{"id":535,"date":"2018-07-22T13:26:45","date_gmt":"2018-07-22T04:26:45","guid":{"rendered":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/how-to-determine-sample-size-in-proportion-test\/"},"modified":"2024-10-28T22:48:40","modified_gmt":"2024-10-28T13:48:40","slug":"how-to-determine-sample-size-in-proportion-test","status":"publish","type":"post","link":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/how-to-determine-sample-size-in-proportion-test\/","title":{"rendered":"R \u3067\u5272\u5408\u306e\u63a8\u5b9a\u30fb\u691c\u5b9a\u306b\u5fc5\u8981\u306a\u30b5\u30f3\u30d7\u30eb\u6570\u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5"},"content":{"rendered":"\n

\u5272\u5408\u306b\u95a2\u3059\u308b\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97\u306e\u65b9\u6cd5<\/p>\n\n\n\n

\u63a8\u5b9a\u7cbe\u5ea6\u3068\u691c\u5b9a\u306e 2 \u7a2e\u985e\u3042\u308a<\/p>\n\n\n\n\n\n\n\n

\u63a8\u5b9a\u7cbe\u5ea6\u306b\u57fa\u3065\u304f\u65b9\u6cd5<\/h2>\n\n\n\n

\u76f8\u5bfe\u7cbe\u5ea6delta\u3067\uff0c\u5272\u5408\u3092\u63a8\u5b9a\u3059\u308b\u969b\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97\u306f\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306a R \u30b9\u30af\u30ea\u30d7\u30c8\u3067\u8a08\u7b97\u3067\u304d\u308b\u3002<\/p>\n\n\n\n

myPsize <- function(p,delta){\n  n <- 4*(1-p)\/(p*delta^2)\n  c(\"N at least\"=n)\n}\n<\/code><\/pre>\n\n\n\n
\u305f\u3068\u3048\u30708%\u306e\u5272\u5408\u3092\u76f8\u5bfe\u7cbe\u5ea620%\uff0895%\u4fe1\u983c\u533a\u9593\u304c\u00b11.6%\u3068\u3044\u3046\u610f\u5473\uff09\u3067\u63a8\u5b9a\u3059\u308b\u306a\u3089\u3001\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u306f1150\u306b\u306a\u308b\u3002<\/p>\n\n\n\n
> myPsize(0.08,0.2)\nN at least \n      1150 <\/code><\/pre>\n\n\n\n
\u78ba\u8a8d\u306e\u305f\u3081\u4e8c\u9805\u5206\u5e03\u306795%\u4fe1\u983c\u533a\u9593\u3092\u6c42\u3081\u3066\u307f\u308b\u3068\u3001\u304a\u304a\u3088\u305d\u00b11.6%\uff086.5%~9.7%\uff09\u306b\u53ce\u307e\u3063\u3066\u3044\u308b\u3053\u3068\u304c\u308f\u304b\u308b\u3002<\/p>\n\n\n\n
> binom.test(1150*0.08, 1150)\n\n\tExact binomial test\n\ndata:  1150 * 0.08 and 1150\nnumber of successes = 92, number of trials = 1150, p-value < 2.2e-16\nalternative hypothesis: true probability of success is not equal to 0.5\n95 percent confidence interval:\n 0.06497587 0.09721197\nsample estimates:\nprobability of success \n                  0.08 <\/code><\/pre>\n\n\n\n
\u305f\u3068\u3048\u3070\u3001\u300c\u306f\u3044\u300d\u306e\u56de\u7b54\u304c80%\u3067\u3042\u308b\u3053\u3068\u3092\u3001\u63a8\u5b9a\u7cbe\u5ea610%\uff08\u00b18%\uff09\u3067\u63a8\u5b9a\u3057\u305f\u3044\u3068\u3059\u308c\u3070\u3001\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u306f100\u4eba\u3068\u8a08\u7b97\u3055\u308c\u308b\u3002<\/p>\n\n\n\n
