{"id":407,"date":"2020-04-26T21:59:06","date_gmt":"2020-04-26T12:59:06","guid":{"rendered":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/prop-test-sample-size\/"},"modified":"2024-10-21T13:39:02","modified_gmt":"2024-10-21T04:39:02","slug":"prop-test-sample-size","status":"publish","type":"post","link":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/prop-test-sample-size\/","title":{"rendered":"R \u3067\u5272\u5408\u306e\u5dee\u306e\u691c\u5b9a\u306b\u5fc5\u8981\u306a\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5"},"content":{"rendered":"\n

\u5272\u5408\u306e\u5dee\u306e\u691c\u5b9a\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97\u3092 R \u3067\u884c\u3046\u65b9\u6cd5\u3001\u30a8\u30af\u30bb\u30eb\u3067\u884c\u3046\u65b9\u6cd5<\/p>\n\n\n\n\n\n\n\n

\u5272\u5408\u306e\u5dee\u306e\u691c\u5b9a\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97 R \u306e\u95a2\u6570\u3092\u4f7f\u3063\u3066<\/h2>\n\n\n\n

\u7d71\u8a08\u30bd\u30d5\u30c8R\u306b\u306f\u3001power.prop.test()\u3068\u3044\u3046\u95a2\u6570\u304c\u7528\u610f\u3055\u308c\u3066\u3044\u3066\u3001\u7c21\u5358\u306b\u8a08\u7b97\u3067\u304d\u308b\u3002<\/p>\n\n\n\n

\u7b2c1\u7fa4\u304c50%(0.5)\u3001\u7b2c2\u7fa4\u304c75%(0.75)\u3068\u60f3\u5b9a\u3055\u308c\u305f\u5834\u5408\u3001\u6709\u610f\u6c34\u6e96\u03b1\u30925%(0.05)\u3001\u691c\u51fa\u529b\u309280%(0.8)\u3001\u3068\u3059\u308b\u3068\u3001\u5fc5\u8981\u306a\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u306f\u3001\u4e00\u7fa458\u4f8b\u3068\u8a08\u7b97\u3055\u308c\u308b\u3002<\/p>\n\n\n\n

><\/span> power.prop.test<\/span>(<\/span>p1=<\/span>0.5<\/span>,<\/span> p2=<\/span>0.75<\/span>,<\/span> power=<\/span>0.8<\/span>)<\/span>\nTwo-<\/span>sample comparison of proportions power calculation\nn =<\/span> 57.67344<\/span>\np1 =<\/span> 0.5<\/span>\np2 =<\/span> 0.75<\/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
\u691c\u51fa\u529b\u309290%(0.9)\u306b\u4e0a\u3052\u308b\u3068\u5fc5\u8981\u306a\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u306f\u5927\u304d\u304f\u306a\u308a\u3001\u4e00\u7fa477\u4f8b\u3068\u306a\u308b\u3002<\/p>\n\n\n\n
><\/span> power.prop.test<\/span>(<\/span>p1=<\/span>0.5<\/span>,<\/span> p2=<\/span>0.75<\/span>,<\/span> power=<\/span>0.9<\/span>)<\/span>\nTwo-<\/span>sample comparison of proportions power calculation\nn =<\/span> 76.70693<\/span>\np1 =<\/span> 0.5<\/span>\np2 =<\/span> 0.75<\/span>\nsig.level =<\/span> 0.05<\/span>\npower =<\/span> 0.9<\/span>\nalternative =<\/span> two.sided\nNOTE:<\/span> n is number in<\/span> *<\/span>each*<\/span> group\n<\/code><\/pre>\n\n\n\n
\u5272\u5408\u306e\u5dee\u306e\u691c\u5b9a\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97\u3092 power.prop.test() \u3092\u4f7f\u308f\u305a\u306b<\/h2>\n\n\n\n
