{"id":509,"date":"2018-08-22T20:55:09","date_gmt":"2018-08-22T11:55:09","guid":{"rendered":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/how-to-determine-sample-size-in-intraclass-correlation-coefficient-case1\/"},"modified":"2025-05-06T21:33:04","modified_gmt":"2025-05-06T12:33:04","slug":"how-to-determine-sample-size-in-intraclass-correlation-coefficient-case1","status":"publish","type":"post","link":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/how-to-determine-sample-size-in-intraclass-correlation-coefficient-case1\/","title":{"rendered":"R \u3067\u7d1a\u5185\u76f8\u95a2\u4fc2\u6570 ICC(1,1) \u306b\u5fc5\u8981\u306a\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5"},"content":{"rendered":"\n

ICC(1,1) \u306e\u8a08\u7b97\u3068\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97\u3092 R \u3067\u884c\u3046\u65b9\u6cd5<\/p>\n\n\n\n\n\n\n\n

\u7d1a\u5185\u76f8\u95a2\u4fc2\u6570 ICC(1,1) \u306e\u8a08\u7b97<\/h2>\n\n\n\n

\u7d1a\u5185\u76f8\u95a2\u4fc2\u6570\uff08ICC\uff09\u306f\u3001\u4fe1\u983c\u6027\u6307\u6a19\u306b\u4f7f\u3048\u308b\u3002<\/p>\n\n\n\n

ICC Case1\u306f\u3001\u4e00\u4eba\u306e\u691c\u67fb\u3092\u3059\u308b\u4eba\uff08\u691c\u8005\u3001\u3051\u3093\u3058\u3083\uff09\u306e\u4e00\u8cab\u6027\u3092\u78ba\u8a8d\u3059\u308b\u6307\u6a19\u3060\u3002<\/p>\n\n\n\n

ICC(1,1)\u306f\u3001\u4e00\u4eba\u306e\u691c\u8005\u304ck\u56de\u6e2c\u5b9a\u3092\u884c\u3063\u305f\u30c7\u30fc\u30bf\u305d\u306e\u3082\u306e\u3092\u4f7f\u3063\u3066\u8a08\u7b97\u3059\u308b\u3002<\/p>\n\n\n\n

ICC(1,k)\u306f\u3001k\u56de\u6e2c\u5b9a\u306e\u5e73\u5747\u5024\u3092\u4f7f\u3046\u65b9\u6cd5\u3002<\/p>\n\n\n\n

psych \u30d1\u30c3\u30b1\u30fc\u30b8\u306e ICC \u3067\u884c\u3046\u65b9\u6cd5<\/h3>\n\n\n\n

R \u3067\u306f\u3001psych \u30d1\u30c3\u30b1\u30fc\u30b8 \u306e ICC() \u3067\u8a08\u7b97\u3067\u304d\u308b\u3002<\/p>\n\n\n\n

\u30c7\u30fc\u30bf\u62dd\u501f\u5143\uff1a\u7d1a\u5185\u76f8\u95a2\u4fc2\u6570\uff5c\u7d71\u8a08\u89e3\u6790\u30bd\u30d5\u30c8 \u30a8\u30af\u30bb\u30eb\u7d71\u8a08<\/a><\/p>\n\n\n\n

