{"id":412,"date":"2019-09-24T00:00:00","date_gmt":"2019-09-23T15:00:00","guid":{"rendered":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/bonferroni-sample-size-in-r\/"},"modified":"2024-10-05T12:24:42","modified_gmt":"2024-10-05T03:24:42","slug":"bonferroni-sample-size-in-r","status":"publish","type":"post","link":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/bonferroni-sample-size-in-r\/","title":{"rendered":"R \u3067\u591a\u91cd\u6bd4\u8f03\u306b\u5fc5\u8981\u3068\u306a\u308b\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5"},"content":{"rendered":"\n

\u591a\u91cd\u6bd4\u8f03\u306e\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

\u30dc\u30f3\u30d5\u30a7\u30ed\u30fc\u30cb\u578b \u591a\u91cd\u6bd4\u8f03\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97<\/h2>\n\n\n\n

Bonferroni\uff08\u30dc\u30f3\u30d5\u30a7\u30ed\u30fc\u30cb\uff09\u578b\u591a\u91cd\u6bd4\u8f03\u3068\u306f\u3001\u6bd4\u8f03\u3059\u308b\u6570\u3067\u6709\u610f\u6c34\u6e96\u3092\u5272\u3063\u3066\u3001\u5272\u3063\u305f\u6709\u610f\u6c34\u6e96\u3088\u308a\u5c0f\u3055\u3044\u6709\u610f\u78ba\u7387\u306e\u5834\u5408\u3001\u7d71\u8a08\u5b66\u7684\u6709\u610f\u3068\u8003\u3048\u308b\u65b9\u6cd5\u3002<\/p>\n\n\n\n

\u4e09\u7fa4\u3042\u3063\u3066\u3001\u7dcf\u5f53\u305f\u308a\u3067\u4e09\u3064\u306e\u6bd4\u8f03\u3092\u3059\u308b\u5834\u5408\u3001\u6709\u610f\u6c34\u6e96\u305f\u3068\u3048\u30700.05\u30923\u3067\u5272\u3063\u3066\u3001\u4e00\u3064\u306e\u6bd4\u8f03\u306b\u5bfe\u3057\u3066\u6709\u610f\u6c34\u6e96\u30920.0167\u3068\u3059\u308b\u65b9\u6cd5\u3002<\/p>\n\n\n\n

\u8a73\u3057\u304f\u306f\u904e\u53bb\u8a18\u4e8b\u3092\u53c2\u7167\u3002<\/p>\n\n\n\n

\u3088\u308a\u73fe\u5b9f\u7684\u3067\u9069\u5207\u306a\u65b9\u6cd5\u3068\u3057\u3066\u3001Holm\u3084Hochberg\u306e\u65b9\u6cd5\u3082\u7d39\u4ecb\u3057\u3066\u3044\u308b\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\tR \u3067\u30dc\u30f3\u30d5\u30a7\u30ed\u30fc\u30cb\u3092\u5b9f\u884c\u3059\u308b\u65b9\u6cd5<\/a>\n\t\t\t\t\t\t\u691c\u8a3c\u8a66\u9a13\u306b\u304a\u3044\u3066\u3001\u4e09\u7fa4\u4ee5\u4e0a\u306e\u5e73\u5747\u5024\u3092\u6bd4\u8f03\u3057\u305f\u3044\u3068\u304d\u306b\u3001\u5358\u7d14\u306b\u4e8c\u7fa4\u6bd4\u8f03\u3092\u7e70\u308a\u8fd4\u3059\u3068\u6709\u610f\u6c34\u6e96\u304c\u7518\u304f\u306a\u308b\u3002 \u6709\u610f\u6c34\u6e96\u306e\u8abf\u6574\u306b\u3088\u3063\u3066\u7c21\u5358\u306b\u51e6\u7406\u3059\u308b\u65b9\u6cd5\u304c\u30dc\u30f3\u30d5\u30a7\u30ed\u30fc\u30cb…<\/span>\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/div>\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\tR \u3067\u30d5\u30a3\u30c3\u30b7\u30e3\u30fc\u306e\u6b63\u78ba\u78ba\u7387\u691c\u5b9a\u30fb\u30ab\u30a4\u4e8c\u4e57\u691c\u5b9a \u3067 3 \u7fa4\u4ee5\u4e0a\u306e\u6bd4\u8f03\u3092\u5b9f\u884c\u3059\u308b\u65b9\u6cd5<\/a>\n\t\t\t\t\t\t\u30d5\u30a3\u30c3\u30b7\u30e3\u30fc\u306e\u6b63\u78ba\u78ba\u7387\u691c\u5b9a\u3001\u30ab\u30a4\u4e8c\u4e57\u691c\u5b9a\u306e3\u7fa4\u4ee5\u4e0a\u306e\u6bd4\u8f03\u3092R\u3067\u5b9f\u65bd\u3059\u308b\u65b9\u6cd5\u306e\u89e3\u8aac\u3002 \u30ab\u30a4\u4e8c\u4e57\u691c\u5b9a\u306e3\u7fa4\u4ee5\u4e0a\u306e\u6bd4\u8f03 \u4e09\u7fa4\u4ee5\u4e0a\u306e\u5272\u5408\u306e\u6bd4\u8f03\u306f\u3069\u3046\u3084\u308c\u3070\u3044\u3044\u306e\u304b\uff1f Bonfe…<\/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

