{"id":531,"date":"2018-07-27T21:33:17","date_gmt":"2018-07-27T12:33:17","guid":{"rendered":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/how-to-determine-sample-size-in-anova\/"},"modified":"2024-10-13T22:12:09","modified_gmt":"2024-10-13T13:12:09","slug":"how-to-determine-sample-size-in-anova","status":"publish","type":"post","link":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/how-to-determine-sample-size-in-anova\/","title":{"rendered":"R \u3067\u5206\u6563\u5206\u6790\u306b\u5fc5\u8981\u306a\u30b5\u30f3\u30d7\u30eb\u6570\u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5"},"content":{"rendered":"\n

\u5206\u6563\u5206\u6790\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u3001\u30b5\u30f3\u30d7\u30eb\u6570\u3001n \u6570\u306e\u8a08\u7b97\u3092 R \u3067\u3084\u3063\u3066\u307f\u305f\u3002<\/p>\n\n\n\n\n\n\n\n

\u5206\u6563\u5206\u6790\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97\uff08\u8aa4\u5dee\u5206\u6563\u304c\u308f\u304b\u3063\u3066\u3044\u308b\u5834\u5408\uff09<\/h2>\n\n\n\n

\u7fa4\u306e\u6570\u3092k\u3001\u7fa4\u9593\u3067\u6700\u5927\u306e\u5dee\uff08\u6bcd\u5e73\u5747\u306e\u5dee\u306e\u6700\u5927\u5024\uff09\u3092d\u3001\u8aa4\u5dee\u306e\u6bcd\u5206\u6563\u306e\u5e73\u65b9\u6839\u3092 sigma0 \u3068\u3059\u308b\u3002<\/p>\n\n\n\n

\u3053\u306e\u5834\u5408\u306e\u6bcd\u5206\u6563\u306f\u3001\u305d\u308c\u305e\u308c\u306e\u7fa4\u306e\u6bcd\u5206\u6563\u3092\u6307\u3057\u3066\u3044\u308b\u3002<\/p>\n\n\n\n

\u305d\u308c\u3089\u3059\u3079\u3066\u304c\u7b49\u3057\u304f\u65e2\u77e5\u3068\u3044\u3046\u306e\u304c\u524d\u63d0\u3002<\/p>\n\n\n\n

\u691c\u51fa\u529b\u304c80%\u304b90%\u3001\u6709\u610f\u6c34\u6e96\u304c5%\u304b1%\u3067\u3001\u5408\u8a084\u901a\u308a\u306b\u5bfe\u5fdc\u3067\u304d\u308b\u30b9\u30af\u30ea\u30d7\u30c8\u304c\u4ee5\u4e0b\u306e\u901a\u308a\u3002<\/p>\n\n\n\n

anova.sample.size <-<\/span> function<\/span>(<\/span>k,<\/span> d,<\/span> sigma0,<\/span> alpha=<\/span>0.05<\/span>,<\/span> power=<\/span>.8<\/span>){<\/span>\nDELTA <-<\/span> d^<\/span>2<\/span>\/<\/span>(<\/span>2<\/span>*<\/span>sigma0^<\/span>2<\/span>)<\/span>\nphiA <-<\/span> k-<\/span>1<\/span>\nif<\/span> (<\/span>power==<\/span>.8<\/span> &<\/span> alpha==<\/span>.05<\/span>)<\/span> {<\/span>lambda <-<\/span> 4.860<\/span>+<\/span>3.584<\/span>*<\/span>sqrt<\/span>(<\/span>phiA)}<\/span>\nelse<\/span> if<\/span> (<\/span>power==<\/span>.9<\/span> &<\/span> alpha==<\/span>.05<\/span>)<\/span> {<\/span>lambda <-<\/span> 7.049<\/span>+<\/span>4.244<\/span>*<\/span>sqrt<\/span>(<\/span>phiA)}<\/span>\nelse<\/span> if<\/span> (<\/span>power==<\/span>.8<\/span> &<\/span> alpha==<\/span>.01<\/span>)<\/span> {<\/span>lambda <-<\/span> 7.736<\/span>+<\/span>4.551<\/span>*<\/span>sqrt<\/span>(<\/span>phiA)}<\/span>\nelse<\/span> if<\/span> (<\/span>power==<\/span>.9<\/span> &<\/span> alpha==<\/span>.01<\/span>)<\/span> {<\/span>lambda <-<\/span> 10.439<\/span>+<\/span>5.213<\/span>*<\/span>sqrt<\/span>(<\/span>phiA)}<\/span>\nn <-<\/span> lambda\/<\/span>DELTA\nMETHOD <-<\/span> \"ANOVA Sample Size Calculation\"<\/span>\nstructure<\/span>(<\/span>list<\/span>(<\/span>n=<\/span>n,<\/span> delta=<\/span>d,<\/span> sd=<\/span>sigma0,<\/span> sig.level=<\/span>alpha,<\/span> power=<\/span>power,<\/span> method=<\/span>METHOD),<\/span>class=<\/span>\"power.htest\"<\/span>)<\/span>\n}<\/span>\n<\/code><\/pre>\n\n\n\n
\u7fa4\u306e\u6570\u304c4\u3001\u6700\u5927\u306e\u7fa4\u9593\u5dee\u304c2\u3001\u8aa4\u5dee\u5206\u6563\u306e\u5e73\u65b9\u6839\u30921\u3001\u691c\u51fa\u529b80%\u3001\u6709\u610f\u6c34\u6e965%\u3068\u3059\u308b\u3068\u3001\u4e00\u7fa46\u4f8b\u3068\u8a08\u7b97\u3055\u308c\u308b\u3002<\/p>\n\n\n\n
><\/span> anova.sample.size<\/span>(<\/span>k=<\/span>4<\/span>,<\/span> d=<\/span>2<\/span>,<\/span> sigma0=<\/span>1<\/span>)<\/span>\nANOVA Sample Size Calculation\nn =<\/span> 5.533835<\/span>\ndelta =<\/span> 2<\/span>\nsd =<\/span> 1<\/span>\nsig.level =<\/span> 0.05<\/span>\npower =<\/span> 0.8<\/span>\n<\/code><\/pre>\n\n\n\n
\u691c\u51fa\u529b\u309290%\u306b\u3059\u308b\u3068\u3001\u4e00\u7fa48\u4f8b\u3068\u8a08\u7b97\u3055\u308c\u308b\u3002<\/p>\n\n\n\n
><\/span> anova.sample.size<\/span>(<\/span>k=<\/span>4<\/span>,<\/span> d=<\/span>2<\/span>,<\/span> sigma0=<\/span>1<\/span>,<\/span> power=<\/span>.9<\/span>)<\/span>\nANOVA Sample Size Calculation\nn =<\/span> 7.199912<\/span>\ndelta =<\/span> 2<\/span>\nsd =<\/span> 1<\/span>\nsig.level =<\/span> 0.05<\/span>\npower =<\/span> 0.9<\/span>\n<\/code><\/pre>\n\n\n\n
\u5b9f\u969b\u306b\u306f\u3001\u6bcd\u5206\u6563\u306f\u308f\u304b\u3063\u3066\u3044\u308b\u3053\u3068\u306f\u306a\u3044\u305f\u3081\u3001\u904e\u53bb\u306e\u6587\u732e\u306a\u3069\u304b\u3089\u4eee\u5b9a\u3057\u3066\u3001\u4ee5\u4e0b\u306e\u300c\u8aa4\u5dee\u5206\u6563\u304c\u308f\u304b\u3089\u306a\u3044\u5834\u5408\u300d\u306e\u624b\u9806\u3092\u7528\u3044\u308b\u307b\u3046\u304c\u3088\u3044\u3002<\/p>\n\n\n\n
\u5206\u6563\u5206\u6790\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97\uff08\u8aa4\u5dee\u5206\u6563\u304c\u672a\u77e5\u306e\u5834\u5408\uff09<\/h2>\n\n\n\n
\u901a\u5e38\u3001\u8aa4\u5dee\u5206\u6563\u306f\u672a\u77e5\u306a\u306e\u3067\u3001\u3053\u3061\u3089\u3092\u4f7f\u3046\u307b\u3046\u304c\u3088\u3044\u3002<\/p>\n\n\n\n
