{"id":401,"date":"2020-12-06T21:41:25","date_gmt":"2020-12-06T12:41:25","guid":{"rendered":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/repeated-measure-anova-sample-size\/"},"modified":"2024-10-04T23:20:44","modified_gmt":"2024-10-04T14:20:44","slug":"repeated-measure-anova-sample-size","status":"publish","type":"post","link":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/repeated-measure-anova-sample-size\/","title":{"rendered":"R \u3067\u5206\u5272\u30d7\u30ed\u30c3\u30c8\u5206\u6563\u5206\u6790\u306b\u5fc5\u8981\u306a\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5"},"content":{"rendered":"\n

\u5206\u5272\u30d7\u30ed\u30c3\u30c8\u5206\u6563\u5206\u6790\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97\u306e\u65b9\u6cd5\u3002<\/p>\n\n\n\n\n\n\n\n

\u5206\u5272\u30d7\u30ed\u30c3\u30c8\u5206\u6563\u5206\u6790\u3068\u306f\uff1f<\/h2>\n\n\n\n

\u540c\u3058\u5bfe\u8c61\u8005\u306e\u3042\u308b\u6307\u6a19\u3092\u53cd\u5fa9\u3057\u3066\u6e2c\u5b9a\u3057\u305f\u3068\u304d\u306e\u30c7\u30fc\u30bf\u3092\u5206\u6790\u3057\u305f\u3044\u3053\u3068\u304c\u3042\u308b\u3002<\/p>\n\n\n\n

\u5bfe\u8c61\u8005\u3092\u3044\u304f\u3064\u304b\u306e\u7fa4\u306b\u632f\u308a\u5206\u3051\u3066\u6bd4\u8f03\u3057\u305f\u3044\u3053\u3068\u304c\u591a\u3044\u3002<\/p>\n\n\n\n

\u3053\u3053\u3067\u306f\u3001\u3053\u306e\u89e3\u6790\u65b9\u6cd5\u3092\u300c\u5206\u5272\u30d7\u30ed\u30c3\u30c8\u5206\u6563\u5206\u6790\u300d\u3068\u547c\u3093\u3067\u3044\u308b\u3002<\/p>\n\n\n\n

\u5206\u5272\u30d7\u30ed\u30c3\u30c8\u30c7\u30b6\u30a4\u30f3\u3068\u3082\u547c\u3070\u308c\u308b\u65b9\u6cd5\u3060\u3002<\/p>\n\n\n\n

\u53c2\u8003\u3068\u306a\u308b\u904e\u53bb\u8a18\u4e8b\u306f\u3053\u3061\u3089\u3002<\/p>\n\n\n

\u6295\u7a3f\u304c\u898b\u3064\u304b\u308a\u307e\u305b\u3093\u3002<\/div>\n\n\n

\u5206\u5272\u30d7\u30ed\u30c3\u30c8\u5206\u6563\u5206\u6790\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97\u306e\u305f\u3081\u306b pwr.anova.test() \u306e\u4e00\u90e8\u3092\u629c\u304d\u51fa\u3059<\/h2>\n\n\n\n

\u307e\u305a\u306f\u3001\u5206\u6563\u5206\u6790\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97\u30b9\u30af\u30ea\u30d7\u30c8\u3092 pwr \u30d1\u30c3\u30b1\u30fc\u30b8\u306e pwr.anova.test() \u304b\u3089\u629c\u304d\u51fa\u3057\u3066\u307f\u308b\u3002<\/p>\n\n\n\n

