{"id":553,"date":"2018-07-01T21:34:10","date_gmt":"2018-07-01T12:34:10","guid":{"rendered":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/what-is-binomial-distribution-when-used\/"},"modified":"2025-02-16T00:08:10","modified_gmt":"2025-02-15T15:08:10","slug":"what-is-binomial-distribution-when-used","status":"publish","type":"post","link":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/what-is-binomial-distribution-when-used\/","title":{"rendered":"R \u3067\u4e8c\u9805\u5206\u5e03\u306e\u30b0\u30e9\u30d5\u3092\u63cf\u304f\u65b9\u6cd5"},"content":{"rendered":"\n

R \u3067\u4e8c\u9805\u5206\u5e03\u306e\u30b0\u30e9\u30d5\u3092\u66f8\u3044\u3066\u307f\u305f<\/p>\n\n\n\n\n\n\n\n

\u4e8c\u9805\u5206\u5e03\u306e\u30b0\u30e9\u30d5\u306e\u524d\u306b \u4e8c\u9805\u3068\u306f\uff1f<\/h2>\n\n\n\n

\u4e8c\u9805\u3068\u306f\u30010\u304b1\u304b\u3001Yes\u304bNo\u304b\u3001\u8868\u304b\u88cf\u304b\u3001\u306a\u3069\u4e8c\u3064\u306b\u4e00\u3064\u304c\u9078\u3070\u308c\u308b\u3053\u3068\u3002<\/p>\n\n\n\n

\u4e8c\u9805\u5206\u5e03\u306f\u3001\u4e8c\u9805\u306e\u5834\u5408\u306e\u5206\u5e03\u3068\u3044\u3046\u610f\u5473\u3067\u3042\u308b\u3002<\/p>\n\n\n\n

\u4e8c\u9805\u5206\u5e03\u306e\u30b0\u30e9\u30d5\u3092\u66f8\u3044\u3066\u307f\u308b<\/h2>\n\n\n\n

\u305f\u3068\u3048\u3070\u300110\u4f8b\u3067\u3001\u78ba\u73875\u5272\u306e\u3053\u3068\u300110\u56de\u30b3\u30a4\u30f3\u3092\u6295\u3052\u3066\u3001\u8868\u88cf\u3069\u3061\u3089\u3082\u78ba\u73875\u5272\u300110\u56de\u6311\u6226\u3057\u3066\u307f\u3066\u3001\u6210\u529f\u78ba\u7387\u306f\u4e94\u5206\u4e94\u5206\u3002<\/p>\n\n\n\n

\u3053\u306e\u3068\u304d0\u56de\u304b\u308910\u56de\u307e\u3067\u306e\u3001\u8d77\u304d\u308b\u78ba\u7387\u3001\u8868\u306e\u78ba\u7387\u3001\u6210\u529f\u78ba\u7387\u3092\u30b0\u30e9\u30d5\u63cf\u753b\u3059\u308b\u30685\u56de\u304c\u6700\u3082\u78ba\u7387\u304c\u9ad8\u304f\u306a\u308b\u3002<\/p>\n\n\n\n

R \u3067\u306e\u4e8c\u9805\u5206\u5e03\u306e\u30b0\u30e9\u30d5\u3092\u66f8\u304f\u30b9\u30af\u30ea\u30d7\u30c8\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3002<\/p>\n\n\n\n