first <-<\/span> c(2.8,5.4,4.0,4.9,5.2,2.2,3.5)<\/span>\nsecond <-<\/span> c(3.1,4.4,4.3,4.2,4.5,3.4,3.9)<\/span>\nthird <-<\/span> c(2.6,4.3,4.0,4.7,4.2,2.7,3.3)<\/span>\ndat.oneway <-<\/span> cbind(<\/span>first,<\/span> second,<\/span> third)<\/span>\nrownames(<\/span>dat.oneway)<\/span> <-<\/span> c(1:7)<\/span>\ndat.oneway\n\ninstall.packages(\"psych\") # \u6700\u521d\u4e00\u56de\u3060\u3051\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\u3059\u308b\nlibrary(<\/span>psych)<\/span>\nICC(<\/span>dat.oneway)<\/span>\n<\/code><\/pre>\n\n\n\n
3\u56de\u306e\u6e2c\u5b9a\u5024\u3092\u305d\u306e\u307e\u307e\u3064\u304b\u3046ICC1\u306f0.77\u30013\u56de\u306e\u5e73\u5747\u3092\u4f7f\u3046ICC1k\u306f0.91\u3068\u8a08\u7b97\u3055\u308c\u305f\u3002<\/p>\n\n\n\n
><\/span> library<\/span>(<\/span>psych)<\/span>\n><\/span>\n><\/span> ICC<\/span>(<\/span>dat.oneway)<\/span>\nCall:<\/span> ICC<\/span>(<\/span>x =<\/span> dat.oneway)<\/span>\nIntraclass correlation coefficients\n                         type  ICC  F<\/span> df1 df2       p lower bound upper bound\nSingle_raters_absolute   ICC1 0.77<\/span> 11<\/span>   6<\/span>  14<\/span> 0.00011<\/span>        0.43<\/span>        0.95<\/span>\nSingle_random_raters     ICC2 0.77<\/span> 12<\/span>   6<\/span>  12<\/span> 0.00022<\/span>        0.43<\/span>        0.95<\/span>\nSingle_fixed_raters      ICC3 0.78<\/span> 12<\/span>   6<\/span>  12<\/span> 0.00022<\/span>        0.41<\/span>        0.95<\/span>\nAverage_raters_absolute ICC1k 0.91<\/span> 11<\/span>   6<\/span>  14<\/span> 0.00011<\/span>        0.69<\/span>        0.98<\/span>\nAverage_random_raters   ICC2k 0.91<\/span> 12<\/span>   6<\/span>  12<\/span> 0.00022<\/span>        0.69<\/span>        0.98<\/span>\nAverage_fixed_raters    ICC3k 0.91<\/span> 12<\/span>   6<\/span>  12<\/span> 0.00022<\/span>        0.68<\/span>        0.98<\/span>\nNumber of subjects =<\/span> 7<\/span>     Number of Judges =<\/span>  3<\/span>\n<\/code><\/pre>\n\n\n\n
\u8907\u6570\u691c\u8005\u3092\u60f3\u5b9a\u3057\u305fICC2\u3084ICC3\u304c\u540c\u6642\u306b\u8a08\u7b97\u3055\u308c\u308b\u304c\u3001\u691c\u67fb\u306e\u30c7\u30b6\u30a4\u30f3\uff08\u4e00\u4eba\u306e\u691c\u8005\u304c3\u56de\u305a\u3064\u6e2c\u5b9a\uff09\u306e\u89b3\u70b9\u304b\u3089\u3001\u8a08\u7b97\u7d50\u679c\u306f\u63a1\u7528\u3057\u306a\u3044\u3002<\/p>\n\n\n\n
irr \u30d1\u30c3\u30b1\u30fc\u30b8\u306e icc \u3067\u884c\u3046\u65b9\u6cd5<\/h3>\n\n\n\n
irr \u30d1\u30c3\u30b1\u30fc\u30b8\u306e icc \u95a2\u6570\u3067\u3082\u8a08\u7b97\u3067\u304d\u308b<\/p>\n\n\n\n
first <-<\/span> c(2.8,5.4,4.0,4.9,5.2,2.2,3.5)<\/span>\nsecond <-<\/span> c(3.1,4.4,4.3,4.2,4.5,3.4,3.9)<\/span>\nthird <-<\/span> c(2.6,4.3,4.0,4.7,4.2,2.7,3.3)<\/span>\ndat.oneway <-<\/span> cbind(<\/span>first,<\/span> second,<\/span> third)<\/span>\nrownames(<\/span>dat.oneway)<\/span> <-<\/span> c(1:7)<\/span>\ndat.oneway\n\ninstall.packages(\"irr\") # \u6700\u521d\u4e00\u56de\u3060\u3051\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\u3059\u308b\nlibrary(irr)<\/span>\nicc(dat.oneway)<\/code><\/pre>\n\n\n\n