95%\u4fe1\u983c\u533a\u9593\u306f71%\u304b\u308987%\u3068\u63a8\u5b9a\u3055\u308c\u3001\u00b18%\u306b\u306f\u3060\u3044\u3060\u3044\u53ce\u307e\u3063\u3066\u3044\u308b\u3002<\/p>\n\n\n\n
> myPsize(0.8, 0.1)\nN at least \n       100 \n\n> binom.test(80,100)\n\n\tExact binomial test\n\ndata:  80 and 100\nnumber of successes = 80, number of trials = 100, p-value = 1.116e-09\nalternative hypothesis: true probability of success is not equal to 0.5\n95 percent confidence interval:\n 0.7081573 0.8733444\nsample estimates:\nprobability of success \n                   0.8 <\/code><\/pre>\n\n\n\n
\u63a8\u5b9a\u7cbe\u5ea6\u306b\u57fa\u3065\u304f\u65b9\u6cd5\u3092\u30a8\u30af\u30bb\u30eb\u3067<\/h2>\n\n\n\n
\u6bcd\u6bd4\u7387\u3092\u6c42\u3081\u308b\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97\u3092\u63a8\u5b9a\u7cbe\u5ea6\u306b\u57fa\u3065\u3044\u3066\u884c\u3046\u65b9\u6cd5\u3092\u30a8\u30af\u30bb\u30eb\u3067\u5b9f\u884c\u3067\u304d\u308b\u3002<\/p>\n\n\n\n
\u3088\u3051\u308c\u3070\u3069\u3046\u305e\u3002<\/p>\n\n\n\n
\u30a2\u30f3\u30b1\u30fc\u30c8\u306f\u4f55\u4eba\u306b\u53d6\u308c\u3070\u3044\u3044\uff1f\u2015\u5272\u5408\u306e\u4fe1\u983c\u533a\u9593\u2015\u3010\u30a8\u30af\u30bb\u30eb\u3067\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u3011 | TKER SHOP<\/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>
\u691c\u5b9a\u306b\u57fa\u3065\u304f\u65b9\u6cd5<\/h2>\n\n\n\n
\u6bcd\u96c6\u56e3\u306e\u5272\u5408\u304c\u308f\u304b\u3063\u3066\u3044\u3066\u3001\u305d\u306e\u5272\u5408\u3068\u7d71\u8a08\u5b66\u7684\u6709\u610f\u306b\u7570\u306a\u308b\u5272\u5408\u3067\u3042\u308b\u3053\u3068\u3092\u691c\u51fa\u3059\u308b\u305f\u3081\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u8a08\u7b97\u3002<\/p>\n\n\n\n
\u5fc5\u8981\u306a\u306e\u306f\u6bcd\u96c6\u56e3\u306e\u5272\u5408\u3068\u30b5\u30f3\u30d7\u30eb\u3067\u306e\u5272\u5408\u3068\u691c\u51fa\u529b\u3002<\/p>\n\n\n\n
R \u306e\u30b9\u30af\u30ea\u30d7\u30c8\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3002<\/p>\n\n\n\n
samplesize.pop.prop.test <-\n  function (P0, P, power, alpha=.05){\n    A <- sqrt((P0*(1-P0))\/(P*(1-P)))\n    n <- ((qnorm(power)+qnorm(alpha\/2,lower.tail=F)*A)*\n            sqrt(P*(1-P))\/(P-P0))^2\n    METHOD <-\n      \"Sample size calculation of the one-sample proportion test.\"\n    structure(list(n=n, p=P, p0=P0, sig.level=alpha, power=power,\n                   alternative=\"Two sided\", method=METHOD), class=\"power.htest\")\n  }\n<\/code><\/pre>\n\n\n\n
\u4f8b\u3048\u3070\u3001\u4f55\u3082\u52b9\u679c\u304c\u306a\u3051\u308c\u3070\u4e94\u5206\u4e94\u5206\u306e50%\u3060\u304c\u3001\u52b9\u679c\u304c\u3042\u3063\u3066\u300c\u306f\u3044\u300d\u3068\u56de\u7b54\u3059\u308b\u4eba\u304c80%\u306b\u306a\u308b\u3068\u4e88\u60f3\u3059\u308b\u3002<\/p>\n\n\n\n
