{"id":4197,"date":"2025-07-11T13:56:57","date_gmt":"2025-07-11T04:56:57","guid":{"rendered":"https:\/\/best-biostatistics.com\/toukei-er\/?p=4197"},"modified":"2025-07-11T13:56:59","modified_gmt":"2025-07-11T04:56:59","slug":"bootstrap-method-calculate-95-percent-confidence-interval-mean","status":"publish","type":"post","link":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/bootstrap-method-calculate-95-percent-confidence-interval-mean\/","title":{"rendered":"\u30d6\u30fc\u30c8\u30b9\u30c8\u30e9\u30c3\u30d7\u6cd5\u3067\u5e73\u5747\u5024\u306e95%\u4fe1\u983c\u533a\u9593\u3092\u6c42\u3081\u3088\u3046\uff01"},"content":{"rendered":"\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p>\u300c\u3053\u306e\u30c7\u30fc\u30bf\u3001\u672c\u5f53\u306b\u4fe1\u983c\u3067\u304d\u308b\u306e\u304b\uff1f\u300d\u305d\u3046\u601d\u3063\u305f\u3053\u3068\u306f\u306a\u3044\u3060\u308d\u3046\u304b\u3002\u9650\u3089\u308c\u305f\u30c7\u30fc\u30bf\u304b\u3089\u5168\u4f53\u50cf\u3092\u63a8\u6e2c\u3059\u308b\u969b\u3001\u7d71\u8a08\u7684\u306a\u300c\u4fe1\u983c\u533a\u9593\u300d\u306f\u975e\u5e38\u306b\u91cd\u8981\u306a\u6982\u5ff5\u3067\u3042\u308b\u3002\u3057\u304b\u3057\u3001\u4fe1\u983c\u533a\u9593\u3092\u7b97\u51fa\u3059\u308b\u306b\u306f\u3001\u30c7\u30fc\u30bf\u306e\u5206\u5e03\u306b\u7279\u5b9a\u306e\u4eee\u5b9a\u304c\u5fc5\u8981\u3068\u306a\u308b\u30b1\u30fc\u30b9\u304c\u5c11\u306a\u304f\u306a\u3044\u3002<\/p>\n\n\n\n<p>\u305d\u3053\u3067\u4eca\u56de\u306f\u3001\u305d\u3093\u306a\u4eee\u5b9a\u306b\u7e1b\u3089\u308c\u305a\u3001\u3082\u3063\u3068\u67d4\u8edf\u306b\u4fe1\u983c\u533a\u9593\u3092\u63a8\u5b9a\u3067\u304d\u308b\u300c\u30d6\u30fc\u30c8\u30b9\u30c8\u30e9\u30c3\u30d7\u6cd5\u300d\u3092\u7d39\u4ecb\u3059\u308b\u3002\u7279\u306b\u3001\u5e73\u5747\u5024\u306e95%\u4fe1\u983c\u533a\u9593\u3092\u6c42\u3081\u308b\u65b9\u6cd5\u306b\u7126\u70b9\u3092\u5f53\u3066\u3001\u5177\u4f53\u7684\u306a\u624b\u9806\u304b\u3089R\u3092\u4f7f\u3063\u305f\u8a08\u7b97\u4f8b\u3001\u305d\u3057\u3066\u7d50\u679c\u306e\u89e3\u91c8\u307e\u3067\u3092\u5206\u304b\u308a\u3084\u3059\u304f\u89e3\u8aac\u3059\u308b\u3002<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<!--more-->\n\n\n\n<h2 class=\"wp-block-heading\">\u6982\u8981<\/h2>\n\n\n\n<p>\u30d6\u30fc\u30c8\u30b9\u30c8\u30e9\u30c3\u30d7\u6cd5\u306f\u3001\u624b\u5143\u306b\u3042\u308b\u30c7\u30fc\u30bf\u304b\u3089\u7e70\u308a\u8fd4\u3057\u30ea\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\uff08\u5fa9\u5143\u62bd\u51fa\uff09\u3092\u884c\u3046\u3053\u3068\u3067\u3001\u5143\u306e\u30c7\u30fc\u30bf\u306e\u5206\u5e03\u306b\u95a2\u3059\u308b\u4eee\u5b9a\u3092\u7f6e\u304f\u3053\u3068\u306a\u304f\u3001\u63a8\u5b9a\u91cf\u306e\u6a19\u672c\u5206\u5e03\u3092\u8fd1\u4f3c\u3057\u3001\u4fe1\u983c\u533a\u9593\u3092\u63a8\u5b9a\u3059\u308b\u30ce\u30f3\u30d1\u30e9\u30e1\u30c8\u30ea\u30c3\u30af\u306a\u7d71\u8a08\u7684\u624b\u6cd5\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<p>\u5e73\u5747\u5024\u306e95%\u4fe1\u983c\u533a\u9593\u3092\u30d6\u30fc\u30c8\u30b9\u30c8\u30e9\u30c3\u30d7\u6cd5\u3067\u6c42\u3081\u308b\u57fa\u672c\u7684\u306a\u624b\u9806\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<ol