{"id":9219,"date":"2026-07-24T10:05:49","date_gmt":"2026-07-24T01:05:49","guid":{"rendered":"https:\/\/since2020.jp\/media\/?p=9219"},"modified":"2026-07-24T10:05:49","modified_gmt":"2026-07-24T01:05:49","slug":"normal-distribution-to-chi-square-t-and-f","status":"publish","type":"post","link":"https:\/\/since2020.jp\/media\/normal-distribution-to-chi-square-t-and-f\/","title":{"rendered":"\u6b63\u898f\u5206\u5e03\u304b\u3089\u5c0e\u304f\u4e09\u3064\u306e\u5206\u5e03"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\">3\u3064\u306e\u5206\u5e03\u3092\u516c\u5f0f\u3068\u3057\u3066\u899a\u3048\u3066\u3044\u307e\u305b\u3093\u304b\uff1f<\/h2>\n\n\n\n<p>\u7d71\u8a08\u5b66\u3092\u5b66\u3073\u59cb\u3081\u308b\u3068\u3001\u6b63\u898f\u5206\u5e03\u3001\u4e8c\u9805\u5206\u5e03\u3001\u30dd\u30a2\u30bd\u30f3\u5206\u5e03\u306a\u3069\u6bd4\u8f03\u7684\u65e9\u3044\u6bb5\u968e\u3067\u76ee\u306b\u3059\u308b\u78ba\u7387\u5206\u5e03\u304c\u3042\u308b\u3002\u305d\u306e\u5f8c\u3001\u7d71\u8a08\u7684\u63a8\u6e2c\u3084\u4eee\u8a2d\u691c\u5b9a\u3092\u5b66\u3076\u9803\u306b\u306f\u4ee5\u4e0b\u306e3\u3064\u306e\u5206\u5e03\u304c\u767b\u5834\u3059\u308b\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><math data-latex=\"\\chi^2\"><semantics><msup><mi>\u03c7<\/mi><mn>2<\/mn><\/msup><annotation encoding=\"application\/x-tex\">\\chi^2<\/annotation><\/semantics><\/math> \u5206\u5e03<\/li>\n\n\n\n<li><math data-latex=\"t\"><semantics><mi>t<\/mi><annotation encoding=\"application\/x-tex\">t<\/annotation><\/semantics><\/math> \u5206\u5e03<\/li>\n\n\n\n<li><math data-latex=\"F\"><semantics><mi>F<\/mi><annotation encoding=\"application\/x-tex\">F<\/annotation><\/semantics><\/math> \u5206\u5e03<\/li>\n<\/ul>\n\n\n\n<p>\u3053\u308c\u3089\u3092\u521d\u3081\u3066\u5b66\u3093\u3060\u3068\u304d\u3001\u3069\u306e\u3088\u3046\u306b\u899a\u3048\u305f\u3060\u308d\u3046\u304b\u3002\u305d\u308c\u305e\u308c\u306e\u5206\u5e03\u3092\u63cf\u753b\u3057\u3001\u305d\u306e\u5f62\u3067\u899a\u3048\u308b\u3002\u3082\u3057\u304f\u306f\u3001\u305d\u308c\u305e\u308c\u306b\u3064\u3044\u3066\u671f\u5f85\u5024\u3084\u5206\u6563\u3001\u81ea\u7531\u5ea6\u3092\u516c\u5f0f\u3068\u3057\u3066\u3001\u307e\u305f\u306f\u305d\u308c\u3089\u306e\u5206\u5e03\u306e\u767b\u5834\u5834\u9762\u3067\u899a\u3048\u305f\u65b9\u3082\u591a\u3044\u306e\u3067\u306f\u306a\u3044\u3060\u308d\u3046\u304b\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u6bcd\u5206\u6563\u306e\u691c\u5b9a\u306f <math data-latex=\"\\chi^2\"><semantics><msup><mi>\u03c7<\/mi><mn>2<\/mn><\/msup><annotation encoding=\"application\/x-tex\">\\chi^2<\/annotation><\/semantics><\/math> \u5206\u5e03<\/li>\n\n\n\n<li>\u6bcd\u5e73\u5747\u306e\u691c\u5b9a\u3067\u306f <math data-latex=\"t\"><semantics><mi>t<\/mi><annotation encoding=\"application\/x-tex\">t<\/annotation><\/semantics><\/math> \u5206\u5e03<\/li>\n\n\n\n<li>\u5206\u6563\u306e\u6bd4\u8f03\u3067\u306f <math data-latex=\"F\"><semantics><mi>F<\/mi><annotation encoding=\"application\/x-tex\">F<\/annotation><\/semantics><\/math> \u5206\u5e03<\/li>\n<\/ul>\n\n\n\n<p>\u306a\u3069\u3068\u3044\u3063\u305f\u8981\u9818\u3067\u3002<\/p>\n\n\n\n<p>\u3067\u306f\u3053\u308c\u3089\u306e\u691c\u5b9a\u3067\u305d\u308c\u3089\u306e\u5206\u5e03\u304c\u767b\u5834\u3059\u308b\u306e\u306f\u306a\u305c\u304b\uff1f\u672c\u8a18\u4e8b\u3067\u306f\u3001\u6a19\u6e96\u6b63\u898f\u5206\u5e03\u3092\u539f\u70b9\u3068\u3057\u3066\u305d\u308c\u3089\u306e\u5206\u5e03\u304c\u3069\u3046\u7d44\u307f\u7acb\u3066\u3089\u308c\u308b\u306e\u304b\u3092\u89e3\u660e\u3057\u3066\u3044\u304f\u3002<\/p>\n\n\n\n<p class=\"has-text-align-center\"><math data-latex=\"Z \\sim N \\:(0,\\:1)\\:\\:\\Rightarrow\\:\\: \\displaystyle \\sum_{i = 1}^{\\nu} Z_i^2 \\sim\\chi^2(\\nu)\\:\\:\\Rightarrow\\:\\:\\dfrac{\\:Z\\:}{\\:\\sqrt{U\/\\nu}\\:}\\sim t(\\nu)\\:\\:\\Rightarrow\\:\\: \\dfrac{\\:U_1\/\\nu_1\\:}{\\:U_2\/\\nu_2\\:}\\sim F(\\nu_1,\\:\\nu_2)\"><semantics><mrow><mi>Z<\/mi><mo>\u223c<\/mo><mi>N<\/mi><mspace width=\"0.2222em\"><\/mspace><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>0<\/mn><mo separator=\"true\">,<\/mo><mspace width=\"0.2222em\"><\/mspace><mn>1<\/mn><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mspace width=\"0.2222em\"><\/mspace><mspace width=\"0.2222em\"><\/mspace><mo stretchy=\"false\">\u21d2<\/mo><mspace width=\"0.2222em\"><\/mspace><mspace width=\"0.2222em\"><\/mspace><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><munderover><mo movablelimits=\"false\">\u2211<\/mo><mrow><mi>i<\/mi><mo>=<\/mo><mn>1<\/mn><\/mrow><mi>\u03bd<\/mi><\/munderover><\/mrow><msubsup><mi>Z<\/mi><mi>i<\/mi><mn>2<\/mn><\/msubsup><mo>\u223c<\/mo><msup><mi>\u03c7<\/mi><mn>2<\/mn><\/msup><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>\u03bd<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mspace width=\"0.2222em\"><\/mspace><mspace width=\"0.2222em\"><\/mspace><mo stretchy=\"false\">\u21d2<\/mo><mspace width=\"0.2222em\"><\/mspace><mspace width=\"0.2222em\"><\/mspace><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mrow><mspace width=\"0.2222em\"><\/mspace><mi>Z<\/mi><mspace width=\"0.2222em\"><\/mspace><\/mrow><mrow><mspace width=\"0.2222em\"><\/mspace><msqrt><mrow><mi>U<\/mi><mi>\/<\/mi><mi>\u03bd<\/mi><\/mrow><\/msqrt><mspace width=\"0.2222em\"><\/mspace><\/mrow><\/mfrac><\/mstyle><mo>\u223c<\/mo><mi>t<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>\u03bd<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mspace width=\"0.2222em\"><\/mspace><mspace width=\"0.2222em\"><\/mspace><mo stretchy=\"false\">\u21d2<\/mo><mspace width=\"0.2222em\"><\/mspace><mspace width=\"0.2222em\"><\/mspace><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mrow><mspace