80%\u306e\u7d50\u679c\u304c\u300150%\u3068\u306f\u7d71\u8a08\u5b66\u7684\u6709\u610f\u306b\u7570\u306a\u308b\u3068\u7d50\u8ad6\u4ed8\u3051\u308b\u305f\u3081\u306b\u306f\u3001\u3069\u306e\u304f\u3089\u3044\u306e\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u304c\u5fc5\u8981\u304b\uff1f<\/p>\n\n\n\n
> samplesize.pop.prop.test(P0=0.5, P=0.8, power=0.8)\n\n     Sample size calculation of the one-sample proportion test. \n\n              n = 19.26129\n              p = 0.8\n             p0 = 0.5\n      sig.level = 0.05\n          power = 0.8\n    alternative = Two sided<\/code><\/pre>\n\n\n\n
\u7b54\u3048\u306f\u300120\u4eba\u5fc5\u8981\u3068\u8a08\u7b97\u3055\u308c\u308b\u3002<\/p>\n\n\n\n
\u975e\u5e38\u306b\u5c0f\u3055\u3044\u8abf\u67fb\u3067\u3088\u3044\u3053\u3068\u304c\u308f\u304b\u308b\u3002<\/p>\n\n\n\n
95%\u4fe1\u983c\u533a\u9593\u3092\u6c42\u3081\u3066\u307f\u308b\u3068\u300156%\u304b\u308994%\u3067\u300150%\u3068\u306f\u7d71\u8a08\u5b66\u7684\u6709\u610f\u306b\u7570\u306a\u308b\u3053\u3068\u304c\u78ba\u8a8d\u3067\u304d\u305f\u3002<\/p>\n\n\n\n
> binom.test(16,20)\n\n\tExact binomial test\n\ndata:  16 and 20\nnumber of successes = 16, number of trials = 20, p-value = 0.01182\nalternative hypothesis: true probability of success is not equal to 0.5\n95 percent confidence interval:\n 0.563386 0.942666\nsample estimates:\nprobability of success \n                   0.8 <\/code><\/pre>\n\n\n\n
\u307e\u305f\u3001\u4f8b\u3048\u3070\u3001\u6bcd\u96c6\u56e3\u3067\u306f\u767a\u751f\u304c10%=0.1\u3068\u308f\u304b\u3063\u3066\u3044\u308b\u3053\u3068\u304c\u3042\u308b\u3002<\/p>\n\n\n\n
\u65b0\u3057\u3044\u4e88\u9632\u6cd5\u3067\u306f\u767a\u751f\u304c5%=0.05\u306b\u6291\u3048\u3089\u308c\u308b\u53ef\u80fd\u6027\u304c\u3042\u308b\u3002<\/p>\n\n\n\n
\u6bcd\u96c6\u56e3\u306e0.1\u3068\u6709\u610f\u306b\u7570\u306a\u308b\u3068\u3044\u3046\u7d50\u679c\u3092\u5c0e\u304f\u306b\u306f\u3001\u691c\u51fa\u529b80%\u3068\u3057\u305f\u3068\u304d\u306b\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u306f\u3044\u304f\u3064\u306b\u306a\u308b\u304b\uff1f<\/p>\n\n\n\n
> samplesize.pop.prop.test(P0=0.1, P=0.05, power=0.8)\n\n     Sample size calculation of the one-sample proportion test. \n\n              n = 238.0332\n              p = 0.05\n             p0 = 0.1\n      sig.level = 0.05\n          power = 0.8\n    alternative = Two sided<\/code><\/pre>\n\n\n\n
\u7d50\u679c\u306f\u3001239\u4f8b\u5fc5\u8981\u3068\u8a08\u7b97\u3055\u308c\u305f\u3002<\/p>\n\n\n\n
\u3064\u307e\u308a\u3001239\u4f8b\u3092\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u3057\u3066\u30015%\u3064\u307e\u308a\u7d0412\u4f8b\u3067\u75c5\u6c17\u304c\u767a\u751f\u3057\u305f\u3068\u3059\u308b\u3068\u3001\u6bcd\u96c6\u56e3\u306e10%\u3068\u306f\u7d71\u8a08\u5b66\u7684\u6709\u610f\u306b\u7570\u306a\u3063\u3066\u4f4e\u3044\u3068\u7d50\u8ad6\u3065\u3051\u3089\u308c\u308b\u3002<\/p>\n\n\n\n