\u7fa4\u306e\u6570\u3092k\u3001\u7fa4\u9593\u3067\u6700\u5927\u306e\u5dee\uff08\u6bcd\u5e73\u5747\u306e\u5dee\u306e\u6700\u5927\u5024\uff09\u3092d\u3001\u8aa4\u5dee\u306e\u6bcd\u5206\u6563\u306e\u5e73\u65b9\u6839\u3092 sigma0 \u3068\u3059\u308b\u306e\u306f\u524d\u7bc0\u3068\u540c\u3058\u3002<\/p>\n\n\n\n
\u8aa4\u5dee\u5206\u6563\u304c\u65e2\u77e5\u3068\u307f\u306a\u3057\u3066\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97\u3092\u3057\u3066\u3001\u305d\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba n \u3067\u8aa4\u5dee\u5206\u6563\u672a\u77e5\u306e\u5834\u5408\u306e\u691c\u51fa\u529b\u3092\u8a08\u7b97\u3057\u3001\u691c\u51fa\u529b\u304c\u5e0c\u671b\u901a\u308a\u306b\u306a\u308b\u3088\u3046\u306b\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u3092\u5fae\u8abf\u6574\u3057\u3066\u3001\u6700\u7d42\u7684\u306a\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u3092\u6c42\u3081\u3066\u3044\u308b\u3002<\/p>\n\n\n\n
anova.power.michi <-<\/span> function<\/span>(<\/span>k,<\/span> n,<\/span> d,<\/span> sigma0,<\/span> alpha=<\/span>.05<\/span>){<\/span>\nDELTA <-<\/span> d^<\/span>2<\/span>\/<\/span>(<\/span>2<\/span>*<\/span>sigma0^<\/span>2<\/span>)<\/span>\nphiA <-<\/span> k-<\/span>1<\/span>\nphiE <-<\/span> k*<\/span>(<\/span>n-<\/span>1<\/span>)<\/span>\nlambda <-<\/span> n*<\/span>DELTA\ncA <-<\/span> (<\/span>phiA+<\/span>2<\/span>*<\/span>lambda)<\/span>\/<\/span>(<\/span>phiA+<\/span>lambda)<\/span>\nphiA.star <-<\/span> (<\/span>phiA+<\/span>lambda)<\/span>^<\/span>2<\/span>\/<\/span>(<\/span>phiA+<\/span>2<\/span>*<\/span>lambda)<\/span>\nw <-<\/span> qf<\/span>(<\/span>p=<\/span>alpha,<\/span> df1=<\/span>phiA,<\/span> df2=<\/span>phiE,<\/span> lower.tail=<\/span>FALSE<\/span>)<\/span>\nu <-<\/span> (<\/span>sqrt<\/span>(<\/span>w\/<\/span>phiE)<\/span>*<\/span>sqrt<\/span>(<\/span>2<\/span>*<\/span>phiE-<\/span>1<\/span>)<\/span>-<\/span>sqrt<\/span>(<\/span>cA\/<\/span>phiA)<\/span>*<\/span>sqrt<\/span>(<\/span>2<\/span>*<\/span>phiA.star-<\/span>1<\/span>))<\/span>\/<\/span>(<\/span>sqrt<\/span>(<\/span>cA\/<\/span>phiA+<\/span>w\/<\/span>phiE))<\/span>\npower <-<\/span> 1<\/span>-<\/span>pnorm<\/span>(<\/span>u)<\/span>\nMETHOD <-<\/span> \"ANOVA Power Calculation Variance unknown\"<\/span>\nstructure<\/span>(<\/span>list<\/span>(<\/span>n=<\/span>n,<\/span> delta=<\/span>d,<\/span> sd=<\/span>sigma0,<\/span> sig.level=<\/span>alpha,<\/span> power=<\/span>power,<\/span> method=<\/span>METHOD),<\/span> class=<\/span>\"power.htest\"<\/span>)<\/span>\n}<\/span>\n<\/code><\/pre>\n\n\n\n