\u5272\u5408\u306e\u5dee\u306e\u691c\u5b9a\u306e\u305f\u3081\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97\u3092 power.prop.test() \u3092\u4f7f\u308f\u305a\u306b\u884c\u3063\u3066\u307f\u308b\u3002<\/p>\n\n\n\n
power.prop.test() \u306e\u30d7\u30ed\u30b0\u30e9\u30e0\u306e\u4e00\u90e8\u3092\u629c\u304d\u51fa\u3057\u3066\u3001\u72ec\u81ea\u306e\u95a2\u6570 prop.test.sample.size() \u3092\u4f5c\u308b\u3002<\/p>\n\n\n\n
prop.test.sample.size <-<\/span> function<\/span> (<\/span>p1,<\/span> p2,<\/span>\nsig.level=<\/span>0.05<\/span>,<\/span> power=<\/span>0.8<\/span>,<\/span>\nalternative=<\/span>c<\/span>(<\/span>\"two.sided\"<\/span>,<\/span>\"one.sided\"<\/span>))<\/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>\nZa <-<\/span> qnorm<\/span>(<\/span>sig.level\/<\/span>tside,<\/span> lower.tail=<\/span>FALSE<\/span>)<\/span>\nZb <-<\/span> qnorm<\/span>(<\/span>power)<\/span>\nd <-<\/span> abs<\/span>(<\/span>p1-<\/span>p2)<\/span>\nq1 <-<\/span> 1<\/span>-<\/span>p1\nq2 <-<\/span> 1<\/span>-<\/span>p2\npbar <-<\/span> (<\/span>p1+<\/span>p2)<\/span>\/<\/span>2<\/span>\nqbar <-<\/span> 1<\/span>-<\/span>pbar\nv1 <-<\/span> p1*<\/span>q1\nv2 <-<\/span> p2*<\/span>q2\nvbar <-<\/span> pbar*<\/span>qbar\nn <-<\/span> ((<\/span>Za*<\/span>sqrt<\/span>(<\/span>2<\/span>*<\/span>vbar)<\/span>+<\/span>Zb*<\/span>sqrt<\/span>(<\/span>v1+<\/span>v2))<\/span>\/<\/span>d)<\/span>^<\/span>2<\/span>\nNOTE<\/span> <-<\/span> \"n is number in *each* group\"<\/span>\nMETHOD <-<\/span> \"Two-sample comparison of proportions sample size\"<\/span>\nstructure<\/span>(<\/span>list<\/span>(<\/span>n=<\/span>n,<\/span> p1=<\/span>p1,<\/span> p2=<\/span>p2,<\/span>\nsig.level=<\/span>sig.level,<\/span> power=<\/span>power,<\/span>\nalternative=<\/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
\u7b2c1\u7fa40.5\u3001\u7b2c2\u7fa40.75\u3001\u6709\u610f\u6c34\u6e960.05\u3001\u691c\u51fa\u529b0.8\u3067\u306e\u5fc5\u8981\u4f8b\u6570\u306f\u3001\u3055\u304d\u307b\u3069\u3068\u540c\u3058\u304f\u4e00\u7fa458\u4f8b\u3068\u8a08\u7b97\u3055\u308c\u308b\u3002<\/p>\n\n\n\n
><\/span> prop.test.sample.size<\/span>(<\/span>p1=<\/span>0.5<\/span>,<\/span> p2=<\/span>0.75<\/span>)<\/span>\nTwo-<\/span>sample comparison of proportions sample size\nn =<\/span> 57.67344<\/span>\np1 =<\/span> 0.5<\/span>\np2 =<\/span> 0.75<\/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
\u691c\u51fa\u529b\u30920.9\u306b\u4e0a\u3052\u308b\u3068\u300177\u4f8b\u306b\u5fc5\u8981\u4f8b\u6570\u304c\u4e0a\u6607\u3059\u308b\u306e\u3082\u540c\u3058\u3060\u3002\u9069\u5207\u306b\u629c\u304d\u51fa\u305b\u3066\u3044\u308b\u3002<\/p>\n\n\n\n
><\/span> prop.test.sample.size<\/span>(<\/span>p1=<\/span>0.5<\/span>,<\/span> p2=<\/span>0.75<\/span>,<\/span> power=<\/span>0.9<\/span>)<\/span>\nTwo-<\/span>sample comparison of proportions sample size\nn =<\/span> 76.70693<\/span>\np1 =<\/span> 0.5<\/span>\np2 =<\/span> 0.75<\/span>\nsig.level =<\/span> 0.05<\/span>\npower =<\/span> 0.9<\/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>
