u5404\u7fa4\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u304c\u540c\u7a0b\u5ea6\u3067\u3042\u308b\u3053\u3068\u304c\u6761\u4ef6\u304b\uff1f<\/h2>\n\n\n\n

\u30cd\u30c3\u30c8\u4e0a\u306b\u306f\u3001\u5404\u7fa4\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u304c\u7570\u306a\u308b\u3053\u3068\u3092\u5fc3\u914d\u3057\u3066\u76f8\u8ac7\u3057\u3066\u3044\u308b\u76f8\u8ac7\u8005\u304c\u6563\u898b\u3055\u308c\u305f\u304c\u3001\u30af\u30e9\u30b9\u30ab\u30eb\u30a6\u30a9\u30ea\u30b9\u691c\u5b9a\u306b\u304a\u3044\u3066\u3001\u5404\u7fa4\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u304c\u540c\u7a0b\u5ea6\u3067\u3042\u308b\u3053\u3068\u304c\u6761\u4ef6\u3067\u3042\u308b\u3068\u3044\u3046\u8a18\u8ff0\u306f\u898b\u3064\u304b\u3089\u306a\u304b\u3063\u305f\u3002<\/p>\n\n\n\n

\u539f\u8457\u8ad6\u6587\u306e\u8a08\u7b97\u5f0f\u3092\u78ba\u8a8d\u3057\u3066\u3082\u3001\u305d\u306e\u3088\u3046\u306a\u6761\u4ef6\u306f\u66f8\u3044\u3066\u3044\u306a\u3044\u3002<\/p>\n\n\n\n

\u3057\u305f\u304c\u3063\u3066\u3001\u5404\u7fa4\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u304c\u540c\u7a0b\u5ea6\u3067\u3042\u308b\u3053\u3068\u304c\u6761\u4ef6\u3067\u3042\u308b\u3068\u306f\u8a00\u3048\u306a\u3044\u3002<\/p>\n\n\n\n

\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>\r\n

\u21911\u4e07\u4eba\u4ee5\u4e0a\u306e\u533b\u7642\u5f93\u4e8b\u8005\u304c\u8cfc\u8aad\u4e2d<\/span><\/strong><\/span><\/p><\/div>

\u30af\u30e9\u30b9\u30ab\u30eb\u30a6\u30a9\u30ea\u30b9\u691c\u5b9a\u306b\u304a\u3051\u308b \u30bf\u30a4\u30c7\u30fc\u30bf\u306e\u652f\u969c\u306e\u7a0b\u5ea6\u306f\u3069\u306e\u304f\u3089\u3044\u304b\uff1f<\/h2>\n\n\n\n

\u30bf\u30a4 (tie) \u30c7\u30fc\u30bf\u3068\u3044\u3046\u306e\u306f\u3001\u9023\u7d9a\u30c7\u30fc\u30bf\u3067\u540c\u3058\u5024\u306e\u30c7\u30fc\u30bf\u3067\u3001\u9806\u4f4d\u306b\u5909\u63db\u3059\u308b\u3068\u540c\u9806\u4f4d\u306b\u306a\u308b\u30c7\u30fc\u30bf\u306e\u3053\u3068\u3002<\/p>\n\n\n\n

\u30bf\u30a4\u30c7\u30fc\u30bf\u304c\u3042\u308b\u5834\u5408\u306f\u3001\u305d\u306e\u6570\u306b\u5fdc\u3058\u3066\u691c\u5b9a\u7d71\u8a08\u91cf\u3092\u8abf\u6574\u3059\u308b\u3053\u3068\u306b\u306a\u308b\u3002<\/p>\n\n\n\n

\u30bf\u30a4\u30c7\u30fc\u30bf\u306f\u3001\u4ee5\u4e0b\u306e\u5f0f\u3067\u8abf\u6574\u5024\u3092\u8a08\u7b97\u3057\u3066\u3001\u305d\u306e\u5024\u3067\u691c\u5b9a\u7d71\u8a08\u91cf H \u3092\u5272\u308b\u3002<\/p>\n\n\n\n

\\begin{equation}
1 – \\frac{\\sum T}{N^3-N}
\\end{equation}<\/p>\n\n\n\n

\u3053\u3053\u3067\u3001$ T = (t – 1) t (t + 1) = t^3 – t $ \u3068\u8a08\u7b97\u3059\u308b\u306e\u3060\u304c\u3001t \u306f\u3001\u30bf\u30a4\u9806\u4f4d\u30b0\u30eb\u30fc\u30d7\u5185\u306e\u500b\u6570\u3067\u3042\u308b\u3002<\/p>\n\n\n\n

5\u500b\u30bf\u30a4\u304c\u3042\u308b\u9806\u4f4d\u304c\u3042\u308b\u3068\u3059\u308b\u3068\u305d\u306e\u6642\u306e T \u306f\u3001$ 5^3 – 5 = 125 – 5 = 120 $ \u3068\u306a\u308b\u3002<\/p>\n\n\n\n

10\u500b\u30bf\u30a4\u304c\u3042\u308b\u9806\u4f4d\u306e\u5834\u5408\u306f\u3001$ T = 10^3 – 10 = 1000 – 10 = 990 $ \u3068\u306a\u308a\u3001\u30bf\u30a4\u304c\u5897\u3048\u308b\u3068 T \u306f\u3069\u3093\u3069\u3093\u5927\u304d\u304f\u306a\u308b\u304c\u3001\u5206\u5b50\u304c\u5206\u6bcd\u3092\u8d85\u3048\u308b\u3053\u3068\u306f\u306a\u3044\u3002<\/p>\n\n\n\n

