{"id":863,"date":"2023-07-28T12:11:13","date_gmt":"2023-07-28T12:11:13","guid":{"rendered":"https:\/\/statorials.org\/ja\/python%e3%81%ae%e4%bf%a1%e9%a0%bc%e5%8c%ba%e9%96%93\/"},"modified":"2023-07-28T12:11:13","modified_gmt":"2023-07-28T12:11:13","slug":"python%e3%81%ae%e4%bf%a1%e9%a0%bc%e5%8c%ba%e9%96%93","status":"publish","type":"post","link":"https:\/\/statorials.org\/ja\/python%e3%81%ae%e4%bf%a1%e9%a0%bc%e5%8c%ba%e9%96%93\/","title":{"rendered":"Python \u3067\u4fe1\u983c\u533a\u9593\u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>\u5e73\u5747\u5024\u306e\u4fe1\u983c\u533a\u9593\u306f\u3001<\/strong>\u4e00\u5b9a\u306e\u4fe1\u983c\u30ec\u30d9\u30eb\u3067\u6bcd\u96c6\u56e3\u5e73\u5747\u304c\u542b\u307e\u308c\u308b\u53ef\u80fd\u6027\u304c\u9ad8\u3044\u5024\u306e\u7bc4\u56f2\u3067\u3059\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u6b21\u306e\u3088\u3046\u306b\u8a08\u7b97\u3055\u308c\u307e\u3059\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>\u4fe1\u983c\u533a\u9593 =<\/strong> <strong><span style=\"text-decoration: overline;\">x<\/span> +\/- t*(s\/\u221an)<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u91d1\uff1a<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong><span style=\"text-decoration: overline;\">x<\/span> :<\/strong>\u30b5\u30f3\u30d7\u30eb\u5e73\u5747<\/span><\/li>\n<li><span style=\"color: #000000;\"><strong>t:<\/strong>\u4fe1\u983c\u6c34\u6e96\u306b\u5bfe\u5fdc\u3059\u308b t \u5024<\/span><\/li>\n<li><span style=\"color: #000000;\"><strong>s:<\/strong>\u30b5\u30f3\u30d7\u30eb\u306e\u6a19\u6e96\u504f\u5dee<\/span><\/li>\n<li><span style=\"color: #000000;\"><strong>n:<\/strong>\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba<\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000;\">\u3053\u306e\u30c1\u30e5\u30fc\u30c8\u30ea\u30a2\u30eb\u3067\u306f\u3001Python \u3067\u4fe1\u983c\u533a\u9593\u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5\u3092\u8aac\u660e\u3057\u307e\u3059\u3002<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>t \u5206\u5e03\u3092\u4f7f\u7528\u3057\u305f\u4fe1\u983c\u533a\u9593<\/strong><\/span><\/h3>\n<p><span style=\"color: #000000;\">\u5c0f\u898f\u6a21\u306a\u30b5\u30f3\u30d7\u30eb (n &lt; 30) \u3092\u6271\u3046\u5834\u5408\u306f\u3001scipy.stats \u30e9\u30a4\u30d6\u30e9\u30ea\u306e<a href=\"https:\/\/docs.scipy.org\/doc\/scipy\/reference\/generated\/scipy.stats.t.html\" target=\"_blank\" rel=\"noopener\">t.interval() \u95a2\u6570<\/a>\u3092\u4f7f\u7528\u3057\u3066\u6bcd\u96c6\u56e3\u5e73\u5747\u306e\u4fe1\u983c\u533a\u9593\u3092\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u6b21\u306e\u4f8b\u306f\u300115 \u500b\u306e\u690d\u7269\u306e\u30b5\u30f3\u30d7\u30eb\u3092\u4f7f\u7528\u3057\u3066\u3001\u7279\u5b9a\u306e\u690d\u7269\u7a2e\u306e\u771f\u306e\u5e73\u5747\u500b\u4f53\u7fa4\u9ad8\u3055 (\u30a4\u30f3\u30c1\u5358\u4f4d) \u306e\u4fe1\u983c\u533a\u9593\u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #107d3f;\">import<\/span> numpy <span style=\"color: #107d3f;\">as<\/span> np\n<span style=\"color: #107d3f;\">import<\/span> scipy.stats <span style=\"color: #107d3f;\">as<\/span> st\n\n<span style=\"color: #008080;\">#define sample data<\/span>\ndata = [12, 12, 13, 13, 15, 16, 17, 22, 23, 25, 26, 27, 28, 28, 29]\n\n<span style=\"color: #008080;\">#create 95% confidence interval for population mean weight\n<\/span>st.t.interval(alpha=0.95, df=len(data)-1, loc=np.mean(data), scale=st.sem(data)) \n\n(16.758, 