pwr.anova.test.n <-<\/span> function<\/span>(<\/span>k,<\/span> f,<\/span> sig.level=<\/span>0.05<\/span>,<\/span> power=<\/span>0.8<\/span>)<\/span>\n{<\/span>\np.body <-<\/span> quote<\/span>({<\/span>\nlambda <-<\/span> k*<\/span>n*<\/span>f^<\/span>2<\/span>\npf<\/span>(<\/span>qf<\/span>(<\/span>sig.level,<\/span> k-<\/span>1<\/span>,<\/span> (<\/span>n-<\/span>1<\/span>)<\/span>*<\/span>k,<\/span> lower=<\/span>FALSE<\/span>),<\/span> k-<\/span>1<\/span>,<\/span> (<\/span>n-<\/span>1<\/span>)<\/span>*<\/span>k,<\/span> lambda,<\/span> lower=<\/span>FALSE<\/span>)<\/span>\n})<\/span>\nn <-<\/span> uniroot<\/span>(<\/span>function<\/span>(<\/span>n)<\/span> eval<\/span>(<\/span>p.body)<\/span>-<\/span>power,<\/span> c<\/span>(<\/span>2<\/span>+<\/span>1e-10<\/span>,<\/span> 1e+09<\/span>))$<\/span>root\nNOTE<\/span> <-<\/span> \"n is number in each group\"<\/span>\nMETHOD <-<\/span> \"Balanced one-way analysis of variance power calculation\"<\/span>\nstructure <\/span>(<\/span>list<\/span>(<\/span>k=<\/span>k,<\/span> n=<\/span>n,<\/span> f=<\/span>f,<\/span> sig.level=<\/span>sig.level,<\/span> power=<\/span>power,<\/span> note=<\/span>NOTE<\/span>,<\/span> method=<\/span>METHOD),<\/span>\nclass=<\/span>\"power.htest\"<\/span>)<\/span>\n}<\/span>\n<\/code><\/pre>\n\n\n\n
\u4f8b\u3048\u3070\u30014\u30b0\u30eb\u30fc\u30d7\u306e\u6bd4\u8f03\u3067\u3001effect size (f) \u304c\u4e2d\u7a0b\u5ea6\u30670.25\u3060\u3063\u305f\u3068\u3059\u308b\u3068\u3001\u4e00\u7fa445\u4f8b\u5fc5\u8981\u3068\u8a08\u7b97\u3055\u308c\u308b\u3002<\/p>\n\n\n\n
><\/span> pwr.anova.test.n<\/span>(<\/span>k=<\/span>4<\/span>,<\/span>f=<\/span>0.25<\/span>)<\/span>\nBalanced one-<\/span>way analysis of variance power calculation\nk =<\/span> 4<\/span>\nn =<\/span> 44.59927<\/span>\nf =<\/span> 0.25<\/span>\nsig.level =<\/span> 0.05<\/span>\npower =<\/span> 0.8<\/span>\nNOTE:<\/span> n is number in<\/span> each group\n<\/code><\/pre>\n\n\n\n
\u3053\u308c\u3092\u3082\u3068\u306b\u3001\u5206\u5272\u30d7\u30ed\u30c3\u30c8\u5206\u6563\u5206\u6790\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97\u306e\u30b9\u30af\u30ea\u30d7\u30c8\u3092\u4f5c\u6210\u3057\u3066\u307f\u305f\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>
\u5206\u5272\u30d7\u30ed\u30c3\u30c8\u5206\u6563\u5206\u6790\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97\u95a2\u6570<\/h2>\n\n\n\n
\u6bd4\u8f03\u3059\u308b\u7fa4\u306e\u6570\u3092p\u3001\u53cd\u5fa9\u3057\u3066\u6e2c\u5b9a\u3059\u308b\u56de\u6570\u3092q\u3001\u7fa4\u9593\u6bd4\u8f03\u306eeffect size\u3092f.A.CR\u3001\u5bfe\u8c61\u8005\u306e\u6e2c\u5b9a\u5024\u306b\u304a\u3051\u308b\u81ea\u5df1\u76f8\u95a2\u3092rho\u3068\u3059\u308b\u3068\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u95a2\u6570\u306b\u306a\u308b\u3002<\/p>\n\n\n\n