N \u306f\u3001\u3059\u3079\u3066\u306e\u7fa4\u306e\u4f8b\u6570\u3092\u8db3\u3057\u5408\u308f\u305b\u305f\u7dcf\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u3067\u3042\u308b\u3002<\/p>\n\n\n\n

\u30bf\u30a4\u306e\u6570\u304c\u5927\u304d\u304f\u306a\u308c\u3070\u306a\u308b\u307b\u3069\u3001\u5206\u5b50\u304c\u5927\u304d\u304f\u306a\u308a\u3001\u5f0f\u5168\u4f53\u306e\u5024\u306f\uff11\u3088\u308a\u5c0f\u3055\u304f\u306a\u3063\u3066\u3044\u304f\u3002<\/p>\n\n\n\n

\uff11\u3088\u308a\u5c0f\u3055\u3044\u5024\u3067\u691c\u5b9a\u7d71\u8a08\u91cf\u3092\u5272\u308b\u3068\u3001\u691c\u5b9a\u7d71\u8a08\u91cf\u306f\u5927\u304d\u304f\u306a\u308b\u3002<\/p>\n\n\n\n

\u3064\u307e\u308a\u306f\u3001\u3088\u308a\u7d71\u8a08\u5b66\u7684\u6709\u610f\u306b\u8fd1\u304f\u306a\u308b\u308f\u3051\u3067\u3042\u308b\u3002<\/p>\n\n\n\n

\u3068\u3044\u3046\u3053\u3068\u306f\u3001\u30bf\u30a4\u30c7\u30fc\u30bf\u304c\u5897\u3048\u3066\u3082\u3001\u5c11\u306a\u304f\u3068\u3082\u7d71\u8a08\u5b66\u7684\u306b\u4e0d\u5229\u3068\u306a\u308b\u3053\u3068\u306f\u306a\u3055\u305d\u3046\u3060\u3002<\/p>\n\n\n\n

\u307e\u3068\u3081<\/h2>\n\n\n\n

\u30af\u30e9\u30b9\u30ab\u30eb\u30a6\u30a9\u30ea\u30b9\u691c\u5b9a\u3092\u539f\u8457\u306b\u7acb\u3061\u8fd4\u3063\u3066\u3001\u5c11\u3005\u306e\u8a08\u7b97\u5f0f\u3092\u4ea4\u3048\u306a\u304c\u3089\u3001\u308f\u304b\u308a\u3084\u3059\u304f\u89e3\u8aac\u3057\u305f\u3002<\/p>\n\n\n\n

\u30af\u30e9\u30b9\u30ab\u30eb\u30a6\u30a9\u30ea\u30b9\u691c\u5b9a\u304c\u9069\u5207\u3067\u3042\u308b\u6761\u4ef6\u3068\u3057\u3066\u3001\u5404\u7fa4\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u304c\u540c\u7a0b\u5ea6\u3067\u3042\u308b\u3053\u3068\u304c\u5fc5\u8981\u304b\u3069\u3046\u304b\u78ba\u8a8d\u3057\u305f\u3068\u3053\u308d\u3001\u305d\u306e\u3088\u3046\u306a\u8a18\u8f09\u306f\u898b\u3064\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u306a\u304b\u3063\u305f\u3002<\/p>\n\n\n\n

\u307e\u305f\u3001\u30bf\u30a4\u30c7\u30fc\u30bf\u304c\u5897\u3048\u308b\u3053\u3068\u304c\u4f55\u304b\u652f\u969c\u304c\u3042\u308b\u304b\u3069\u3046\u304b\u3092\u78ba\u8a8d\u3057\u305f\u3068\u3053\u308d\u3001\u652f\u969c\u3092\u304d\u305f\u3059\u3068\u3044\u3046\u8a3c\u62e0\u306f\u5f97\u3089\u308c\u306a\u304b\u3063\u305f\u3002<\/p>\n\n\n\n

\u3057\u305f\u304c\u3063\u3066\u3001\u30af\u30e9\u30b9\u30ab\u30eb\u30a6\u30a9\u30ea\u30b9\u691c\u5b9a\u306f\u3001\u5404\u7fa4\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u306e\u5927\u304d\u3055\u304c\u7570\u306a\u3063\u3066\u3044\u3066\u3082\u5fc3\u914d\u305b\u305a\u5b9f\u65bd\u3067\u304d\u308b\u3057\u3001\u30bf\u30a4\u30c7\u30fc\u30bf\u304c\u591a\u304f\u3066\u3082\u5fc3\u914d\u305b\u305a\u306b\u5b9f\u65bd\u3067\u304d\u308b\u3068\u8a00\u3048\u308b\u3002<\/p>\n\n\n\n

\u539f\u8457\u8ad6\u6587\u30ea\u30f3\u30af<\/h2>\n\n\n\n

William H. Kruskal and W. Allen Wallis. Use of Ranks in One-Criterion Variance Analysis<\/p>\n\n\n\n

https:\/\/people.ucalgary.ca\/~jefox\/Kruskal%20and%20Wallis%201952.pdf<\/a><\/p>\n\n\n\n

\u53c2\u8003\u30ea\u30f3\u30af<\/h2>\n\n\n\n

Kruskal Wallis test for unequal group size?<\/p>\n\n\n\n

Kruskal Wallis test for unequal group size? | ResearchGate<\/a><\/p>\n\n\n\n

spss – Non-parametric test for unequal samples with subsequent post-hoc analysis? – Cross Validated<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

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