{"id":248,"date":"2022-09-18T18:50:46","date_gmt":"2022-09-18T09:50:46","guid":{"rendered":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/kendall-rank-correlation-coefficient\/"},"modified":"2024-09-05T22:18:51","modified_gmt":"2024-09-05T13:18:51","slug":"kendall-rank-correlation-coefficient","status":"publish","type":"post","link":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/kendall-rank-correlation-coefficient\/","title":{"rendered":"R \u3067\u30b1\u30f3\u30c9\u30fc\u30eb\u306e\u9806\u4f4d\u76f8\u95a2\u4fc2\u6570\u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5"},"content":{"rendered":"\n

\u30b1\u30f3\u30c9\u30fc\u30eb\u306e\u9806\u4f4d\u76f8\u95a2\u4fc2\u6570\u306f\u3069\u306e\u3088\u3046\u306b\u8a08\u7b97\u3059\u308b\u304b\u7d39\u4ecb\u3059\u308b<\/p>\n\n\n\n\n\n\n\n

\u30b1\u30f3\u30c9\u30fc\u30eb\u306e\u9806\u4f4d\u76f8\u95a2\u4fc2\u6570<\/h2>\n\n\n\n

\u30b1\u30f3\u30c9\u30fc\u30eb\uff08Kendall\uff09\u306e\u9806\u4f4d\u76f8\u95a2\u4fc2\u6570 $ \\tau $ \u306f\u3001\u9806\u4f4d\u3092\u4f7f\u308f\u306a\u3044\u76f8\u95a2\u4fc2\u6570\u3067\u3042\u308b\u3002<\/p>\n\n\n\n

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\u305d\u3046\u3067\u306a\u3044\u5834\u5408\u3092\uff0d\uff11\u3068\u3059\u308b\u3002<\/p>\n\n\n\n

\u3053\u308c\u3092\u5168\u90e8\u306e\u7d44\u307f\u5408\u308f\u305b\u306b\u3064\u3044\u3066\u884c\u3046\u3002<\/p>\n\n\n\n

\u3053\u306e\u5408\u8a08\u3092 S \u3068\u3059\u308b\u3068\u4ee5\u4e0b\u306e\u5f0f\u3067\u66f8\u3051\u308b\u3002<\/p>\n\n\n\n

\\begin{equation} S = \\sum_{i \\lt j} (\\mathrm{sign} (x_j – x_i) \\times \\mathrm{sign} (y_j – y_i)) \\end{equation}<\/p>\n\n\n\n\n\n\n\n

\uff0b\uff11\u306e\u6570\u3068\uff0d\uff11\u306e\u6570\u306e\u5dee\u3092\u3001\u5168\u90e8\u306e\u7d44\u307f\u5408\u308f\u305b\u306e\u6570 $ D = \\frac{n(n – 1)}{2} $ \u3067\u5272\u308b\u3002<\/p>\n\n\n\n

\u3053\u308c\u304c\u30b1\u30f3\u30c9\u30fc\u30eb\u306e\u9806\u4f4d\u76f8\u95a2\u4fc2\u6570 $ \\tau = \\frac{S}{D} $ \u3067\u3042\u308b\u3002<\/p>\n\n\n\n

\u3064\u307e\u308a\u3001\u9806\u4f4d\u306f\u4f7f\u308f\u306a\u3044\u9806\u4f4d\u76f8\u95a2\u4fc2\u6570\u3068\u3044\u3046\u3053\u3068\u3067\u3042\u308b\u3002<\/p>\n\n\n\n

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2\u3064\u306eX,Y\u30da\u30a2\u3092\u53d6\u308a\u51fa\u3057\u305f\u3068\u304d\u3001X\u540c\u58eb\u3001\u53ca\u3073\/\u53c8\u306f\u3001Y\u540c\u58eb\u304c\u540c\u3058\u5024\u3067\u3042\u3063\u305f\u5834\u5408\u306f\u3069\u3046\u3059\u308b\u306e\u304b\uff1f<\/p>\n\n\n\n

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\u30b1\u30f3\u30c9\u30fc\u30eb\u306e\u9806\u4f4d\u76f8\u95a2\u4fc2\u6570 | \u7d71\u8a08\u7528\u8a9e\u96c6 | \u7d71\u8a08WEB<\/a><\/p>\n\n\n\n

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\u30af\u30ed\u30b9\u96c6\u8a08\u8868\u306e\u7d71\u8a08<\/a><\/p>\n\n\n\n

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R \u3067\u8a08\u7b97\u3057\u3066\u307f\u308b\u3002<\/p>\n\n\n\n

Kendall \u30d1\u30c3\u30b1\u30fc\u30b8\u3092\u4f7f\u7528\u3059\u308b\u3002<\/p>\n\n\n\n

library<\/span>(<\/span>Kendall)<\/span>\nx<-<\/span>c<\/span>(<\/span>1.5<\/span>,<\/span>1.5<\/span>,<\/span>3<\/span>,<\/span>4<\/span>,<\/span>6<\/span>,<\/span>6<\/span>,<\/span>6<\/span>,<\/span>8<\/span>,<\/span>9.5<\/span>,<\/span>9.5<\/span>,<\/span>11<\/span>,<\/span>12<\/span>)<\/span>\ny<-<\/span>c<\/span>(<\/span>2.5<\/span>,<\/span>2.5<\/span>,<\/span>7<\/span>,<\/span>4.5<\/span>,<\/span>1<\/span>,<\/span>4.5<\/span>,<\/span>6<\/span>,<\/span>11.5<\/span>,<\/span>11.5<\/span>,<\/span>8.5<\/span>,<\/span>8.5<\/span>,<\/span>10<\/span>)<\/span>\n<\/code><\/pre>\n\n\n\n
x \u3068 y \u306e\u6563\u5e03\u56f3\u3092\u66f8\u3044\u3066\u307f\u308b\u3068\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308b\u3002<\/p>\n\n\n\n
\"\"<\/figure>\n\n\n\n
<\/span><\/p>\n\n\n\n
\u53f3\u80a9\u4e0a\u304c\u308a\u306a\u306e\u3067\u3001x \u3068 y \u304c\u540c\u3058\u65b9\u5411\u6027\u3067\u3042\u308b\u306e\u3067\u3001\u30d7\u30e9\u30b9\u306e\u5024\u306b\u306a\u308b\u3053\u3068\u304c\u4e88\u60f3\u3055\u308c\u308b<\/p>\n\n\n\n
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\"\"<\/figure>\n\n\n\n
<\/span><\/p>\n\n\n\n
$ \\tau = 0.553 $ \u306a\u306e\u3067\u3001\u307e\u305a\u307e\u305a\u306e\u76f8\u95a2\u3068\u8a00\u3048\u308b\u3002<\/p>\n\n\n\n
\u307e\u3068\u3081<\/h2>\n\n\n\n
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\u53c2\u8003\u30b5\u30a4\u30c8<\/h2>\n\n\n\n
\u30b1\u30f3\u30c9\u30fc\u30eb\u306e\u9806\u4f4d\u76f8\u95a2\u4fc2\u6570 | \u7d71\u8a08\u7528\u8a9e\u96c6 | \u7d71\u8a08WEB<\/a><\/p>\n\n\n\n
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\u30b1\u30f3\u30c9\u30fc\u30eb\u306e\u9806\u4f4d\u76f8\u95a2\u4fc2\u6570 \u7d71\u8a08\u5b66\u5165\u9580<\/a><\/p>\n\n\n\n
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\u30af\u30ed\u30b9\u96c6\u8a08\u8868\u306e\u7d71\u8a08<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"
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