width=\"0.2222em\"><\/mspace><msub><mi>U<\/mi><mn>1<\/mn><\/msub><mi>\/<\/mi><msub><mi>\u03bd<\/mi><mn>1<\/mn><\/msub><mspace width=\"0.2222em\"><\/mspace><\/mrow><mrow><mspace width=\"0.2222em\"><\/mspace><msub><mi>U<\/mi><mn>2<\/mn><\/msub><mi>\/<\/mi><msub><mi>\u03bd<\/mi><mn>2<\/mn><\/msub><mspace width=\"0.2222em\"><\/mspace><\/mrow><\/mfrac><\/mstyle><mo>\u223c<\/mo><mi>F<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msub><mi>\u03bd<\/mi><mn>1<\/mn><\/msub><mo separator=\"true\">,<\/mo><mspace width=\"0.2222em\"><\/mspace><msub><mi>\u03bd<\/mi><mn>2<\/mn><\/msub><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mstyle><\/mrow><annotation encoding=\"application\/x-tex\">Z \\sim N \\:(0,\\:1)\\:\\:\\Rightarrow\\:\\: \\displaystyle \\sum_{i = 1}^{\\nu} Z_i^2 \\sim\\chi^2(\\nu)\\:\\:\\Rightarrow\\:\\:\\dfrac{\\:Z\\:}{\\:\\sqrt{U\/\\nu}\\:}\\sim t(\\nu)\\:\\:\\Rightarrow\\:\\: \\dfrac{\\:U_1\/\\nu_1\\:}{\\:U_2\/\\nu_2\\:}\\sim F(\\nu_1,\\:\\nu_2)<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p>\u6700\u5de6\u8fba\u306e\u6a19\u6e96\u6b63\u898f\u5206\u5e03\u304b\u3089\u5404\u5206\u5e03\u3078\u3064\u306a\u304c\u308b\u4e0a\u5f0f\u306b\u304a\u3044\u3066\u3001\u6b63\u898f\u4e71\u6570\u3084 <math data-latex=\"\\chi^2\"><semantics><msup><mi>\u03c7<\/mi><mn>2<\/mn><\/msup><annotation encoding=\"application\/x-tex\">\\chi^2<\/annotation><\/semantics><\/math> \u4e71\u6570\u306f\u4e92\u3044\u306b\u72ec\u7acb\u3068\u4eee\u5b9a\u3057\u3066\u304a\u304f\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u6b63\u898f\u5206\u5e03\u306e\u4e8c\u4e57<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">\u81ea\u7531\u5ea6 1 \u306e <math data-latex=\"\\chi^2\"><semantics><msup><mi>\u03c7<\/mi><mn>2<\/mn><\/msup><annotation encoding=\"application\/x-tex\">\\chi^2<\/annotation><\/semantics><\/math> \u5206\u5e03<\/h3>\n\n\n\n<p class=\"has-text-align-left\">\u307e\u305a\u306f\u3058\u3081\u306b\u6a19\u6e96\u6b63\u898f\u4e71\u6570<\/p>\n\n\n\n<p class=\"has-text-align-center\"><br><math data-latex=\"Z\\sim N(0,\\:1)\"><semantics><mrow><mi>Z<\/mi><mo>\u223c<\/mo><mi>N<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>0<\/mn><mo separator=\"true\">,<\/mo><mspace width=\"0.2222em\"><\/mspace><mn>1<\/mn><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">Z\\sim N(0,\\:1)<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"has-text-align-left\">\u3092\u8003\u3048\u308b\u3002\u3053\u306e <math data-latex=\"Z\"><semantics><mi>Z<\/mi><annotation encoding=\"application\/x-tex\">Z<\/annotation><\/semantics><\/math> \u3092\u4e8c\u4e57\u3057\u305f<\/p>\n\n\n\n<p class=\"has-text-align-center\"><br><math data-latex=\"Z^2\"><semantics><msup><mi>Z<\/mi><mn>2<\/mn><\/msup><annotation encoding=\"application\/x-tex\">Z^2<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"has-text-align-left\">\u306f\u975e\u8ca0\u306e\u5024\u3092\u53d6\u308a\u3001 <math data-latex=\"Z\"><semantics><mi>Z<\/mi><annotation encoding=\"application\/x-tex\">Z<\/annotation><\/semantics><\/math> \u306e\u5e73\u5747\u304c 0 \u3067\u3042\u308b\u3053\u3068\u304b\u3089\u3001 <math data-latex=\"Z^2\"><semantics><msup><mi>Z<\/mi><mn>2<\/mn><\/msup><annotation encoding=\"application\/x-tex\">Z^2<\/annotation><\/semantics><\/math> \u3082 0 \u306b\u5024\u304c\u96c6\u4e2d\u3059\u308b\u3053\u3068\u3068\u306a\u308b\u3002\u4e00\u65b9\u3001<math data-latex=\"\\lvert Z \\rvert\"><semantics><mrow><mo form=\"prefix\" stretchy=\"false\">|<\/mo><mi>Z<\/mi><mo form=\"postfix\" stretchy=\"false\">|<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">\\lvert Z \\rvert<\/annotation><\/semantics><\/math> \u304c\u5927\u304d\u3044\u5024\u3092\u53d6\u308b\u3053\u3068\u306f\u7a00\u3060\u304c\u3001\u4e8c\u4e57\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u88fe\u306f\u53f3\u306b\u9577\u304f\u306a\u308b\u3002\u3053\u306e <math data-latex=\"Z^2\"><semantics><msup><mi>Z<\/mi><mn>2<\/mn><\/msup><annotation encoding=\"application\/x-tex\">Z^2<\/annotation><\/semantics><\/math> \u306e\u5206\u5e03\u3092\u3001\u81ea\u7531\u5ea6 1 \u306e <math data-latex=\"\\chi^2\"><semantics><msup><mi>\u03c7<\/mi><mn>2<\/mn><\/msup><annotation encoding=\"application\/x-tex\">\\chi^2<\/annotation><\/semantics><\/math> \u5206\u5e03\u3068\u547c\u3076\u3002<\/p>\n\n\n\n<p class=\"has-text-align-center\"><br><math data-latex=\"Z^2\\sim \\chi^2(1)\"><semantics><mrow><msup><mi>Z<\/mi><mn>2<\/mn><\/msup><mo>\u223c<\/mo><msup><mi>\u03c7<\/mi><mn>2<\/mn><\/msup><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>1<\/mn><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">Z^2\\sim \\chi^2(1)<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u81ea\u7531\u5ea6 <math data-latex=\"\\nu\"><semantics><mi>\u03bd<\/mi><annotation encoding=\"application\/x-tex\">\\nu<\/annotation><\/semantics><\/math> \u306e <math data-latex=\"\\chi^2\"><semantics><msup><mi>\u03c7<\/mi><mn>2<\/mn><\/msup><annotation encoding=\"application\/x-tex\">\\chi^2<\/annotation><\/semantics><\/math> \u5206\u5e03<\/h3>\n\n\n\n<p>\u72ec\u7acb\u306a\u6a19\u6e96\u6b63\u898f\u4e71\u6570<\/p>\n\n\n\n<p class=\"has-text-align-center\"><br><math data-latex=\"Z_1,\\:Z_2,\\:\\cdots,\\:Z_\\nu\\overset{\\text\\small\\textrm{i.i.d}}{\\sim} N(0,\\:1)\"><semantics><mrow><msub><mi>Z<\/mi><mn>1<\/mn><\/msub><mo separator=\"true\">,<\/mo><mspace width=\"0.2222em\"><\/mspace><msub><mi>Z<\/mi><mn>2<\/mn><\/msub><mo separator=\"true\">,<\/mo><mspace width=\"0.2222em\"><\/mspace><mo>\u22ef<\/mo><mspace width=\"0.1667em\"><\/mspace><mo separator=\"true\">,<\/mo><mspace width=\"0.2222em\"><\/mspace><msub><mi>Z<\/mi><mi>\u03bd<\/mi><\/msub><mrow><mover><mo>\u223c<\/mo><mrow><mstyle