plot<\/span>(<\/span>x=<\/span>0<\/span>:<\/span>10<\/span>,<\/span> y=<\/span>dbinom<\/span>(<\/span>x=<\/span>0<\/span>:<\/span>10<\/span>,<\/span> size=<\/span>10<\/span>,<\/span> prob=<\/span>0.5<\/span>),<\/span> type=<\/span>\"h\"<\/span>)<\/span>\n<\/code><\/pre>\n\n\n\n
\u4e8c\u9805\u5206\u5e03\u306e\u30b0\u30e9\u30d5\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3002<\/p>\n\n\n\n
\"\"<\/figure>\n\n\n\n
<\/span>\u3053\u306e\u3068\u304d\u30010 \u304b\u3089 10 \u307e\u3067\u306e\u767a\u751f\u78ba\u7387 y \u306f\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u6570\u5024\u306b\u306a\u3063\u3066\u3044\u3066\u3001\u3053\u308c\u304c Y \u8ef8\u306e\u9ad8\u3055\u306b\u306a\u3063\u3066\u3044\u308b\u3002<\/p>\n\n\n\n
> x <- 0:10\n> y <- dbinom(x=0:10, size=10, prob=0.5)\n> cbind(x, y)\n       x            y\n [1,]  0 0.0009765625\n [2,]  1 0.0097656250\n [3,]  2 0.0439453125\n [4,]  3 0.1171875000\n [5,]  4 0.2050781250\n [6,]  5 0.2460937500\n [7,]  6 0.2050781250\n [8,]  7 0.1171875000\n [9,]  8 0.0439453125\n[10,]  9 0.0097656250\n[11,] 10 0.0009765625<\/code><\/pre>\n\n\n\n
\u4eba\u6570\u3084\u8a66\u884c\u306e\u6570\u30925\u300120\u300150\u306e3\u30d1\u30bf\u30fc\u30f3\u306b\u3059\u308b\u3002\u305d\u308c\u305e\u308c\u3001\u6210\u529f\u78ba\u7387\u30920.3\u30010.5\u30010.7\u3068\u3059\u308b\u3002<\/p>\n\n\n\n
\u5168\u90e8\u30679\u30d1\u30bf\u30fc\u30f3\u306e\u30b0\u30e9\u30d5\u3092\u63cf\u753b\u3059\u308b\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
layout<\/span>(<\/span>matrix<\/span>(<\/span>1<\/span>:<\/span>9<\/span>,<\/span>nr=<\/span>3<\/span>))<\/span>\nplot<\/span>(<\/span>0<\/span>:<\/span>5<\/span>,<\/span> dbinom<\/span>(<\/span>0<\/span>:<\/span>5<\/span>,<\/span> 5<\/span>,<\/span> 0.3<\/span>),<\/span> type=<\/span>\"h\"<\/span>,<\/span> ylim=<\/span>c<\/span>(<\/span>0<\/span>,<\/span>0.4<\/span>))<\/span>\nplot<\/span>(<\/span>0<\/span>:<\/span>5<\/span>,<\/span> dbinom<\/span>(<\/span>0<\/span>:<\/span>5<\/span>,<\/span> 5<\/span>,<\/span> 0.5<\/span>),<\/span> type=<\/span>\"h\"<\/span>,<\/span> ylim=<\/span>c<\/span>(<\/span>0<\/span>,<\/span>0.4<\/span>))<\/span>\nplot<\/span>(<\/span>0<\/span>:<\/span>5<\/span>,<\/span> dbinom<\/span>(<\/span>0<\/span>:<\/span>5<\/span>,<\/span> 5<\/span>,<\/span> 0.7<\/span>),<\/span> type=<\/span>\"h\"<\/span>,<\/span> ylim=<\/span>c<\/span>(<\/span>0<\/span>,<\/span>0.4<\/span>))<\/span>\nplot<\/span>(<\/span>0<\/span>:<\/span>20<\/span>,<\/span> dbinom<\/span>(<\/span>0<\/span>:<\/span>20<\/span>,<\/span> 20<\/span>,<\/span> 0.3<\/span>),<\/span> type=<\/span>\"h\"<\/span>,<\/span> ylim=<\/span>c<\/span>(<\/span>0<\/span>,<\/span>0.4<\/span>))<\/span>\nplot<\/span>(<\/span>0<\/span>:<\/span>20<\/span>,<\/span> dbinom<\/span>(<\/span>0<\/span>:<\/span>20<\/span>,<\/span> 20<\/span>,<\/span> 0.5<\/span>),<\/span> type=<\/span>\"h\"<\/span>,<\/span> ylim=<\/span>c<\/span>(<\/span>0<\/span>,<\/span>0.4<\/span>))<\/span>\nplot<\/span>(<\/span>0<\/span>:<\/span>20<\/span>,<\/span> dbinom<\/span>(<\/span>0<\/span>:<\/span>20<\/span>,<\/span> 