\u591a\u91cd\u6bd4\u8f03\u306e\u524d\u306b\u5e73\u5747\u5024\u306e\u5dee\u306e\u691c\u5b9a\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97<\/h2>\n\n\n\n

\u591a\u91cd\u6bd4\u8f03\u306e\u524d\u306b\u4e8c\u7fa4\u306e\u6bd4\u8f03\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97\u3092\u5b9f\u884c\u3057\u3066\u307f\u308b\u3002<\/p>\n\n\n\n

\u7d71\u8a08\u30bd\u30d5\u30c8R\u3067\u306f\u3001power.t.test()\u3067\u8a08\u7b97\u3067\u304d\u308b\u3002\u691c\u51fa\u529b power\u3068\u5dee\uff08SD\u3092\u6307\u5b9a\u3057\u306a\u3044\u5834\u5408\u6a19\u6e96\u5316\u3057\u305f\u5dee\uff09delta \u3092\u6307\u5b9a\u3059\u308b\u3068\u8a08\u7b97\u3067\u304d\u308b\u3002<\/p>\n\n\n\n

delta\u306b\u3064\u3044\u3066\u306f\u3053\u3061\u3089\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\tR \u3067 t \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\tt \u691c\u5b9a\u306e\u30b5\u30f3\u30d7\u30eb\u6570\u8a08\u7b97\u306e\u65b9\u6cd5 t \u691c\u5b9a\u306e\u30b5\u30f3\u30d7\u30eb\u6570\u8a08\u7b97\uff081:1\u306e\u5834\u5408\uff09 R \u306e power.t.test()\u3092\u7528\u3044\u308b\u3002 \u5fc5\u8981\u306a\u60c5\u5831\u306f\u3001\u691c\u51fa\u529b\u3092\u3069\u3046\u3059\u308b\u304b\u3068\u3001\u4e8c\u7fa4\u306e\u5e73\u5747\u5024\u306e\u5dee\u3002 \u6a19\u6e96\u504f…<\/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\u51fa\u529b\u30920.8\uff0880%\uff09\u3001\u6a19\u6e96\u5316\u3057\u305f\u5dee\u30920.8\uff08\u5927\u304d\u76ee\uff09\u3068\u3059\u308b\u3002<\/p>\n\n\n\n