ICC(1,1) \u306e\u5834\u5408\u306f\u3001icc \u95a2\u6570\u306b\u691c\u67fb\u7d50\u679c\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u3092\u6295\u5165\u3059\u308b\uff08\u3053\u306e\u4f8b\u3067\u3042\u308c\u3070icc(dat.oneway)<\/code>\uff09\u3060\u3051\u3067\u3088\u3044<\/p>\n\n\n\n
\u7d50\u679c\u306f\u4ee5\u4e0b\u306e\u3068\u304a\u308a\u51fa\u529b\u3055\u308c\u308b<\/p>\n\n\n\n
> icc(dat.oneway)\n Single Score Intraclass Correlation\n\n   Model: oneway \n   Type : consistency \n\n   Subjects = 7 \n     Raters = 3 \n     ICC(1) = 0.774\n\n F-Test, H0: r0 = 0 ; H1: r0 > 0 \n    F(6,14) = 11.3 , p = 0.000112 \n\n 95%-Confidence Interval for ICC Population Values:\n  0.426 < ICC < 0.951<\/code><\/pre>\n\n\n\n
\u4e0a\u8a18\u306e\u6e2c\u5b9a\u5024\u3092\u305d\u306e\u307e\u307e\u4f7f\u3046\u3068\u304d\u3068\u540c\u3058\u7d50\u679c\uff080.774\uff09\u3068\u306a\u3063\u305f<\/p>\n\n\n\n
\u5e73\u5747\u5024\u3092\u4f7f\u3046\u5834\u5408 ICC(1,k) \u306f\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b unit=\"average\"<\/code> \u3092\u8ffd\u52a0\u3059\u308b<\/p>\n\n\n\n
icc(dat.oneway, unit=\"average\")<\/code><\/pre>\n\n\n\n
\u7d50\u679c\u306f\u4ee5\u4e0b\u306e\u3068\u304a\u308a<\/p>\n\n\n\n
> icc(dat.oneway, unit=\"average\")\n Average Score Intraclass Correlation\n\n   Model: oneway \n   Type : consistency \n\n   Subjects = 7 \n     Raters = 3 \n     ICC(3) = 0.911\n\n F-Test, H0: r0 = 0 ; H1: r0 > 0 \n    F(6,14) = 11.3 , p = 0.000112 \n\n 95%-Confidence Interval for ICC Population Values:\n  0.69 < ICC < 0.983<\/code><\/pre>\n\n\n\n
\u3053\u3061\u3089\u3082\u4e0a\u8a18\u3068\u540c\u69d8\u306e\u7d50\u679c\uff080.911\uff09\u3068\u306a\u3063\u305f<\/p>\n\n\n\n
\u7d1a\u5185\u76f8\u95a2\u4fc2\u6570 ICC(1,1) \u306e\u89e3\u91c8<\/h2>\n\n\n\n
\u4e00\u3064\u306b\u306f\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u57fa\u6e96\u304c\u3042\u308b\u306e\u3067\u53c2\u7167\u3055\u308c\u305f\u3044<\/p>\n\n\n\n
ICC<\/td>\u89e3\u91c8<\/td><\/tr>
< 0.5<\/td>Poor<\/td><\/tr>
0.5 – < 0.75<\/td>Moderate<\/td><\/tr>
0.75 – < 0.9<\/td>Good<\/td><\/tr>
>= 0.9<\/td>Excellent<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
\u51fa\u5178\uff1aA Guideline of Selecting and Reporting Intraclass Correlation Coefficients for Reliability Research<\/a><\/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>
\u7d1a\u5185\u76f8\u95a2\u4fc2\u6570 ICC(1,1) \u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97<\/h2>\n\n\n\n
ICC.Sample.Size \u30d1\u30c3\u30b1\u30fc\u30b8\u306e calculateIccSampleSize() \u3092\u4f7f\u3046\u3068\u3001ICC(1,1) \u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97\u304c\u3067\u304d\u308b\u3002<\/p>\n\n\n\n
\u6700\u521d\u306b\u4e00\u56de\u3060\u3051\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\u304c\u5fc5\u8981\u3060\u3002<\/p>\n\n\n\n
install.packages<\/span>(<\/span>\"ICC.Sample.Size\"<\/span>)<\/span>\n<\/code><\/pre>\n\n\n\n
ICC\u304c0.8\u3067\u3001\u4e00\u4eba\u306e\u88ab\u691c\u8005\u3055\u3093\u3042\u305f\u308a2\u56de\u6e2c\u5b9a\uff08k=2\uff09\u306e\u5834\u5408\u3001<\/p>\n\n\n\n