\u524d\u7bc0\u306e\u4f8b\u3060\u3068\u3001\u7fa4\u306e\u6570\u304c4\u3067\u3001\u5dee\u304c2\u3001\u8aa4\u5dee\u5206\u6563\u5e73\u65b9\u6839\u304c1\u3060\u3068\u3059\u308b\u3068\u3001\u4e00\u7fa46\u4f8b\u3068\u8a08\u7b97\u3055\u308c\u305f\u306e\u3067\u3001\u305d\u306e\u901a\u308a\u8a08\u7b97\u3059\u308b\u3068\u3001\u691c\u51fa\u529b\u306f80%\u306b\u5230\u9054\u305b\u305a76%\u306b\u306a\u308b\u3002<\/p>\n\n\n\n
><\/span> anova.power.michi<\/span>(<\/span>k=<\/span>4<\/span>,<\/span> n=<\/span>6<\/span>,<\/span> d=<\/span>2<\/span>,<\/span> sigma0=<\/span>1<\/span>)<\/span>\nANOVA Power Calculation Variance unknown\nn =<\/span> 6<\/span>\ndelta =<\/span> 2<\/span>\nsd =<\/span> 1<\/span>\nsig.level =<\/span> 0.05<\/span>\npower =<\/span> 0.7579354<\/span>\n<\/code><\/pre>\n\n\n\n
\u4e00\u7fa4\u306b1\u4f8b\u305a\u3064\u8db3\u3057\u3066\u3001\u4e00\u7fa47\u4f8b\u3068\u3059\u308b\u3068\u691c\u51fa\u529b\u306f\u3069\u3046\u306a\u308b\u304b\uff1f<\/p>\n\n\n\n
84%\u306b\u306a\u308a\u3001\u691c\u51fa\u529b80%\u3092\u8d85\u3048\u308b\u3002<\/p>\n\n\n\n
\u3086\u3048\u306b\u4e00\u7fa47\u4f8b\u304c\u9069\u5207\u3068\u3044\u3048\u308b\u3002<\/p>\n\n\n\n
><\/span> anova.power.michi<\/span>(<\/span>k=<\/span>4<\/span>,<\/span> n=<\/span>7<\/span>,<\/span> d=<\/span>2<\/span>,<\/span> sigma0=<\/span>1<\/span>)<\/span>\nANOVA Power Calculation Variance unknown\nn =<\/span> 7<\/span>\ndelta =<\/span> 2<\/span>\nsd =<\/span> 1<\/span>\nsig.level =<\/span> 0.05<\/span>\npower =<\/span> 0.8388784<\/span>\n<\/code><\/pre>\n\n\n\n
\u3082\u3046\u4e00\u3064\u524d\u7bc0\u306e\u4f8b\u3067\u3001\u7fa4\u306e\u6570\u304c4\u3001\u5dee\u304c2\u3001\u8aa4\u5dee\u5206\u6563\u5e73\u65b9\u6839\u304c1\u3001\u691c\u51fa\u529b90%\u306e\u3068\u304d\u306f\u3001\u4e00\u7fa48\u4f8b\u3068\u8a08\u7b97\u3055\u308c\u308b\u3002<\/p>\n\n\n\n
><\/span> anova.sample.size<\/span>(<\/span>k=<\/span>4<\/span>,<\/span> d=<\/span>2<\/span>,<\/span> sigma0=<\/span>1<\/span>,<\/span> power=<\/span>.9<\/span>)<\/span>\nANOVA Sample Size Calculation\nn =<\/span> 7.199912<\/span>\ndelta =<\/span> 2<\/span>\nsd =<\/span> 1<\/span>\nsig.level =<\/span> 0.05<\/span>\npower =<\/span> 0.9<\/span>\n<\/code><\/pre>\n\n\n\n
\u8aa4\u5dee\u5206\u6563\u304c\u672a\u77e5\u306e\u3068\u304d\u306e\u30b9\u30af\u30ea\u30d7\u30c8\u3067\u3001\u4e00\u7fa48\u4f8b\u30689\u4f8b\u306e\u3068\u304d\u306e\u691c\u51fa\u529b\u3092\u8a08\u7b97\u3059\u308b\u3068\u30018\u4f8b\u306e\u6642\u306f\u691c\u51fa\u529b90%\u3092\u308f\u305a\u304b\u306b\u4e0b\u56de\u308a\u30019\u4f8b\u306e\u6642\u306f\u691c\u51fa\u529b90%\u3092\u4e0a\u56de\u308b\u3002<\/p>\n\n\n\n