pwr.split.plot.test.n <-<\/span> function<\/span>(<\/span>p,<\/span> q,<\/span> f.A.CR,<\/span> rho,<\/span> sig.level=<\/span>0.05<\/span>,<\/span> power=<\/span>0.8<\/span>)<\/span>\n{<\/span>\np.body <-<\/span> quote<\/span>({<\/span>\nf.A <-<\/span> f.A.CR\/<\/span>sqrt<\/span>(<\/span>1<\/span>+<\/span>(<\/span>q-<\/span>1<\/span>)<\/span>*<\/span>rho)<\/span>\nlambda <-<\/span> p*<\/span>q*<\/span>n*<\/span>f.A^<\/span>2<\/span>\npf<\/span>(<\/span>qf<\/span>(<\/span>sig.level,<\/span> p-<\/span>1<\/span>,<\/span> (<\/span>n-<\/span>1<\/span>)<\/span>*<\/span>p,<\/span> lower=<\/span>FALSE<\/span>),<\/span> p-<\/span>1<\/span>,<\/span> (<\/span>n-<\/span>1<\/span>)<\/span>*<\/span>p,<\/span> lambda,<\/span> lower=<\/span>FALSE<\/span>)<\/span>\n})<\/span>\nn <-<\/span> uniroot<\/span>(<\/span>function<\/span>(<\/span>n)<\/span> eval<\/span>(<\/span>p.body)<\/span>-<\/span>power,<\/span> c<\/span>(<\/span>2<\/span>+<\/span>1e-10<\/span>,<\/span> 1e+09<\/span>))$<\/span>root\nNOTE<\/span> <-<\/span> \"n is number in each group\"<\/span>\nMETHOD <-<\/span> \"Split-plot design analysis of variance power calculation\"<\/span>\nstructure <\/span>(<\/span>list<\/span>(<\/span>p=<\/span>p,<\/span> q=<\/span>q,<\/span> n=<\/span>n,<\/span> f.A.CR=<\/span>f.A.CR,<\/span> rho=<\/span>rho,<\/span>\nsig.level=<\/span>sig.level,<\/span> power=<\/span>power,<\/span> note=<\/span>NOTE<\/span>,<\/span> method=<\/span>METHOD),<\/span>\nclass=<\/span>\"power.htest\"<\/span>)<\/span>\n}<\/span>\n<\/code><\/pre>\n\n\n\n
\u7fa4\u306e\u6570\u30924\u3001\u53cd\u5fa9\u56de\u6570\u30824\u3001f.A.CR\u30920.25\u3001rho\u30920.5\u3068\u3059\u308b\u3068\u3001\u4e00\u7fa429\u4f8b\u3068\u8a08\u7b97\u3055\u308c\u308b\u3002<\/p>\n\n\n\n
><\/span> pwr.split.plot.test.n<\/span>(<\/span>p=<\/span>4<\/span>,<\/span> q=<\/span>4<\/span>,<\/span> f.A.CR=<\/span>0.25<\/span>,<\/span> rho=<\/span>0.5<\/span>)<\/span>\nSplit-<\/span>plot design analysis of variance power calculation\np =<\/span> 4<\/span>\nq =<\/span> 4<\/span>\nn =<\/span> 28.2526<\/span>\nf.A.CR =<\/span> 0.25<\/span>\nrho =<\/span> 0.5<\/span>\nsig.level =<\/span> 0.05<\/span>\npower =<\/span> 0.8<\/span>\nNOTE:<\/span> n is number in<\/span> each group\n<\/code><\/pre>\n\n\n\n
rho\u304c1\uff08\u5b8c\u74a7\u306a\u81ea\u5df1\u76f8\u95a2\uff09\u306e\u5834\u5408\u3001\u4e00\u7fa445\u4f8b\u3068\u8a08\u7b97\u3055\u308c\u308b\u3002<\/p>\n\n\n\n
><\/span> pwr.split.plot.test.n<\/span>(<\/span>p=<\/span>4<\/span>,<\/span> q=<\/span>4<\/span>,<\/span> f.A.CR=<\/span>0.25<\/span>,<\/span> rho=<\/span>1<\/span>)<\/span>\nSplit-<\/span>plot design analysis of variance power calculation\np =<\/span> 4<\/span>\nq =<\/span> 4<\/span>\nn =<\/span> 44.59927<\/span>\nf.A.CR =<\/span> 0.25<\/span>\nrho =<\/span> 1<\/span>\nsig.level =<\/span> 0.05<\/span>\npower =<\/span> 0.8<\/span>\nNOTE:<\/span> n is number in<\/span> each group\n<\/code><\/pre>\n\n\n\n