\u5272\u5408\u306e\u5dee\u306e\u691c\u5b9a\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97 1:k \u306e\u5272\u308a\u4ed8\u3051\u6bd4\u306e\u5834\u5408<\/h2>\n\n\n\n
\u5272\u5408\u306e\u5dee\u306e\u691c\u5b9a\u3067\u3001\u540c\u6570\u306e\u4e8c\u7fa4\u3067\u306f\u306a\u304f\u3001\u5272\u308a\u4ed8\u3051\u6bd4\u4f8b\u3048\u3070 1:2 \u3068\u304b\u30011:3 \u3068\u304b\u3067\u4f8b\u6570\u306b\u5dee\u3092\u3064\u3051\u305f\u3044\u5834\u5408\u304c\u3042\u308b\u3002<\/p>\n\n\n\n
\u4e0a\u8a18\u95a2\u6570\u3092\u5c11\u3057\u6539\u9020\u3057\u3066\u3001\u305d\u306e\u3088\u3046\u306a\u5834\u5408\u306e\u95a2\u6570\u3092\u4f5c\u3063\u305f\u3002<\/p>\n\n\n\n
prop.test.sample.size.unequal <-<\/span> function<\/span> (<\/span>p1,<\/span> p2,<\/span>\nsig.level=<\/span>0.05<\/span>,<\/span> power=<\/span>0.8<\/span>,<\/span>\nalternative=<\/span>c<\/span>(<\/span>\"two.sided\"<\/span>,<\/span>\"one.sided\"<\/span>),<\/span>\nctrl.ratio=<\/span>1<\/span>)<\/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>\nZa <-<\/span> qnorm<\/span>(<\/span>sig.level\/<\/span>tside,<\/span> lower.tail=<\/span>FALSE<\/span>)<\/span>\nZb <-<\/span> qnorm<\/span>(<\/span>power)<\/span>\nk <-<\/span> ctrl.ratio\nd <-<\/span> abs<\/span>(<\/span>p1-<\/span>p2)<\/span>\nq1 <-<\/span> 1<\/span>-<\/span>p1\nq2 <-<\/span> 1<\/span>-<\/span>p2\npbar <-<\/span> (<\/span>p1+<\/span>p2)<\/span>\/<\/span>2<\/span>\nqbar <-<\/span> 1<\/span>-<\/span>pbar\nv1 <-<\/span> p1*<\/span>q1\nv2 <-<\/span> p2*<\/span>q2\nvbar <-<\/span> pbar*<\/span>qbar\nn <-<\/span> ((<\/span>Za*<\/span>sqrt<\/span>(<\/span>2<\/span>*<\/span>vbar)<\/span>+<\/span>Zb*<\/span>sqrt<\/span>(<\/span>v1+<\/span>v2))<\/span>\/<\/span>d)<\/span>^<\/span>2<\/span>\nnA <-<\/span> 1<\/span>\/<\/span>k*<\/span>((<\/span>Za*<\/span>sqrt<\/span>((<\/span>k+<\/span>1<\/span>)<\/span>*<\/span>vbar)<\/span>+<\/span>Zb*<\/span>sqrt<\/span>(<\/span>k*<\/span>v1+<\/span>v2))<\/span>\/<\/span>d)<\/span>^<\/span>2<\/span>\nnB <-<\/span> k*<\/span>nA\nNOTE<\/span> <-<\/span> \"n is number in *each* group\"<\/span>\nMETHOD <-<\/span> \"Two-sample comparison of proportions sample size\"<\/span>\nstructure<\/span>(<\/span>list<\/span>(<\/span>n.equal=<\/span>n,<\/span> n.unequal.1=<\/span>nA,<\/span>\nn.unequal.2=<\/span>nB,<\/span> control.ratio=<\/span>ctrl.ratio,<\/span>\np1=<\/span>p1,<\/span> p2=<\/span>p2,<\/span>\nsig.level=<\/span>sig.level,<\/span> power=<\/span>power,<\/span>\nalternative=<\/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
\u53c2\u8003\u6587\u66f8\uff1a\u6bd4\u7387\u306e\u5dee\u306e\u691c\u5b9a\u306e\u4f8b\u6570\u8a2d\u8a08<\/p>\n\n\n\n
\u5272\u308a\u4ed8\u3051\u6bd4 ctrl.ratio \u30921\u306b\u3059\u308b\u3068\uff08\u30c7\u30d5\u30a9\u30eb\u30c8\u306a\u306e\u3067\u6307\u5b9a\u4e0d\u8981\uff09\u3001\u6539\u9020\u524d\u306e\u7d50\u679c\u3068\u540c\u4e00\u306b\u306a\u308b\u3002<\/p>\n\n\n\n