24.042)<\/strong><\/pre>\n<p><span style=\"color: #000000;\">\u771f\u306e\u5e73\u5747\u6bcd\u96c6\u56e3\u30b5\u30a4\u30ba\u306e 95% \u4fe1\u983c\u533a\u9593\u306f<strong>(16.758, 24.042)<\/strong>\u3067\u3059\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u4fe1\u983c\u6c34\u6e96\u304c\u9ad8\u304f\u306a\u308b\u307b\u3069\u3001\u4fe1\u983c\u533a\u9593\u304c\u5e83\u304f\u306a\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002\u305f\u3068\u3048\u3070\u3001\u307e\u3063\u305f\u304f\u540c\u3058\u30c7\u30fc\u30bf\u306e 99% CI \u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#create 99% confidence interval for same sample\n<\/span>st.t.interval(alpha= <span style=\"color: #008000;\">0.99<\/span> , df=len(data)-1, loc=np.mean(data), scale=st.sem(data)) \n\n(15.348, 25.455)<\/strong><\/pre>\n<p><span style=\"color: #000000;\">\u771f\u306e\u5e73\u5747\u6bcd\u96c6\u56e3\u30b5\u30a4\u30ba\u306e 99% \u4fe1\u983c\u533a\u9593\u306f<strong>(15.348, 25.455)<\/strong>\u3067\u3059\u3002\u3053\u306e\u533a\u9593\u306f\u524d\u306e 95% \u4fe1\u983c\u533a\u9593\u3088\u308a\u3082\u5e83\u3044\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002<\/span><\/p>\n<h3><span style=\"color: #000000;\"><strong>\u6b63\u898f\u5206\u5e03\u3092\u4f7f\u7528\u3057\u305f\u4fe1\u983c\u533a\u9593<\/strong><\/span><\/h3>\n<p><span style=\"color: #000000;\">\u3088\u308a\u5927\u304d\u306a\u30b5\u30f3\u30d7\u30eb (n\u226530) \u3092\u6271\u3046\u5834\u5408\u306f\u3001(<a href=\"https:\/\/statorials.org\/ja\/\u4e2d\u5fc3\u6975\u9650\u5b9a\u7406\/\" target=\"_blank\" rel=\"noopener\">\u4e2d\u5fc3\u6975\u9650\u5b9a\u7406<\/a>\u306e\u304a\u304b\u3052\u3067) \u30b5\u30f3\u30d7\u30eb\u5e73\u5747\u306e\u30b5\u30f3\u30d7\u30eb\u5206\u5e03\u304c\u6b63\u898f\u5206\u5e03\u3057\u3066\u3044\u308b\u3068\u4eee\u5b9a\u3067\u304d\u3001\u4ee3\u308f\u308a\u306b<a href=\"https:\/\/docs.scipy.org\/doc\/scipy\/reference\/generated\/scipy.stats.norm.html\" target=\"_blank\" rel=\"noopener\">\u30ce\u30eb\u30e0\u95a2\u6570\u3092\u4f7f\u7528\u3067\u304d\u307e\u3059\u3002<\/a> scipy .stats\u30e9\u30a4\u30d6\u30e9\u30ea\u306e<a href=\"https:\/\/docs.scipy.org\/doc\/scipy\/reference\/generated\/scipy.stats.norm.html\" target=\"_blank\" rel=\"noopener\">interval()<\/a> \u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u6b21\u306e\u4f8b\u306f\u300150 \u500b\u306e\u690d\u7269\u306e\u30b5\u30f3\u30d7\u30eb\u3092\u4f7f\u7528\u3057\u3066\u3001\u7279\u5b9a\u306e\u690d\u7269\u7a2e\u306e\u771f\u306e\u5e73\u5747\u500b\u4f53\u7fa4\u9ad8\u3055 (\u30a4\u30f3\u30c1\u5358\u4f4d) \u306e\u4fe1\u983c\u533a\u9593\u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #107d3f;\">import<\/span> numpy <span style=\"color: #107d3f;\">as<\/span> np\n<span style=\"color: #107d3f;\">import<\/span> scipy.stats <span style=\"color: #107d3f;\">as<\/span> st\n\n<span style=\"color: #008080;\">#define sample data<\/span>\nnp.random.seed(0)\ndata = np.random.randint(10, 30, 50)\n\n<span style=\"color: #008080;\">#create 95% confidence interval for population mean weight\n<\/span>st.norm.interval(alpha=0.95, loc=np.mean(data), scale=st.sem(data))\n\n(17.40, 21.08)<\/strong><\/pre>\n<p><span style=\"color: #000000;\">\u771f\u306e\u5e73\u5747\u6bcd\u96c6\u56e3\u30b5\u30a4\u30ba\u306e 95% \u4fe1\u983c\u533a\u9593\u306f<strong>(17.40, 21.08)<\/strong>\u3067\u3059\u3002<\/span><\/p>\n<p> <span style=\"color: #000000;\">t \u5206\u5e03\u3068\u540c\u69d8\u306b\u3001\u4fe1\u983c\u6c34\u6e96\u304c\u9ad8\u3044\u307b\u3069\u4fe1\u983c\u533a\u9593\u3082\u5e83\u304f\u306a\u308a\u307e\u3059\u3002\u305f\u3068\u3048\u3070\u3001\u307e\u3063\u305f\u304f\u540c\u3058\u30c7\u30fc\u30bf\u306e 99% CI \u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#create 99% confidence interval for same sample\n<\/span>st.norm.interval(alpha= <span style=\"color: #008000;\">0.99<\/span> , loc=np.mean(data), scale=st.sem(data))\n\n(16.82, 21.66)<\/strong><\/pre>\n<p><span style=\"color: #000000;\">\u771f\u306e\u5e73\u5747\u6bcd\u96c6\u56e3\u30b5\u30a4\u30ba\u306e 95% \u4fe1\u983c\u533a\u9593\u306f<strong>(17.82, 21.66)<\/strong>\u3067\u3059\u3002<\/span><\/p>\n<h3><strong><span style=\"color: #000000;\">\u4fe1\u983c\u533a\u9593\u306e\u89e3\u91c8\u65b9\u6cd5<\/span><\/strong><\/h3>\n<p><span style=\"color: #000000;\">\u690d\u7269\u7a2e\u306e\u771f\u306e\u5e73\u5747\u9ad8\u3055\u306e 95% \u4fe1\u983c\u533a\u9593\u304c\u6b21\u306e\u3088\u3046\u306b\u306a\u308b\u3068\u4eee\u5b9a\u3057\u307e\u3059\u3002<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>95% \u4fe1\u983c\u533a\u9593 = (16.758, 24.042)<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u3053\u306e\u4fe1\u983c\u533a\u9593\u3092\u89e3\u91c8\u3059\u308b\u65b9\u6cd5\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002<\/span><\/p>\n<blockquote data-slot-rendered-dynamic=\"true\">\n<p> <span style=\"color: #000000;\">[16.758, 24.042] \u306e\u4fe1\u983c\u533a\u9593\u306b\u96c6\u56e3\u306e\u771f\u306e\u5e73\u5747\u8349\u4e08\u304c\u542b\u307e\u308c\u308b\u78ba\u7387\u306f 95% \u3067\u3059\u3002<\/span><\/p>\n<\/blockquote>\n<p><span style=\"color: #000000;\">\u540c\u3058\u3053\u3068\u3092\u5225\u306e\u8a00\u3044\u65b9\u3067\u8a00\u3048\u3070\u3001\u6bcd\u96c6\u56e3\u306e\u771f\u306e\u5e73\u5747\u5024\u304c 95% \u4fe1\u983c\u533a\u9593\u306e\u5916\u306b\u3042\u308b\u53ef\u80fd\u6027\u306f 5% \u3057\u304b\u306a\u3044\u3068\u3044\u3046\u3053\u3068\u3067\u3059\u3002\u3064\u307e\u308a\u3001\u5b9f\u969b\u306e\u5e73\u5747\u690d\u7269\u306e\u9ad8\u3055\u304c 16.758 \u30a4\u30f3\u30c1\u672a\u6e80\u306b\u306a\u308b\u304b\u300124.042 \u30a4\u30f3\u30c1\u3092\u8d85\u3048\u308b\u53ef\u80fd\u6027\u306f 5% \u3057\u304b\u3042\u308a\u307e\u305b\u3093\u3002<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5e73\u5747\u5024\u306e\u4fe1\u983c\u533a\u9593\u306f\u3001\u4e00\u5b9a\u306e\u4fe1\u983c\u30ec\u30d9\u30eb\u3067\u6bcd\u96c6\u56e3\u5e73\u5747\u304c\u542b\u307e\u308c\u308b\u53ef\u80fd\u6027\u304c\u9ad8\u3044\u5024\u306e\u7bc4\u56f2\u3067\u3059\u3002 \u6b21\u306e\u3088\u3046\u306b\u8a08\u7b97\u3055\u308c\u307e\u3059\u3002 \u4fe1\u983c\u533a\u9593 = x +\/- t*(s\/\u221an) \u91d1\uff1a x :\u30b5\u30f3\u30d7\u30eb\u5e73\u5747 t:\u4fe1\u983c\u6c34\u6e96\u306b\u5bfe\u5fdc\u3059\u308b t \u5024 s:\u30b5 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[16],"tags":[],"class_list":["post-863","post","type-post","status-publish","format-standard","hentry","category-16"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Python \u3067\u4fe1\u983c\u533a\u9593\u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5 - Statology<\/title>\n<meta name=\"description\" content=\"Python\u3067\u4fe1\u983c\u533a\u9593\u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5\u3092\u308f\u304b\u308a\u3084\u3059\u304f\u89e3\u8aac\u3057\u307e\u3059\u3002\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, 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