20<\/span>,<\/span> 0.7<\/span>),<\/span> type=<\/span>\"h\"<\/span>,<\/span> ylim=<\/span>c<\/span>(<\/span>0<\/span>,<\/span>0.4<\/span>))<\/span>\nplot<\/span>(<\/span>0<\/span>:<\/span>50<\/span>,<\/span> dbinom<\/span>(<\/span>0<\/span>:<\/span>50<\/span>,<\/span> 50<\/span>,<\/span> 0.3<\/span>),<\/span> type=<\/span>\"h\"<\/span>,<\/span> ylim=<\/span>c<\/span>(<\/span>0<\/span>,<\/span>0.4<\/span>))<\/span>\nplot<\/span>(<\/span>0<\/span>:<\/span>50<\/span>,<\/span> dbinom<\/span>(<\/span>0<\/span>:<\/span>50<\/span>,<\/span> 50<\/span>,<\/span> 0.5<\/span>),<\/span> type=<\/span>\"h\"<\/span>,<\/span> ylim=<\/span>c<\/span>(<\/span>0<\/span>,<\/span>0.4<\/span>))<\/span>\nplot<\/span>(<\/span>0<\/span>:<\/span>50<\/span>,<\/span> dbinom<\/span>(<\/span>0<\/span>:<\/span>50<\/span>,<\/span> 50<\/span>,<\/span> 0.7<\/span>),<\/span> type=<\/span>\"h\"<\/span>,<\/span> ylim=<\/span>c<\/span>(<\/span>0<\/span>,<\/span>0.4<\/span>))<\/span>\n<\/code><\/pre>\n\n\n\n
\u30b0\u30e9\u30d5\u306f\u3053\u306e\u3088\u3046\u306b\u66f8\u3051\u308b\u3002<\/p>\n\n\n\n
\"\"<\/figure>\n\n\n\n
<\/span><\/p>\n\n\n\n
\u4eba\u6570\u3084\u8a66\u884c\u304c\u5927\u304d\u304f\u306a\u308b\u3068\u3001\u6b63\u898f\u5206\u5e03\u306b\u8fd1\u3065\u3044\u3066\u3044\u304f\u3002<\/p>\n\n\n\n
\u6b63\u898f\u5206\u5e03\u306b\u8fd1\u3065\u3044\u3066\u3044\u304f\u6027\u8cea\u3092\u4f7f\u3063\u3066\u3001\u6bcd\u6bd4\u7387\u306e\u63a8\u5b9a\u306f\u6b63\u898f\u8fd1\u4f3c\u3067\u884c\u308f\u308c\u3066\u3044\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>
\u4e8c\u9805\u5206\u5e03\u306f\u3069\u3046\u4f7f\u3046\u304b\uff1f<\/h2>\n\n\n\n
\u4e8c\u9805\u5206\u5e03\u306f\u6bcd\u6bd4\u7387\u306e\u533a\u9593\u63a8\u5b9a\u306b\u4f7f\u3048\u308b\u3002<\/p>\n\n\n\n
\u4eba\u6570\u3084\u8a66\u884c\u56de\u6570\u304c\u5927\u304d\u304f\u306a\u308b\u3068\u6b63\u898f\u5206\u5e03\u306b\u8fd1\u3065\u304f\u305f\u3081\u306b\u3001\u3053\u308c\u307e\u3067\u306f\u6b63\u898f\u8fd1\u4f3c\u304c\u7528\u3044\u3089\u308c\u3066\u3044\u305f\u3002<\/p>\n\n\n\n
\u3057\u304b\u3057\u3001\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u30fc\u3092\u4f7f\u3048\u308b\u3088\u3046\u306b\u306a\u3063\u3066\u3001\u8fd1\u4f3c\u3092\u4f7f\u3046\u610f\u5473\u5408\u3044\u306f\u306a\u304f\u306a\u3063\u305f\u3002<\/p>\n\n\n\n
R \u306a\u3089\u3001binom.test()\u3067\u7c21\u5358\u306b\u8a08\u7b97\u3067\u304d\u308b\u3002<\/p>\n\n\n\n
50\u4f8b\u4e2d\u300135\u4f8b\u304cYes\u3060\u3063\u305f\u3068\u3059\u308b\u3002<\/p>\n\n\n\n
\u3053\u306e\u3068\u304d\u306e95%\u4fe1\u983c\u533a\u9593\u306f\u30010.5539177\uff5e0.8213822\u3068\u8a08\u7b97\u3055\u308c\u308b\u3002<\/p>\n\n\n\n
> binom.test(35, 50)\n\n\tExact binomial test\n\ndata:  35 and 50\nnumber of successes = 35, number of trials = 50, p-value = 0.0066\nalternative hypothesis: true probability of success is not equal to 0.5\n95 percent confidence interval:\n 0.5539177 0.8213822\nsample estimates:\nprobability of success \n                   0.7 <\/code><\/pre>\n\n\n\n