\u4e8c\u9805\u5206\u5e03\u3067\u8a08\u7b97\u3057\u305f\u7d50\u679c\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3002<\/p>\n\n\n\n
p\u5024\u306f0.05\u3092\u4e0b\u56de\u3063\u3066\u3001\u6709\u610f\u6c34\u6e965%\u3067\u3001\u7d71\u8a08\u5b66\u7684\u6709\u610f\u3002<\/p>\n\n\n\n
> binom.test(12,239,p=0.1)\n\n\tExact binomial test\n\ndata:  12 and 239\nnumber of successes = 12, number of trials = 239, p-value = 0.009147\nalternative hypothesis: true probability of success is not equal to 0.1\n95 percent confidence interval:\n 0.02620962 0.08606230\nsample estimates:\nprobability of success \n            0.05020921 <\/code><\/pre>\n\n\n\n
\u691c\u51fa\u529b\u3092\u8a08\u7b97\u3059\u308b\u3053\u3068\u3082\u3067\u304d\u308b\u3002<\/p>\n\n\n\n
\u691c\u51fa\u529b\u3092\u8a08\u7b97\u3059\u308b\u30b9\u30af\u30ea\u30d7\u30c8\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3002<\/p>\n\n\n\n
power.pop.prop.test <-\n  function (P0, P, n, alpha=.05){\n    A <- sqrt((P0*(1-P0))\/(P*(1-P)))\n    B <- (P-P0)\/(sqrt((P*(1-P))\/n))\n    power <- pnorm(-1*qnorm(alpha\/2, lower.tail=FALSE)*A-B)+\n      pnorm(qnorm(alpha\/2, lower.tail=FALSE)*A-B, lower.tail=FALSE)\n    METHOD <- \"Power calculation of the one-sample proportion test.\"\n    structure(list(n=n, p=P, p0=P0, sig.level=alpha, power=power,\n                   alternative=\"Two sided\", method=METHOD), class=\"power.htest\")\n  }\n<\/code><\/pre>\n\n\n\n
\u6bcd\u6bd4\u7387\u304c0.1\u3001\u30b5\u30f3\u30d7\u30eb\u306e\u6bd4\u7387\u304c0.05\u3001\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u304c200\u3060\u3068\u3059\u308b\u3068\u3001\u691c\u51fa\u529b\u306f\u3069\u306e\u304f\u3089\u3044\u304b\uff1f<\/p>\n\n\n\n
> power.pop.prop.test(P0=0.1, P=0.05, n=200)\n\n     Power calculation of the one-sample proportion test. \n\n              n = 200\n              p = 0.05\n             p0 = 0.1\n      sig.level = 0.05\n          power = 0.7076557\n    alternative = Two sided<\/code><\/pre>\n\n\n\n
\u8a08\u7b97\u7d50\u679c\u306f71%\u3068\u8a08\u7b97\u3055\u308c\u308b\u3002<\/p>\n\n\n\n
\u691c\u51fa\u529b\u304c80%\u306b\u306a\u308b\u305f\u3081\u306b\u306f\u4e0a\u8a18\u306e\u3088\u3046\u306b\u3042\u306839\u4eba\u5fc5\u8981\u3068\u3044\u3046\u308f\u3051\u3060\u3002<\/p>\n\n\n\n
\u691c\u5b9a\u306b\u57fa\u3065\u304f\u65b9\u6cd5\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\u304c\u3067\u304d\u308b\u3002<\/p>\n\n\n\n
\u3088\u3051\u308c\u3070\u3069\u3046\u305e\u3002<\/p>\n\n\n\n
\u6bcd\u6bd4\u7387\u306e\u691c\u5b9a\uff08\u6bcd\u96c6\u56e3\u306e\u5272\u5408\u306e\u691c\u5b9a\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
\u4f7f\u3044\u65b9\u89e3\u8aac\u52d5\u753b\u3002<\/p>\n\n\n\n
\u3053\u3061\u3089\u3082\u3088\u3051\u308c\u3070\u3069\u3046\u305e\u3002<\/p>\n\n\n\n