mathsize=\"0.9000em\"><\/mstyle><mtext>i.i.d<\/mtext><\/mrow><\/mover><\/mrow><mi>N<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>0<\/mn><mo separator=\"true\">,<\/mo><mspace width=\"0.2222em\"><\/mspace><mn>1<\/mn><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">Z_1,\\:Z_2,\\:\\cdots,\\:Z_\\nu\\overset{\\text\\small\\textrm{i.i.d}}{\\sim} N(0,\\:1)<\/annotation><\/semantics><\/math><br><\/p>\n\n\n\n<p>\u3092\u7528\u610f\u3057\uff08<math data-latex=\"i.i.d\"><semantics><mrow><mi>i<\/mi><mi>.<\/mi><mi>i<\/mi><mi>.<\/mi><mi>d<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">i.i.d<\/annotation><\/semantics><\/math>; <strong>Independent and Identically Distributed<\/strong> \uff09\u3001\u305d\u306e\u4e8c\u4e57\u548c <math data-latex=\"U\"><semantics><mi>U<\/mi><annotation encoding=\"application\/x-tex\">U<\/annotation><\/semantics><\/math> \u3092<\/p>\n\n\n\n<p class=\"has-text-align-center\"><br><math data-latex=\"U\\:=\\:\\displaystyle \\sum_{i=1}^\\nu Z_i^2\"><semantics><mrow><mi>U<\/mi><mspace width=\"0.2222em\"><\/mspace><mo>=<\/mo><mspace width=\"0.2222em\"><\/mspace><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><munderover><mo movablelimits=\"false\">\u2211<\/mo><mrow><mi>i<\/mi><mo>=<\/mo><mn>1<\/mn><\/mrow><mi>\u03bd<\/mi><\/munderover><\/mrow><msubsup><mi>Z<\/mi><mi>i<\/mi><mn>2<\/mn><\/msubsup><\/mstyle><\/mrow><annotation encoding=\"application\/x-tex\">U\\:=\\:\\displaystyle \\sum_{i=1}^\\nu Z_i^2<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p>\u3068\u3059\u308b\u3002\u3053\u306e\u3068\u304d<\/p>\n\n\n\n<p class=\"has-text-align-center\"><br><math data-latex=\"U\\sim \\chi^2 (\\nu)\"><semantics><mrow><mi>U<\/mi><mo>\u223c<\/mo><msup><mi>\u03c7<\/mi><mn>2<\/mn><\/msup><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>\u03bd<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">U\\sim \\chi^2 (\\nu)<\/annotation><\/semantics><\/math><br><\/p>\n\n\n\n<p>\u3067\u3042\u308a\u3001<math data-latex=\"\\mu\"><semantics><mi>\u03bc<\/mi><annotation encoding=\"application\/x-tex\">\\mu<\/annotation><\/semantics><\/math> \u306f\u81ea\u7531\u5ea6\u3068\u547c\u3070\u308c\u308b\u3002<math data-latex=\"\\chi^2 (\\nu)\"><semantics><mrow><msup><mi>\u03c7<\/mi><mn>2<\/mn><\/msup><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>\u03bd<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">\\chi^2 (\\nu)<\/annotation><\/semantics><\/math> \u5206\u5e03\u306e\u5e73\u5747\u3068\u5206\u6563\u306f<\/p>\n\n\n\n<p class=\"has-text-align-center\"><br><math data-latex=\"E[U]\\:=\\:\\nu,\\:\\:\\:\\mathrm{Var}(U) \\:=\\: 2\\nu \ufeff\"><semantics><mrow><mi>E<\/mi><mo form=\"prefix\" stretchy=\"false\">[<\/mo><mi>U<\/mi><mo form=\"postfix\" stretchy=\"false\">]<\/mo><mspace width=\"0.2222em\"><\/mspace><mo>=<\/mo><mspace width=\"0.2222em\"><\/mspace><mi>\u03bd<\/mi><mo separator=\"true\">,<\/mo><mspace width=\"0.2222em\"><\/mspace><mspace