power.t.test<\/span>(<\/span>power=<\/span>0.8<\/span>,<\/span> delta=<\/span>0.8<\/span>)<\/span>\n<\/code><\/pre>\n\n\n\n
\u8a08\u7b97\u7d50\u679c\u306f\u3001\u4e00\u7fa425.5\u3001\uff08\u4eba\u6570\u306a\u306e\u3067\uff09\u5207\u308a\u4e0a\u3052\u308b\u306826\u4f8b\u5fc5\u8981\u3068\u8a08\u7b97\u3055\u308c\u305f\u3002<\/p>\n\n\n\n
><\/span> power.t.test<\/span>(<\/span>power=<\/span>0.8<\/span>,<\/span> delta=<\/span>0.8<\/span>)<\/span>\nTwo-<\/span>sample t test power calculation\nn =<\/span> 25.52463<\/span>\ndelta =<\/span> 0.8<\/span>\nsd =<\/span> 1<\/span>\nsig.level =<\/span> 0.05<\/span>\npower =<\/span> 0.8<\/span>\nalternative =<\/span> two.sided\nNOTE:<\/span> n is number in<\/span> *<\/span>each*<\/span> group\n<\/code><\/pre>\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>
\u5e73\u5747\u5024\u306e\u5dee\u3092\u591a\u91cd\u6bd4\u8f03\u3059\u308b\u306e\u306b\u5fc5\u8981\u306a\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u306e\u8a08\u7b97<\/h2>\n\n\n\n
\u5e73\u5747\u5024\u306e\u5dee\u306e\u691c\u5b9a\u3092\u4e09\u7fa4\u4ee5\u4e0a\u3067\u884c\u3046\u5834\u5408\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97\u306e\u30b9\u30af\u30ea\u30d7\u30c8\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3002<\/p>\n\n\n\n
\u6700\u4f4e\u9650\u3001\u6a19\u6e96\u5316\u3057\u305f\u5dee delta \u3068\u6bd4\u8f03\u30da\u30a2\u6570 num.tests \u306f\u6c7a\u3081\u306a\u3044\u3068\u3044\u3051\u306a\u3044\u3002SD\u30921\u3068\u3057\u3001\u6709\u610f\u6c34\u6e960.05\u3001\u691c\u51fa\u529b0.8\u3001\u4e21\u5074\u691c\u5b9a two.sided\u3092\u30c7\u30d5\u30a9\u30eb\u30c8\u306b\u3057\u3066\u3042\u308b\u3002<\/p>\n\n\n\n
samplesize.bonferroni.mean <-<\/span> function<\/span>(<\/span>sig.level=<\/span>.05<\/span>,<\/span> power=<\/span>.8<\/span>,<\/span> delta,<\/span> sd=<\/span>1<\/span>,<\/span> alternative=<\/span>c<\/span>(<\/span>\"two.sided\"<\/span>,<\/span>\"one.sided\"<\/span>),<\/span> num.tests)<\/span>\n{<\/span>\nalternative <-<\/span> match.arg<\/span>(<\/span>alternative)<\/span>\ntside <-<\/span> switch<\/span>(<\/span>alternative,<\/span> one.sided=<\/span>1<\/span>,<\/span> two.sided=<\/span>2<\/span>)<\/span>\nd <-<\/span> delta\/<\/span>sd\nZa <-<\/span> qnorm<\/span>(<\/span>sig.level\/<\/span>num.tests\/<\/span>tside,<\/span> lower.tail=<\/span>FALSE<\/span>)<\/span>\nZb <-<\/span> qnorm<\/span>(<\/span>power)<\/span>\nn <-<\/span> 2<\/span>*<\/span>((<\/span>Za+<\/span>Zb)<\/span>\/<\/span>d)<\/span>^<\/span>2<\/span>\nNOTE<\/span> <-<\/span> \"n is number in *each* group\"<\/span>\nMETHOD <-<\/span> \"Sample size for Bonferroni-type multiple comparison of the mean\"<\/span>\nstructure<\/span>(<\/span>list<\/span>(<\/span>n =<\/span> n,<\/span> \"Numbers of tests\"<\/span>=<\/span>num.tests,<\/span> \"Difference of a pair\"<\/span> =<\/span> delta,<\/span>\nSD =<\/span> sd,<\/span> sig.level =<\/span> sig.level,<\/span> \"sig.level per test\"<\/span> =<\/span> sig.level\/<\/span>num.tests,<\/span>\npower =<\/span> power,<\/span> alternative =<\/span> alternative,<\/span> note =<\/span> NOTE<\/span>,<\/span>\nmethod =<\/span> METHOD),<\/span> class =<\/span> \"power.htest\"<\/span>)<\/span>\n}<\/span>\n<\/code><\/pre>\n\n\n\n