start=\"1\" class=\"wp-block-list\">\n<li><strong>\u5143\u306e\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u304b\u3089\u5fa9\u5143\u62bd\u51fa\u3067\u65b0\u3057\u3044\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u3092\u751f\u6210\u3059\u308b<\/strong>\uff1a\u5143\u306e\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u3068\u540c\u3058\u30b5\u30a4\u30ba\u306e\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u3092\u3001\u91cd\u8907\u3092\u8a31\u3057\u3066\uff08\u5fa9\u5143\u62bd\u51fa\uff09\u751f\u6210\u3059\u308b\u3002<\/li>\n\n\n\n<li><strong>\u65b0\u3057\u3044\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u306e\u5e73\u5747\u5024\u3092\u8a08\u7b97\u3059\u308b<\/strong>\uff1a\u751f\u6210\u3055\u308c\u305f\u65b0\u3057\u3044\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u306e\u5e73\u5747\u5024\u3092\u8a08\u7b97\u3059\u308b\u3002<\/li>\n\n\n\n<li><strong>1\u30682\u3092B\u56de\uff08\u4f8b\uff1a1,000\u56de\u301c10,000\u56de\uff09\u7e70\u308a\u8fd4\u3059<\/strong>\uff1a\u3053\u308c\u306b\u3088\u308a\u3001B\u500b\u306e\u5e73\u5747\u5024\u304c\u5f97\u3089\u308c\u308b\u3002\u3053\u308c\u3089\u306f\u3001\u5143\u306e\u30c7\u30fc\u30bf\u304b\u3089\u5f97\u3089\u308c\u308b\u53ef\u80fd\u6027\u306e\u3042\u308b\u5e73\u5747\u5024\u306e\u5206\u5e03\uff08\u30d6\u30fc\u30c8\u30b9\u30c8\u30e9\u30c3\u30d7\u6a19\u672c\u5206\u5e03\uff09\u3092\u8fd1\u4f3c\u3059\u308b\u3002<\/li>\n\n\n\n<li><strong>\u5f97\u3089\u308c\u305f\u5e73\u5747\u5024\u306e\u5206\u5e03\u304b\u308995%\u4fe1\u983c\u533a\u9593\u3092\u7b97\u51fa\u3059\u308b<\/strong>\uff1a\u5f97\u3089\u308c\u305fB\u500b\u306e\u5e73\u5747\u5024\u3092\u5c0f\u3055\u3044\u9806\u306b\u4e26\u3079\u3001\u4e0b\u4f4d2.5%\u3068\u4e0a\u4f4d2.5%\u306e\u5024\u3092\u305d\u308c\u305e\u308c95%\u4fe1\u983c\u533a\u9593\u306e\u4e0b\u9650\u3068\u4e0a\u9650\u3068\u3059\u308b\u3002<\/li>\n<\/ol>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\u5177\u4f53\u4f8b\u3068 R \u8a08\u7b97\u4f8b\u30fb\u30b0\u30e9\u30d5\u63cf\u753b<\/h2>\n\n\n\n<p>\u3053\u3053\u3067\u306f\u3001\u67b6\u7a7a\u306e\u30c6\u30b9\u30c8\u306e\u70b9\u6570\u30c7\u30fc\u30bf\u3092\u7528\u3044\u3066\u3001\u30d6\u30fc\u30c8\u30b9\u30c8\u30e9\u30c3\u30d7\u6cd5\u306b\u3088\u308b\u5e73\u5747\u5024\u306e95%\u4fe1\u983c\u533a\u9593\u306e\u7b97\u51fa\u3092R\u3067\u5b9f\u8df5\u3057\u3066\u307f\u3088\u3046\u3002<\/p>\n\n\n\n<p>\u30c7\u30fc\u30bf\u4f8b\uff1a \u3042\u308b\u30af\u30e9\u30b9\u306e\u751f\u5f9210\u4eba\u306e\u30c6\u30b9\u30c8\u306e\u70b9\u6570<\/p>\n\n\n\n<p>scores &lt;- c(65, 70, 72, 68, 75, 60, 80, 78, 63, 70)<\/p>\n\n\n\n<p><strong>R\u3067\u306e\u8a08\u7b97\u4f8b\uff1a<\/strong><\/p>\n\n\n\n<pre class=\"wp-block-code\"><code># \u5fc5\u8981\u306a\u30d1\u30c3\u30b1\u30fc\u30b8\u306e\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb (\u307e\u3060\u306e\u5834\u5408)\n# install.packages(\"boot\")\n# install.packages(\"ggplot2\")\n\n# \u30e9\u30a4\u30d6\u30e9\u30ea\u306e\u8aad\u307f\u8fbc\u307f\nlibrary(boot)\nlibrary(ggplot2)\n\n# \u5143\u306e\u30c7\u30fc\u30bf\nscores &lt;- c(65, 70, 72, 68, 75, 60, 80, 78, 63, 70)\n\n# \u30c7\u30fc\u30bf\u306e\u5e73\u5747\u5024\u3092\u8a08\u7b97\u3059\u308b\u95a2\u6570\nmean_function &lt;- function(data, indices) {\n  return(mean(data&#91;indices]))\n}\n\n# \u30d6\u30fc\u30c8\u30b9\u30c8\u30e9\u30c3\u30d7\u306e\u5b9f\u884c\n# R=10000\u306f\u7e70\u308a\u8fd4\u3057\u56de\u6570\uff08B\u56de\uff09\nset.seed(123) # \u518d\u73fe\u6027\u306e\u305f\u3081\u306e\u30b7\u30fc\u30c9\u8a2d\u5b9a\nboot_results &lt;- boot(data = scores, statistic = mean_function, R = 10000)\n\n# \u30d6\u30fc\u30c8\u30b9\u30c8\u30e9\u30c3\u30d7\u7d50\u679c\u306e\u8868\u793a\nprint(boot_results)\n\n# 95%\u4fe1\u983c\u533a\u9593\u306e\u8a08\u7b97 (\u30d1\u30fc\u30bb\u30f3\u30bf\u30a4\u30eb\u6cd5)\n# type = \"perc\" \u306f\u30d1\u30fc\u30bb\u30f3\u30bf\u30a4\u30eb\u6cd5\u3092\u6307\u5b9a\nboot_ci &lt;- boot.ci(boot_results, type = \"perc\")\nprint(boot_ci)\n\n# \u30d6\u30fc\u30c8\u30b9\u30c8\u30e9\u30c3\u30d7\u6a19\u672c\u5206\u5e03\u306e\u30d2\u30b9\u30c8\u30b0\u30e9\u30e0\u3068\u4fe1\u983c\u533a\u9593\u306e\u53ef\u8996\u5316\nboot_means &lt;- data.frame(mean = boot_results$t)\n\nggplot(boot_means, aes(x = mean)) +\n  geom_histogram(binwidth = 0.5, fill = \"skyblue\", color = \"black\") +\n  geom_vline(xintercept = boot_ci$percent&#91;4], color = \"red\", linetype = \"dashed\", linewidth = 1) + # \u4e0b\u9650\n  geom_vline(xintercept = boot_ci$percent&#91;5], color = \"red\", linetype = \"dashed\", linewidth = 1) + # \u4e0a\u9650\n  labs(title = \"\u30d6\u30fc\u30c8\u30b9\u30c8\u30e9\u30c3\u30d7\u306b\u3088\u308b\u5e73\u5747\u5024\u306e\u6a19\u672c\u5206\u5e03\u306895%\u4fe1\u983c\u533a\u9593\",\n       x = \"\u5e73\u5747\u5024\",\n       y = \"\u5ea6\u6570\") +\n  theme_minimal()\nggsave(\"Bootstrap_graph_example.png\", width = 8, height = 6)\n<\/code><\/pre>\n\n\n\n<p><strong>\u5b9f\u884c\u7d50\u679c\uff1a<\/strong><\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>> print(boot_ci)\nBOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS\nBased on 10000 bootstrap replicates\n\nCALL : \nboot.ci(boot.out = boot_results, type = \"perc\")\n\nIntervals : \nLevel     Percentile     \n95%   (66.4, 73.9 )  \nCalculations and Intervals on Original Scale\n> <\/code><\/pre>\n\n\n\n<p><strong>\u30b0\u30e9\u30d5\u63cf\u753b\uff1a<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" width=\"1024\" height=\"768\" src=\"https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2025\/07\/Bootstrap_graph_example-1024x768.png\" alt=\"\" class=\"wp-image-4198\" srcset=\"https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2025\/07\/Bootstrap_graph_example-1024x768.png 1024w, https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2025\/07\/Bootstrap_graph_example-300x225.png 300w, https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2025\/07\/Bootstrap_graph_example-768x576.png 768w, https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2025\/07\/Bootstrap_graph_example-1536x1152.png 1536w, https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2025\/07\/Bootstrap_graph_example-2048x1536.png 