\u3061\u306a\u307f\u306b\u6b63\u898f\u8fd1\u4f3c\u306795%\u4fe1\u983c\u533a\u9593\u3092\u6c42\u3081\u308b\u3068\u30010.5729775\uff5e0.8270225\u3068\u8a08\u7b97\u3055\u308c\u308b\u3002<\/p>\n\n\n\n
><\/span> 0.7<\/span>+<\/span>c<\/span>(<\/span>-<\/span>1<\/span>,<\/span> 1<\/span>)<\/span>*<\/span>1.96<\/span>*<\/span>sqrt<\/span>(<\/span>0.7<\/span>*<\/span>(<\/span>1<\/span>-<\/span>0.7<\/span>)<\/span>\/<\/span>50<\/span>)<\/span>\n[<\/span>1<\/span>]<\/span> 0.5729775<\/span> 0.8270225<\/span>\n<\/code><\/pre>\n\n\n\n
\u3057\u304b\u3057\u3001\u73fe\u4ee3\u3067\u306f\u3001\u3053\u306e\u8a08\u7b97\u65b9\u6cd5\u306f\u4f7f\u7528\u3057\u306a\u304f\u3066\u3082\u3088\u304f\u306a\u3063\u305f\u3002<\/p>\n\n\n\n
\u307e\u3068\u3081<\/h2>\n\n\n\n
\u4e8c\u9805\u5206\u5e03\u306f\u3001\u4e8c\u9805\u306e\u3046\u3061\u4e00\u65b9\u304c\u8d77\u304d\u308b\u56de\u6570\u306e\u78ba\u7387\u3092\u8868\u3057\u305f\u5206\u5e03\u3002<\/p>\n\n\n\n
\u8a66\u884c\u56de\u6570\u304c\u5927\u304d\u304f\u306a\u308b\u3068\u6b63\u898f\u5206\u5e03\u306b\u8fd1\u3065\u304f\u3002<\/p>\n\n\n\n
R \u306a\u3089\u3001\u4e8c\u9805\u5206\u5e03\u3092\u4f7f\u3063\u305f\u6bcd\u6bd4\u7387\u306e\u533a\u9593\u63a8\u5b9a\u304c binom.test() \u95a2\u6570\u3067\u8a08\u7b97\u3067\u304d\u308b\u3002<\/p>\n\n\n\n
\u53c2\u8003\u66f8\u7c4d<\/h2>\n\n\n\n
The R Tips \u7b2c3\u7248: \u30c7\u30fc\u30bf\u89e3\u6790\u74b0\u5883R\u306e\u57fa\u672c\u6280\u30fb\u30b0\u30e9\u30d5\u30a3\u30c3\u30af\u30b9\u6d3b\u7528\u96c6<\/a><\/p>\n\n\n\n
Statistical Methods in Medical Research<\/a><\/p>\n\n\n\n\n","protected":false},"excerpt":{"rendered":"
R \u3067\u4e8c\u9805\u5206\u5e03\u306e\u30b0\u30e9\u30d5\u3092\u66f8\u3044\u3066\u307f\u305f<\/p>\n","protected":false},"author":2,"featured_media":3041,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"swell_btn_cv_data":"","_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[5,37,134],"tags":[],"class_list":["post-553","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-r","category-37","category-134"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2018\/07\/20200921120047.png","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/posts\/553","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/comments?post=553"}],"version-history":[{"count":3,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/posts\/553\/revisions"}],"predecessor-version":[{"id":3504,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/posts\/553\/revisions\/3504"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/media\/3041"}],"wp:attachment":[{"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/media?parent=553"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/categories?post=553"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/tags?post=553"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}