\u3088\u3063\u3066\u3001\u691c\u51fa\u529b90%\u3067\u691c\u5b9a\u3092\u884c\u3046\u305f\u3081\u306b\u306f\u3001\u4e00\u7fa49\u4f8b\u5fc5\u8981\u3068\u8003\u3048\u308b\u3002<\/p>\n\n\n\n
><\/span> anova.power.michi<\/span>(<\/span>k=<\/span>4<\/span>,<\/span> n=<\/span>c<\/span>(<\/span>8<\/span>,<\/span>9<\/span>),<\/span> d=<\/span>2<\/span>,<\/span> sigma0=<\/span>1<\/span>)<\/span>\nANOVA Power Calculation Variance unknown\nn =<\/span> 8<\/span>,<\/span> 9<\/span>\ndelta =<\/span> 2<\/span>\nsd =<\/span> 1<\/span>\nsig.level =<\/span> 0.05<\/span>\npower =<\/span> 0.8955750<\/span>,<\/span> 0.9338735<\/span>\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>
\u5206\u6563\u5206\u6790\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u3092\u5225\u306e\u4f8b\u3067\u8a08\u7b97\u3057\u3066\u307f\u308b<\/h2>\n\n\n\n
\u904e\u53bb\u8a18\u4e8b\u3067\u7528\u3044\u305f\u30c7\u30fc\u30bf\u3092\u4f7f\u3063\u3066\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97\u3092\u884c\u3063\u3066\u307f\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\u4e00\u5143\u914d\u7f6e\u5206\u6563\u5206\u6790\u3092\u884c\u3046\u65b9\u6cd5<\/a>\n\t\t\t\t\t\tR\u3067\u3001\u4e00\u5143\u914d\u7f6e\u5206\u6563\u5206\u6790\u3092 step by step \u3067\u8a08\u7b97\u3057\u3066\u307f\u305f\u3002 lm() \u3068 Anova() \u3092\u4f7f\u3048\u3070\u3042\u3063\u3068\u3044\u3046\u9593\u3060\u304c\u3001\u5177\u4f53\u7684\u306a\u4e00\u3064\u4e00\u3064\u306e\u8a08\u7b97\u3092\u81ea\u5206\u3067\u7d44\u307f\u7acb\u3066\u3066\u307f\u308b\u3068\u3069\u3046\u304b\uff1f \u6559\u79d1\u66f8…<\/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
\u8a08\u7b97\u306b\u5fc5\u8981\u306a\u3082\u306e\u306f\u3001\u7fa4\u306e\u6570\u3001\u7fa4\u9593\u306e\u6700\u5927\u306e\u5dee\u3001\u8aa4\u5dee\u5206\u6563\u306e\u5e73\u65b9\u6839\u306e\uff13\u3064\u3002<\/p>\n\n\n\n
\u30c7\u30fc\u30bf\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3068\u3066\u3082\u30b7\u30f3\u30d7\u30eb\u3002<\/p>\n\n\n\n
A1 <-<\/span> c<\/span>(<\/span>64<\/span>,<\/span>72<\/span>,<\/span>68<\/span>,<\/span>77<\/span>)<\/span>\nA2 <-<\/span> c<\/span>(<\/span>82<\/span>,<\/span>78<\/span>,<\/span>77<\/span>,<\/span>85<\/span>)<\/span>\nA3 <-<\/span> c<\/span>(<\/span>55<\/span>,<\/span>64<\/span>,<\/span>66<\/span>,<\/span>49<\/span>)<\/span>\n<\/code><\/pre>\n\n\n\n
\u7fa4\u306e\u6570\u306f\uff13\u3002<\/p>\n\n\n\n
\u7fa4\u9593\u306e\u6700\u5927\u306e\u5dee\u306fA2\u3068A3\u306e\u9593\u306722\u3002<\/p>\n\n\n\n