2048w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p>\u4e0a\u8a18\u306eR\u30b3\u30fc\u30c9\u3092\u5b9f\u884c\u3059\u308b\u3068\u3001\u30d6\u30fc\u30c8\u30b9\u30c8\u30e9\u30c3\u30d7\u306b\u3088\u3063\u3066\u5f97\u3089\u308c\u305f\u5e73\u5747\u5024\u306e\u5206\u5e03\u3092\u793a\u3059\u30d2\u30b9\u30c8\u30b0\u30e9\u30e0\u3068\u3001\u305d\u306e\u4e2d\u306b\u7b97\u51fa\u3055\u308c\u305f95%\u4fe1\u983c\u533a\u9593\u306e\u4e0b\u9650\u3068\u4e0a\u9650\u3092\u793a\u3059\u5782\u76f4\u7dda\u304c\u63cf\u753b\u3055\u308c\u308b\u3002\u3053\u306e\u30b0\u30e9\u30d5\u306f\u3001\u5e73\u5747\u5024\u304c\u3069\u306e\u7bc4\u56f2\u306b\u53ce\u307e\u308b\u53ef\u80fd\u6027\u304c\u9ad8\u3044\u304b\u3092\u8996\u899a\u7684\u306b\u7406\u89e3\u3059\u308b\u306e\u306b\u5f79\u7acb\u3064\u3002<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\u7d50\u679c\u89e3\u91c8<\/h3>\n\n\n\n<p>\u4e0a\u8a18\u306eR\u306e\u8a08\u7b97\u4f8b\u3067\u5f97\u3089\u308c\u308b<code>boot_ci<\/code>\u306e\u7d50\u679c\u51fa\u529b\u304b\u3089\u3001\u30d6\u30fc\u30c8\u30b9\u30c8\u30e9\u30c3\u30d7\u6cd5\u306b\u3088\u3063\u3066\u63a8\u5b9a\u3055\u308c\u305f\u5e73\u5747\u5024\u306e95%\u4fe1\u983c\u533a\u9593\u306f\u3001<code>(66.4, 73.9)<\/code>\u3067\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u308b\u3002<\/p>\n\n\n\n<p>\u3053\u308c\u306f\u3001\u300c\u3082\u3057\u3053\u306e\u751f\u5f92\u305f\u3061\u3068\u540c\u3058\u3088\u3046\u306a\u7279\u6027\u3092\u6301\u3064\u7121\u9650\u306e\u6bcd\u96c6\u56e3\u304b\u3089\u30c7\u30fc\u30bf\u3092\u7e70\u308a\u8fd4\u3057\u62bd\u51fa\u3057\u305f\u5834\u5408\u3001\u305d\u306e\u5e73\u5747\u5024\u306e95%\u306f66.4\u70b9\u304b\u308973.9\u70b9\u306e\u9593\u306b\u53ce\u307e\u308b\u3060\u308d\u3046\u300d\u3068\u3044\u3046\u3053\u3068\u3092\u610f\u5473\u3059\u308b\u3002\u8a00\u3044\u63db\u3048\u308c\u3070\u3001\u6211\u3005\u306f95%\u306e\u78ba\u4fe1\u3092\u3082\u3063\u3066\u3001\u771f\u306e\u5e73\u5747\u5024\u304c\u3053\u306e\u533a\u9593\u5185\u306b\u3042\u308b\u3068\u8003\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002<\/p>\n\n\n\n<p>\u30d6\u30fc\u30c8\u30b9\u30c8\u30e9\u30c3\u30d7\u6cd5\u306f\u3001\u7279\u5b9a\u306e\u5206\u5e03\u3092\u4eee\u5b9a\u3057\u306a\u3044\u305f\u3081\u3001\u30c7\u30fc\u30bf\u304c\u6b63\u898f\u5206\u5e03\u306b\u5f93\u308f\u306a\u3044\u5834\u5408\u3084\u3001\u6a19\u672c\u30b5\u30a4\u30ba\u304c\u5c0f\u3055\u3044\u5834\u5408\u3067\u3082\u9069\u7528\u3067\u304d\u308b\u3068\u3044\u3046\u5927\u304d\u306a\u30e1\u30ea\u30c3\u30c8\u304c\u3042\u308b\u3002<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<div id=\"biost-559211992\" class=\"biost- biost-entity-placement\"><p style=\"text-align: center;\"><span style=\"font-size: 20px;\"><strong><a href=\"https:\/\/best-biostatistics.com\/kmhl\">\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 href=\"https:\/\/best-biostatistics.com\/kmhl\"><img class=\"aligncenter wp-image-2794 size-full\" src=\"https:\/\/best-biostatistics.com\/wp\/wp-content\/uploads\/2023\/11\/bn_r_03.png\" alt=\"\" width=\"500\" height=\"327\" \/><\/a>\r\n<p style=\"text-align: center;\"><span style=\"color: #ff0000; font-size: 20px;\"><strong><span class=\"marker2\">\u21911\u4e07\u4eba\u4ee5\u4e0a\u306e\u533b\u7642\u5f93\u4e8b\u8005\u304c\u8cfc\u8aad\u4e2d<\/span><\/strong><\/span><\/p><\/div><h2 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