><\/span> prop.test.sample.size.unequal<\/span>(<\/span>p1=<\/span>0.5<\/span>,<\/span> p2=<\/span>0.75<\/span>)<\/span>\nTwo-<\/span>sample comparison of proportions sample size\nn.equal =<\/span> 57.67344<\/span>\nn.unequal.1 =<\/span> 57.67344<\/span>\nn.unequal.2 =<\/span> 57.67344<\/span>\ncontrol.ratio =<\/span> 1<\/span>\np1 =<\/span> 0.5<\/span>\np2 =<\/span> 0.75<\/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
\u5272\u308a\u4ed8\u3051\u6bd4\u30922\u306b\u3059\u308b\u3068\u3001\u7fa42\u3068\u7fa41\u306e\u6bd4\u304c2\u306b\u306a\u308b\u3002<\/p>\n\n\n\n
\u7fa41\u306e\u4f8b\u6570\u306f\u5c11\u306a\u304f\u3066\u6e08\u3080\u3088\u3046\u306b\u306a\u308b\u304c\u3001\u5408\u8a08\u5fc5\u8981\u4f8b\u6570\u306f116\u4f8b\u304b\u3089132\u4f8b\u306b\u5897\u52a0\u3059\u308b\u3002<\/p>\n\n\n\n
><\/span> prop.test.sample.size.unequal<\/span>(<\/span>p1=<\/span>0.5<\/span>,<\/span> p2=<\/span>0.75<\/span>,<\/span> ctrl.ratio=<\/span>2<\/span>)<\/span>\nTwo-<\/span>sample comparison of proportions sample size\nn.equal =<\/span> 57.67344<\/span>\nn.unequal.1 =<\/span> 43.85406<\/span>\nn.unequal.2 =<\/span> 87.70811<\/span>\ncontrol.ratio =<\/span> 2<\/span>\np1 =<\/span> 0.5<\/span>\np2 =<\/span> 0.75<\/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
\u5272\u308a\u4ed8\u3051\u6bd4\u30923\u306b\u3059\u308b\u3068\u3001\u5408\u8a08\u5fc5\u8981\u4f8b\u6570\u306f\u3055\u3089\u306b\u5927\u304d\u304f\u306a\u308a158\u4f8b\u306b\u306a\u308b\u3002<\/p>\n\n\n\n
><\/span> prop.test.sample.size.unequal<\/span>(<\/span>p1=<\/span>0.5<\/span>,<\/span> p2=<\/span>0.75<\/span>,<\/span> ctrl.ratio=<\/span>3<\/span>)<\/span>\nTwo-<\/span>sample comparison of proportions sample size\nn.equal =<\/span> 57.67344<\/span>\nn.unequal.1 =<\/span> 39.2444<\/span>\nn.unequal.2 =<\/span> 117.7332<\/span>\ncontrol.ratio =<\/span> 3<\/span>\np1 =<\/span> 0.5<\/span>\np2 =<\/span> 0.75<\/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
\u5272\u5408\u306e\u5dee\u306e\u691c\u5b9a\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97 \u30a8\u30af\u30bb\u30eb\u30d5\u30a1\u30a4\u30eb\u306e\u4f7f\u3044\u65b9\u306e\u89e3\u8aac\u3010\u52d5\u753b\u3011<\/h3>\n\n\n\n
\u5272\u5408\u306e\u5dee\u306e\u691c\u5b9a\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\u30b7\u30fc\u30c8\u3067\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97\u304c\u3067\u304d\u308b\u3088\u3046\u306b\u3001\u30a8\u30af\u30bb\u30eb\u30d5\u30a1\u30a4\u30eb\u3092\u4f5c\u6210\u3057\u305f\u3002<\/p>\n\n\n\n
\u3088\u3051\u308c\u3070\u3069\u3046\u305e\u3002<\/p>\n\n\n\n
\u5272\u5408\u306e\u5dee\u306e\u691c\u5b9a\uff08\u5272\u308a\u4ed8\u3051\u6bd4\u306b\u3082\u5bfe\u5fdc\uff09\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
http:\/\/www012.upp.so-net.ne.jp\/doi\/sas\/simulation\/sample_size2\/sample_size_prop.pdf<\/a><\/p>\n\n\n\n