\u4e8c\u7fa4\u6bd4\u8f03\u3067\u691c\u7b97<\/h3>\n\n\n\n
\u4e8c\u7fa4\u6bd4\u8f03\u3067power.t.test()\u306e\u7d50\u679c\u3068\u4e00\u81f4\u3059\u308b\u304b\u78ba\u8a8d\u3057\u3066\u307f\u308b\u3002delta=0.8\u3001\u6bd4\u8f03\u30da\u30a2\u306f1\u3064 num.tests=1\u3060\u3002<\/p>\n\n\n\n
# Two groups<\/span>\nsamplesize.bonferroni.mean<\/span>(<\/span>delta=<\/span>0.8<\/span>,<\/span> num.tests=<\/span>1<\/span>)<\/span>\n<\/code><\/pre>\n\n\n\n
\u7d50\u679c\u306f\u3001\u4e00\u7fa425\u4f8b\u5fc5\u8981\u3068\u8a08\u7b97\u3055\u308c\u305f\u3002power.t.test()\u306f\u975e\u5fc3\uff54\u5206\u5e03\u3092\u4f7f\u3063\u305f\u672c\u683c\u7684\u306a\u8a08\u7b97\u3060\u3063\u305f\u306f\u305a\u3067\u3001\u4e0a\u8a18\u306e\u30b9\u30af\u30ea\u30d7\u30c8\u306e\u3088\u3046\u306a\u8fd1\u4f3c\u306e\u65b9\u6cd5\u3067\u306f\u306a\u3044\u306e\u3067\u3001\u82e5\u5e72\u306e\u305a\u308c\u304c\u3042\u308b\u3002\u3068\u306f\u8a00\u3046\u3082\u306e\u306e\u5b9f\u7528\u306b\u306f\u554f\u984c\u306a\u3044\u7bc4\u56f2\u306e\u305a\u308c\u3068\u601d\u3046\u3002<\/p>\n\n\n\n
><\/span> samplesize.bonferroni.mean<\/span>(<\/span>delta=<\/span>0.8<\/span>,<\/span> num.tests=<\/span>1<\/span>)<\/span>\nSample size for<\/span> Bonferroni-<\/span>type multiple comparison of the mean\nn =<\/span> 24.52775<\/span>\nNumbers of tests =<\/span> 1<\/span>\nDifference of a pair =<\/span> 0.8<\/span>\nSD =<\/span> 1<\/span>\nsig.level =<\/span> 0.05<\/span>\nsig.level per test =<\/span> 0.05<\/span>\npower =<\/span> 0.8<\/span>\nalternative =<\/span> two.sided\nNOTE:<\/span> n is number in<\/span> *<\/span>each*<\/span> group\n<\/code><\/pre>\n\n\n\n
\u4e09\u7fa4\u6bd4\u8f03\uff08\u4e09\u901a\u308a\u306e\u7d44\u307f\u5408\u308f\u305b\uff09<\/h3>\n\n\n\n
\u672c\u984c\u306e\u4e09\u7fa4\u6bd4\u8f03\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97\u3092\u5b9f\u884c\u3057\u3066\u307f\u308b\u3002delta=0.8\u306f\u540c\u3058\u306b\u3057\u3066\u3001num.tests=3\u3068\u3059\u308b\u3002<\/p>\n\n\n\n
delta\u306f\u4e09\u3064\u306e\u6bd4\u8f03\u306e\u5e73\u5747\u7684\u306a\u5dee\u3092\u610f\u5473\u3057\u3066\u3044\u308b\u3002\u305d\u308c\u304c0.8\uff08\u5927\u304d\u76ee\uff09\u3068\u8003\u3048\u3066\u8a08\u7b97\u3059\u308b\u3068\u3044\u3046\u610f\u5473\u306b\u306a\u308b\u3002<\/p>\n\n\n\n
# Three groups<\/span>\nsamplesize.bonferroni.mean<\/span>(<\/span>delta=<\/span>0.8<\/span>,<\/span> num.tests=<\/span>3<\/span>)<\/span>\n<\/code><\/pre>\n\n\n\n
\u8a08\u7b97\u7d50\u679c\u306f\u3001\u4e00\u7fa433\u4f8b\u3068\u8a08\u7b97\u3055\u308c\u305f\u3002\u4e8c\u7fa4\u6bd4\u8f03\u3088\u308a\u3082\u5fc5\u8981\u306a\u4eba\u6570\u304c\u5897\u3048\u308b\u3002\u304b\u306a\u308a\u53b3\u3057\u3044\u8a08\u7b97\u65b9\u6cd5\u3067\u3042\u308b\u3068\u611f\u3058\u308b\u3002<\/p>\n\n\n\n