ICC\u304c0.8\u3067\u3001k=3\u306e\u5834\u5408<\/p>\n\n\n\n
ICC\u304c0.6\u3067\u3001k=4\u306e\u5834\u5408\u3092\u8a08\u7b97\u3057\u3066\u307f\u308b\u3002<\/p>\n\n\n\n
library<\/span>(<\/span>ICC.Sample.Size)<\/span>\ncalculateIccSampleSize<\/span>(<\/span>p=<\/span>0.80<\/span>)<\/span> # \u30c7\u30d5\u30a9\u30eb\u30c8\u306f k=2\ncalculateIccSampleSize<\/span>(<\/span>p=<\/span>0.80<\/span>,<\/span>k=<\/span>3<\/span>)<\/span>\ncalculateIccSampleSize<\/span>(<\/span>p=<\/span>0.60<\/span>,<\/span>k=<\/span>4<\/span>)<\/span>\n<\/code><\/pre>\n\n\n\n
\u7d50\u679c\u306f\u3001\u5fc5\u8981\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u306f8\u4f8b\u30015\u4f8b\u30017\u4f8b\u3068\u8a08\u7b97\u3055\u308c\u305f\u3002<\/p>\n\n\n\n
> calculateIccSampleSize(p=0.80)\n[[1]]\n  N   p p0 k alpha tails power\n1 8 0.8  0 2  0.05     2   0.8\n\n> calculateIccSampleSize(p=0.80,k=3)\n[[1]]\n  N   p p0 k alpha tails power\n1 5 0.8  0 3  0.05     2   0.8\n\n> calculateIccSampleSize(p=0.60,k=4)\n[[1]]\n  N   p p0 k alpha tails power\n1 7 0.6  0 4  0.05     2   0.8<\/code><\/pre>\n\n\n\n
\u3053\u306e\u95a2\u6570\u306e\u512a\u308c\u3082\u306e\u306a\u3068\u3053\u308d\u306f\u3001ICC\u3092\u4e00\u5b9a\u9593\u9694\u3067\u523b\u3093\u3067\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u3092\u8a08\u7b97\u3067\u304d\u308b\u3068\u3053\u308d\u3002<\/p>\n\n\n\n
\u3044\u305a\u308c\u30820.1\u3067\u523b\u3093\u3067\u3001k=2, k=3, k=4\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u3092\u8a08\u7b97\u3057\u3066\u307f\u308b\u3002<\/p>\n\n\n\n
calculateIccSampleSize<\/span>(<\/span>by=<\/span>\"p\"<\/span>,<\/span> step=<\/span>0.1<\/span>)<\/span> # \u30c7\u30d5\u30a9\u30eb\u30c8\u306f k=2\ncalculateIccSampleSize<\/span>(<\/span>by=<\/span>\"p\"<\/span>,<\/span> step=<\/span>0.1<\/span>,<\/span> k=<\/span>3<\/span>)<\/span>\ncalculateIccSampleSize<\/span>(<\/span>by=<\/span>\"p\"<\/span>,<\/span> step=<\/span>0.1<\/span>,<\/span> k=<\/span>4<\/span>)<\/span>\n<\/code><\/pre>\n\n\n\n
ICC\u304c0.0\u304b\u30891.0\u307e\u3067\u30010.1\u523b\u307f\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97\u304c\u5f97\u3089\u308c\u308b\u3002<\/p>\n\n\n\n
k=2, 3, 4\u305d\u308c\u305e\u308c\u8a08\u7b97\u3057\u3066\u307f\u305f\u3002<\/p>\n\n\n\n
\u89b3\u5bdf\u56de\u6570k\u304c\u5897\u3048\u308b\u3068\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u304c\u5c0f\u3055\u304f\u306a\u308b\u3053\u3068\u304c\u308f\u304b\u308b\u3002<\/p>\n\n\n\n
> calculateIccSampleSize(by=\"p\", step=0.1)\n[[1]]\n    N p p0 k alpha tails power\n1 Inf 0  0 2  0.05     2   0.8\n\n[[2]]\n     p   N\n1  0.0 Inf\n2  0.1 781\n3  0.2 192\n4  0.3  83\n5  0.4  45\n6  0.5  28\n7  0.6  18\n8  0.7  12\n9  0.8   8\n10 0.9   5\n11 1.0   2\n\n> calculateIccSampleSize(by=\"p\", step=0.1, k=3)\n[[1]]\n    N p p0 k alpha tails power\n1 Inf 0  0 3  0.05     2   0.8\n\n[[2]]\n     p   N\n1  0.0 Inf\n2  0.1 286\n3  0.2  77\n4  0.3  36\n5  0.4  21\n6  0.5  14\n7  0.6  10\n8  0.7   7\n9  0.8   5\n10 0.9   4\n11 1.0   2\n\n> calculateIccSampleSize(by=\"p\", step=0.1, k=4)\n[[1]]\n    N p p0 k alpha tails power\n1 Inf 0  0 4  0.05     2   0.8\n\n[[2]]\n     p   N\n1  0.0 Inf\n2  0.1 156\n3  0.2  45\n4  0.3  22\n5  0.4  14\n6  0.5  10\n7  0.6   7\n8  0.7   5\n9  0.8   4\n10 0.9   3\n11 1.0   2<\/code><\/pre>\n\n\n\n