width=\"0.2222em\"><\/mspace><mspace width=\"0.2222em\"><\/mspace><mrow><mtext><\/mtext><mi>Var<\/mi><\/mrow><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>U<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mspace width=\"0.2222em\"><\/mspace><mo>=<\/mo><mspace width=\"0.2222em\"><\/mspace><mn>2<\/mn><mi>\u03bd<\/mi><mtext>\ufeff<\/mtext><\/mrow><annotation encoding=\"application\/x-tex\">E[U]\\:=\\:\\nu,\\:\\:\\:\\mathrm{Var}(U) \\:=\\: 2\\nu \ufeff<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p>\u3067\u3042\u308b\u3002\u81ea\u7531\u5ea6\u304c\u5927\u304d\u3044\u307b\u3069\u5206\u5e03\u306e\u4e2d\u5fc3\u306f\u53f3\u3078\u79fb\u52d5\u3057\u3001\u76f8\u5bfe\u7684\u306a\u3070\u3089\u3064\u304d\u306f\u5c0f\u3055\u304f\u306a\u308b\u3002\u30b0\u30e9\u30d5\u306e\u5f62\u3082\u81ea\u7531\u5ea6\u304c\u5c0f\u3055\u3044\u307b\u3069\u53f3\u306b\u5f37\u304f\u6b6a\u3080\u304c\u3001\u5927\u304d\u304f\u306a\u308c\u3070\u306a\u308b\u307b\u3069\u6b63\u898f\u5206\u5e03\u306b\u8fd1\u3044\u5f62\u3068\u306a\u308b\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" width=\"1024\" height=\"536\" src=\"https:\/\/since2020.jp\/media\/wp-content\/uploads\/2026\/07\/image-4-1024x536.png\" alt=\"\" class=\"wp-image-9232\" srcset=\"https:\/\/since2020.jp\/media\/wp-content\/uploads\/2026\/07\/image-4-1024x536.png 1024w, https:\/\/since2020.jp\/media\/wp-content\/uploads\/2026\/07\/image-4-300x157.png 300w, https:\/\/since2020.jp\/media\/wp-content\/uploads\/2026\/07\/image-4-768x402.png 768w, https:\/\/since2020.jp\/media\/wp-content\/uploads\/2026\/07\/image-4-1536x805.png 1536w, https:\/\/since2020.jp\/media\/wp-content\/uploads\/2026\/07\/image-4-2048x1073.png 2048w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p>\u56f31: \u6a19\u6e96\u6b63\u898f\u4e71\u6570\u306e\u4e8c\u4e57\u548c\u3067\u4f5c\u3063\u305f\u30d2\u30b9\u30c8\u30b0\u30e9\u30e0\u3001\u304a\u3088\u3073SciPy\u306e <math data-latex=\"\\chi^2\"><semantics><msup><mi>\u03c7<\/mi><mn>2<\/mn><\/msup><annotation encoding=\"application\/x-tex\">\\chi^2<\/annotation><\/semantics><\/math> \u7406\u8ad6\u5bc6\u5ea6<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u6a19\u672c\u5206\u6563\u3068\u306e\u95a2\u4fc2<\/h3>\n\n\n\n<p>\u5206\u6563\u306e\u691c\u5b9a\u306b <math data-latex=\"\\chi^2\"><semantics><msup><mi>\u03c7<\/mi><mn>2<\/mn><\/msup><annotation encoding=\"application\/x-tex\">\\chi^2<\/annotation><\/semantics><\/math> \u5206\u5e03\u304c\u51fa\u3066\u304f\u308b\u7406\u7531\u306f\u3001\u6b63\u898f\u6bcd\u96c6\u56e3\u306e\u6a19\u672c\u5206\u6563\u304c\u4e8c\u4e57\u548c\u3067\u8868\u3055\u308c\u308b\u304b\u3089\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<p><math data-latex=\"\\chi^2\"><semantics><msup><mi>\u03c7<\/mi><mn>2<\/mn><\/msup><annotation encoding=\"application\/x-tex\">\\chi^2<\/annotation><\/semantics><\/math> \u3092\u72ec\u7acb\u306b<\/p>\n\n\n\n<p