><\/span> mean<\/span>(<\/span>A1)<\/span>-<\/span>mean<\/span>(<\/span>A2)<\/span>\n[<\/span>1<\/span>]<\/span> -<\/span>10.25<\/span>\n><\/span> mean<\/span>(<\/span>A2)<\/span>-<\/span>mean<\/span>(<\/span>A3)<\/span>\n[<\/span>1<\/span>]<\/span> 22<\/span>\n><\/span> mean<\/span>(<\/span>A3)<\/span>-<\/span>mean<\/span>(<\/span>A1)<\/span>\n[<\/span>1<\/span>]<\/span> -<\/span>11.75<\/span>\n<\/code><\/pre>\n\n\n\n
\u8aa4\u5dee\u5206\u6563\u306e\u5e73\u65b9\u6839\u306f\u3001\u5206\u6563\u5206\u6790\u7d50\u679c\u304b\u3089\u8a08\u7b97\u3067\u304d\u308b\u300c\u8aa4\u5dee\u5e73\u5747\u5e73\u65b9\u306e\u5e73\u65b9\u6839\u300d\u3067\u3042\u308b\u3002<\/p>\n\n\n\n
\u5206\u6563\u5206\u6790\u306e\u7d50\u679c\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3002<\/p>\n\n\n\n
><\/span> Anova<\/span>(<\/span>lm1)<\/span>\nAnova Table <\/span>(<\/span>Type II tests)<\/span>\nResponse:<\/span> X.all\nSum Sq Df F<\/span> value   Pr<\/span>(<\/span>><\/span>F<\/span>)<\/span>\nA.all     969.50<\/span>  2<\/span>  13.517<\/span> 0.001945<\/span> **<\/span>\nResiduals 322.75<\/span>  9<\/span>\n---<\/span>\nSignif. codes:<\/span>  0<\/span> \u2018***<\/span>\u2019 0.001<\/span> \u2018**<\/span>\u2019 0.01<\/span> \u2018*<\/span>\u2019 0.05<\/span> \u2018.\u2019 0.1<\/span> \u2018 \u2019 1<\/span>\n<\/code><\/pre>\n\n\n\n
\u8aa4\u5dee\u5e73\u5747\u5e73\u65b9\u306e\u5e73\u65b9\u6839 sqrt(Sum Sq of Residuals \/ Df) \u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u7d04\uff16\u306b\u306a\u308b\u3002<\/p>\n\n\n\n
><\/span> sqrt<\/span>(<\/span>322.75<\/span>\/<\/span>9<\/span>)<\/span>\n[<\/span>1<\/span>]<\/span> 5.988415<\/span>\n<\/code><\/pre>\n\n\n\n
\u7fa4\u306e\u6570\u304c\uff13\u3001\u6700\u5927\u306e\u7fa4\u9593\u5dee\u304c22\u3001\u8aa4\u5dee\u5206\u6563\u306e\u5e73\u65b9\u6839\u306f\uff16\u3068\u3057\u3066\u3001\u6bcd\u5206\u6563\u65e2\u77e5\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u4e00\u7fa4\uff12\u3068\u306a\u308b\u3002<\/p>\n\n\n\n
><\/span> anova.sample.size<\/span>(<\/span>k=<\/span>3<\/span>,<\/span> d=<\/span>22<\/span>,<\/span> sigma0=<\/span>6<\/span>)<\/span>\nANOVA Sample Size Calculation\nn =<\/span> 1.476973<\/span>\ndelta =<\/span> 22<\/span>\nsd =<\/span> 6<\/span>\nsig.level =<\/span> 0.05<\/span>\npower =<\/span> 0.8<\/span>\n<\/code><\/pre>\n\n\n\n
\u6bcd\u5206\u6563\u672a\u77e5\u3068\u3059\u308b\u3068\u3001\u4e00\u7fa4\uff12\u306e\u5834\u5408\u306f\u691c\u51fa\u529b\u304c50%\u3092\u4e0b\u56de\u308b\u3002<\/p>\n\n\n\n
\u4e00\u7fa4\uff13\u3068\u3059\u308b\u3068\u691c\u51fa\u529b80%\u3092\u4e0a\u56de\u308b\u3002<\/p>\n\n\n\n
\u5b9f\u969b\u306e\u30c7\u30fc\u30bf\u3068\u540c\u3058\u4e00\u7fa4\uff14\u3068\u3059\u308b\u3068\u691c\u51fa\u529b90%\u3092\u4e0a\u56de\u308b\u3068\u3044\u3046\u7d50\u679c\u306b\u306a\u3063\u305f\u3002<\/p>\n\n\n\n