><\/span> samplesize.bonferroni.mean<\/span>(<\/span>delta=<\/span>0.8<\/span>,<\/span> num.tests=<\/span>3<\/span>)<\/span>\nSample size for<\/span> Bonferroni-<\/span>type multiple comparison of the mean\nn =<\/span> 32.71598<\/span>\nNumbers of tests =<\/span> 3<\/span>\nDifference of a pair =<\/span> 0.8<\/span>\nSD =<\/span> 1<\/span>\nsig.level =<\/span> 0.05<\/span>\nsig.level per test =<\/span> 0.01666667<\/span>\npower =<\/span> 0.8<\/span>\nalternative =<\/span> two.sided\nNOTE:<\/span> n is number in<\/span> *<\/span>each*<\/span> group\n<\/code><\/pre>\n\n\n\n
\u56db\u7fa4\u6bd4\u8f03\uff08\u516d\u901a\u308a\u306e\u7d44\u307f\u5408\u308f\u305b\uff09<\/h3>\n\n\n\n
\u56db\u7fa4\u306f\u3069\u3046\u304b\uff1f\u56db\u7fa4\u306b\u306a\u308b\u30684\u3064\u306e\u4e2d\u304b\u30892\u3064\u3092\u9078\u3093\u3067\u7d44\u307f\u5408\u308f\u305b\u308b\u306e\u3067\u3001\u30b3\u30f3\u30d3\u30cd\u30fc\u30b7\u30e7\u30f34\u306e2\u306f\u3001(4×3)\/(2×1)=6\u901a\u308a\u3002<\/p>\n\n\n\n
# Four groups<\/span>\nsamplesize.bonferroni.mean<\/span>(<\/span>delta=<\/span>0.8<\/span>,<\/span> num.tests=<\/span>6<\/span>)<\/span>\n<\/code><\/pre>\n\n\n\n
\u7d50\u679c\u306f\u3001\u4e00\u7fa438\u4f8b\u5fc5\u8981\u3068\u8a08\u7b97\u3055\u308c\u305f\u3002<\/p>\n\n\n\n
><\/span> samplesize.bonferroni.mean<\/span>(<\/span>delta=<\/span>0.8<\/span>,<\/span> num.tests=<\/span>6<\/span>)<\/span>\nSample size for<\/span> Bonferroni-<\/span>type multiple comparison of the mean\nn =<\/span> 37.84236<\/span>\nNumbers of tests =<\/span> 6<\/span>\nDifference of a pair =<\/span> 0.8<\/span>\nSD =<\/span> 1<\/span>\nsig.level =<\/span> 0.05<\/span>\nsig.level per test =<\/span> 0.008333333<\/span>\npower =<\/span> 0.8<\/span>\nalternative =<\/span> two.sided\nNOTE:<\/span> n is number in<\/span> *<\/span>each*<\/span> group\n<\/code><\/pre>\n\n\n\n
\u5e73\u5747\u5024\u306e\u5dee\u3092\u591a\u91cd\u6bd4\u8f03\u3059\u308b\u306e\u306b\u5fc5\u8981\u306a\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u3092\u8a08\u7b97\u3067\u304d\u308b\u30a8\u30af\u30bb\u30eb\u30d5\u30a1\u30a4\u30eb<\/h2>\n\n\n\n
\u30a8\u30af\u30bb\u30eb\u30d5\u30a1\u30a4\u30eb\u3067Bonferroni\u578b \u5e73\u5747\u5024\u306e\u591a\u91cd\u6bd4\u8f03\u306e\u305f\u3081\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97\u304c\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
\u30dc\u30f3\u30d5\u30a7\u30ed\u30fc\u30cb\u578b \u5e73\u5747\u5024\u306e\u591a\u91cd\u6bd4\u8f03 \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
\u52d5\u753b\u306b\u3088\u308b\u4f7f\u3044\u65b9\u89e3\u8aac<\/h3>\n\n\n\n
\u3088\u3051\u308c\u3070\u3053\u3061\u3089\u3082\u3069\u3046\u305e\u3002<\/p>\n\n\n\n