\u7d1a\u5185\u76f8\u95a2\u4fc2\u6570\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97\u306e\u30b9\u30af\u30ea\u30d7\u30c8<\/h2>\n\n\n\n
calculateIccSampleSize() \u30d7\u30ed\u30b0\u30e9\u30e0\u306e\u4e2d\u8eab\u304b\u3089\u4e3b\u8981\u306a\u90e8\u5206\u3092\u629c\u304d\u51fa\u3057\u3066\u3001\u8a08\u7b97\u624b\u9806\u3092\u78ba\u8a8d\u3057\u3066\u307f\u305f\u3002<\/p>\n\n\n\n
\u307e\u305f\u3001\u7d50\u679c\u304c\u308f\u304b\u308a\u3084\u3059\u3044\u8868\u793a\u306b\u306a\u308b\u3088\u3046\u306b\u6539\u9020\u3057\u305f\u3002<\/p>\n\n\n\n
icc.sample.size <- function (p=0, p0=0, k=2,\n                             sig.level=0.05, power=0.8,\n                             alternative=c(\"two.sided\",\"one.sided\")){\n  alternative <- match.arg(alternative)\n  side <- switch(alternative, one.sided=1, two.sided=2)\n  Za <- qnorm(sig.level\/side, lower.tail=FALSE)\n  Zb <- qnorm(power)\n  Fp <- (1+(k-1)*p)\/(1-p)\n  Fp0 <- (1+(k-1)*p0)\/(1-p0)\n  Nraw <- 1+(2*(Za+Zb)^2*k)\/((log(Fp\/Fp0))^2*(k-1))\n  N <- ceiling(Nraw)\n  METHOD <- \"ICC Class1 sample size\"\n  structure(list(N=N, p=p, p0=p0, k=k,\n                 sig.level=sig.level, power=power,\n                 alternative=alternative, method=METHOD),\n            class=\"power.htest\")\n}\n<\/code><\/pre>\n\n\n\n
\u4e0a\u8a18\u3068\u540c\u3058\u6761\u4ef6\u3067\u3001\u8a08\u7b97\u3057\u3066\u307f\u305f\u3002\u304d\u3061\u3093\u3068\u540c\u3058\u7b54\u3048\u306b\u306a\u3063\u305f\u3002<\/p>\n\n\n\n
> icc.sample.size(p=0.8)\n\n     ICC Class1 sample size \n\n              N = 8\n              p = 0.8\n             p0 = 0\n              k = 2\n      sig.level = 0.05\n          power = 0.8\n    alternative = two.sided\n\n> icc.sample.size(p=0.8, k=3)\n\n     ICC Class1 sample size \n\n              N = 5\n              p = 0.8\n             p0 = 0\n              k = 3\n      sig.level = 0.05\n          power = 0.8\n    alternative = two.sided\n\n> icc.sample.size(p=0.6, k=4)\n\n     ICC Class1 sample size \n\n              N = 7\n              p = 0.6\n             p0 = 0\n              k = 4\n      sig.level = 0.05\n          power = 0.8\n    alternative = two.sided\n<\/code><\/pre>\n\n\n\n
\u7d1a\u5185\u76f8\u95a2\u4fc2\u6570\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97\u3092\u30a8\u30af\u30bb\u30eb\u3067<\/h2>\n\n\n\n
\u30a8\u30af\u30bb\u30eb\u3067\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97\u3067\u304d\u308b\u3088\u3046\u306b\u3057\u305f\u3002<\/p>\n\n\n\n
\u3088\u3051\u308c\u3070\u3069\u3046\u305e\u3002<\/p>\n\n\n\n
\u7d1a\u5185\u76f8\u95a2\u4fc2\u6570 ICC \u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97\u3010\u30a8\u30af\u30bb\u30eb\u3067\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u3011 | TKER SHOP<\/a><\/p>\n\n\n\n
\u4f7f\u3044\u65b9\u89e3\u8aac\u52d5\u753b\u3082\u3088\u3051\u308c\u3070\u3069\u3046\u305e\u3002<\/p>\n\n\n\n