><\/span> anova.power.michi(<\/span>k=3,<\/span> n=2,<\/span> d=22,<\/span> sigma0=6)<\/span>\nANOVA Power Calculation Variance unknown\nn =<\/span> 2<\/span>\ndelta =<\/span> 22<\/span>\nsd =<\/span> 6<\/span>\nsig.level =<\/span> 0.05<\/span>\npower =<\/span> 0.4644863<\/span>\n\n><\/span> anova.power.michi(<\/span>k=3,<\/span> n=3,<\/span> d=22,<\/span> sigma0=6)<\/span>\nANOVA Power Calculation Variance unknown\nn =<\/span> 3<\/span>\ndelta =<\/span> 22<\/span>\nsd =<\/span> 6<\/span>\nsig.level =<\/span> 0.05<\/span>\npower =<\/span> 0.8729045<\/span>\n\n><\/span> anova.power.michi(<\/span>k=3,<\/span> n=4,<\/span> d=22,<\/span> sigma0=6)<\/span>\nANOVA Power Calculation Variance unknown\nn =<\/span> 4<\/span>\ndelta =<\/span> 22<\/span>\nsd =<\/span> 6<\/span>\nsig.level =<\/span> 0.05<\/span>\npower =<\/span> 0.9794157<\/span>\n<\/code><\/pre>\n\n\n\n
\u3064\u307e\u308a\u3001\u4eca\u56de\u3068\u540c\u3058\u50be\u5411\u306e\u30c7\u30fc\u30bf\u306e\u5834\u5408\u3001\u4e00\u7fa4\uff13\u3067\u7d71\u8a08\u5b66\u7684\u6709\u610f\u3092\u691c\u51fa\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002<\/p>\n\n\n\n
\u5b9f\u969b\u306e\u30c7\u30fc\u30bf\u306f\u4e00\u7fa4\uff14\u4f8b\u3060\u3063\u305f\u306e\u3067\u3001\u554f\u984c\u306a\u3057\u3068\u8a00\u3048\u308b\u3002<\/p>\n\n\n\n
\u4e8b\u5b9fp\u5024\u306f0.001945\u3067\u3001\u6709\u610f\u6c34\u6e965%\u3068\u3059\u308c\u3070\u7d71\u8a08\u5b66\u7684\u6709\u610f\u3067\u3042\u3063\u305f\u3002<\/p>\n\n\n\n
\u4ee5\u4e0b\u518d\u63b2\u3002<\/p>\n\n\n\n
><\/span> Anova<\/span>(<\/span>lm1)<\/span>\nAnova Table <\/span>(<\/span>Type II tests)<\/span>\nResponse:<\/span> X.all\nSum Sq Df F<\/span> value   Pr<\/span>(<\/span>><\/span>F<\/span>)<\/span>\nA.all     969.50<\/span>  2<\/span>  13.517<\/span> 0.001945<\/span> **<\/span>\nResiduals 322.75<\/span>  9<\/span>\n---<\/span>\nSignif. codes:<\/span>  0<\/span> \u2018***<\/span>\u2019 0.001<\/span> \u2018**<\/span>\u2019 0.01<\/span> \u2018*<\/span>\u2019 0.05<\/span> \u2018.\u2019 0.1<\/span> \u2018 \u2019 1<\/span>\n<\/code><\/pre>\n\n\n\n
\u5206\u6563\u5206\u6790\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97\u30a8\u30af\u30bb\u30eb\u30d5\u30a1\u30a4\u30eb<\/h2>\n\n\n\n
\u30a8\u30af\u30bb\u30eb\u3067\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
\u5206\u6563\u5206\u6790 ANOVA \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
\u5206\u6563\u5206\u6790\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97\u30a8\u30af\u30bb\u30eb\u30d5\u30a1\u30a4\u30eb\u4f7f\u3044\u65b9\u89e3\u8aac\u52d5\u753b<\/h2>\n\n\n\n