\u3053\u306e\u5834\u5408\u306f\u901a\u5e38\u306e\u53cd\u5fa9\u6e2c\u5b9a\u3057\u306a\u3044\u5206\u6563\u5206\u6790\u3068\u540c\u3058\u306b\u306a\u308b\u3002<\/p>\n\n\n\n
\u5b8c\u74a7\u306b\u81ea\u5df1\u76f8\u95a2\u3059\u308b\u306a\u30891\u56de\u306e\u6e2c\u5b9a\u3067\u3082\u540c\u3058\u3068\u3044\u3046\u3053\u3068\u3060\u3002<\/p>\n\n\n\n
rho\u304c0\uff08\u5168\u304f\u306e\u81ea\u5df1\u76f8\u95a2\u306a\u3057\uff09\u306e\u5834\u5408\u3001\u4e00\u7fa412\u4f8b\u3068\u8a08\u7b97\u3055\u308c\u308b\u3002<\/p>\n\n\n\n
><\/span> pwr.split.plot.test.n<\/span>(<\/span>p=<\/span>4<\/span>,<\/span> q=<\/span>4<\/span>,<\/span> f.A.CR=<\/span>0.25<\/span>,<\/span> rho=<\/span>0<\/span>)<\/span>\nSplit-<\/span>plot design analysis of variance power calculation\np =<\/span> 4<\/span>\nq =<\/span> 4<\/span>\nn =<\/span> 11.92611<\/span>\nf.A.CR =<\/span> 0.25<\/span>\nrho =<\/span> 0<\/span>\nsig.level =<\/span> 0.05<\/span>\npower =<\/span> 0.8<\/span>\nNOTE:<\/span> n is number in<\/span> each group\n<\/code><\/pre>\n\n\n\n
\u3053\u308c\u306f\u901a\u5e38\u3042\u308a\u5f97\u306a\u3044\u3002<\/p>\n\n\n\n
\u540c\u3058\u5bfe\u8c61\u8005\u306f\u5fc5\u305a\u5c11\u3057\u306f\u76f8\u95a2\u3059\u308b\u3002<\/p>\n\n\n\n
\u4f8b\u3048\u3070\u3001\u8840\u5727\u304c\u9ad8\u3081\u306e\u4eba\u306f\u4f55\u5ea6\u6e2c\u3063\u3066\u3082\u9ad8\u3081\u306e\u306f\u305a\u3002<\/p>\n\n\n\n
\u4f4e\u3081\u306e\u4eba\u306f\u3044\u3064\u3082\u4f4e\u3081\u3002<\/p>\n\n\n\n
\u3053\u308c\u306f\u611f\u899a\u7684\u306b\u308f\u304b\u308b\u3002<\/p>\n\n\n\n
\u5206\u5272\u30d7\u30ed\u30c3\u30c8\u5206\u6563\u5206\u6790\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97\u3092\u3059\u308b\u969b\u306b\u5927\u4e8b\u306a\u3053\u3068<\/h2>\n\n\n\n
\u5206\u5272\u30d7\u30ed\u30c3\u30c8\u5206\u6563\u5206\u6790\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97\u3092\u3059\u308b\u969b\u306b\u6c7a\u3081\u308b\u306e\u304c\u5927\u5909\u306a\u306e\u306f\u3001f.A.CR\u3068\u3042\u308beffect size\u3068rho\u3068\u3044\u3046\u5bfe\u8c61\u8005\u5185\u306e\u81ea\u5df1\u76f8\u95a2\u3060\u308d\u3046\u3002<\/p>\n\n\n\n
f.A.CR\u306f\u3001\u3044\u308f\u3086\u308b\u7fa4\u9593\u306e\u6a19\u6e96\u504f\u5dee\u3068\u3001\u7fa4\u5185\u306e\u6a19\u6e96\u504f\u5dee\u306e\u6bd4\u3067\u3042\u308b\u3002<\/p>\n\n\n\n
\u30d1\u30a4\u30ed\u30c3\u30c8\u30b9\u30bf\u30c7\u30a3\u3084\u5148\u884c\u7814\u7a76\u306a\u3069\u304c\u3042\u308c\u3070\u53c2\u8003\u306b\u3067\u304d\u308b\u304c\u3001\u305d\u3046\u3067\u306a\u3044\u5834\u5408\u306f\u3001\u56f0\u3063\u3066\u3057\u307e\u3046\u3002<\/p>\n\n\n\n
\u884c\u52d5\u79d1\u5b66\u5206\u91ce\u3067\u306f\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u76ee\u5b89\u304c\u3042\u308b\u306e\u3067\u3001\u305d\u308c\u306b\u5f93\u3046\u3053\u3068\u3082\u3067\u304d\u308b\u3002<\/p>\n\n\n\n