class=\"has-text-align-center\"><br><math data-latex=\"X_i\\sim N(\\mu,\\:\\sigma^2)\"><semantics><mrow><msub><mi>X<\/mi><mi>i<\/mi><\/msub><mo>\u223c<\/mo><mi>N<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>\u03bc<\/mi><mo separator=\"true\">,<\/mo><mspace width=\"0.2222em\"><\/mspace><msup><mi>\u03c3<\/mi><mn>2<\/mn><\/msup><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">X_i\\sim N(\\mu,\\:\\sigma^2)<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p>\u304b\u3089\u62bd\u51fa\u3057\u305f\u6a19\u672c\u3068\u3057\u3001\u6a19\u672c\u5e73\u5747\u3092 <math data-latex=\"\\bar{X}\"><semantics><mover><mi>X<\/mi><mo stretchy=\"false\" class=\"tml-capshift\">\u203e<\/mo><\/mover><annotation encoding=\"application\/x-tex\">\\bar{X}<\/annotation><\/semantics><\/math>\u3001\u4e0d\u504f\u5206\u6563 <math data-latex=\"S\"><semantics><mi>S<\/mi><annotation encoding=\"application\/x-tex\">S<\/annotation><\/semantics><\/math> \u3092<\/p>\n\n\n\n<p class=\"has-text-align-center\"><br><math data-latex=\"S^2 \\:=\\: \\dfrac{\\:1\\:}{\\:n-1\\:}\\displaystyle \\sum_{i=1}^n (X_i - \\bar{X})^2\"><semantics><mrow><msup><mi>S<\/mi><mn>2<\/mn><\/msup><mspace width=\"0.2222em\"><\/mspace><mo>=<\/mo><mspace width=\"0.2222em\"><\/mspace><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mrow><mspace width=\"0.2222em\"><\/mspace><mn>1<\/mn><mspace width=\"0.2222em\"><\/mspace><\/mrow><mrow><mspace width=\"0.2222em\"><\/mspace><mi>n<\/mi><mo>\u2212<\/mo><mn>1<\/mn><mspace width=\"0.2222em\"><\/mspace><\/mrow><\/mfrac><\/mstyle><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><munderover><mo movablelimits=\"false\">\u2211<\/mo><mrow><mi>i<\/mi><mo>=<\/mo><mn>1<\/mn><\/mrow><mi>n<\/mi><\/munderover><\/mrow><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msub><mi>X<\/mi><mi>i<\/mi><\/msub><mo>\u2212<\/mo><mover><mi>X<\/mi><mo stretchy=\"false\" class=\"tml-capshift\">\u203e<\/mo><\/mover><msup><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><\/mstyle><\/mrow><annotation encoding=\"application\/x-tex\">S^2 \\:=\\: \\dfrac{\\:1\\:}{\\:n-1\\:}\\displaystyle \\sum_{i=1}^n (X_i &#8211; \\bar{X})^2<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p>\u3068\u3059\u308b\u3002\u3053\u306e\u5f0f\u306e\u4e21\u8fba\u306b <math data-latex=\"(n-1)\/\\sigma ^2\"><semantics><mrow><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>n<\/mi><mo>\u2212<\/mo><mn>1<\/mn><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mi>\/<\/mi><msup><mi>\u03c3<\/mi><mn>2<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">(n-1)\/\\sigma ^2<\/annotation><\/semantics><\/math> \u3092\u304b\u3051\u308b\u3068\uff08 <math data-latex=\"\\sigma\"><semantics><mi>\u03c3<\/mi><annotation encoding=\"application\/x-tex\">\\sigma<\/annotation><\/semantics><\/math> \u306f\u6bcd\u96c6\u56e3\u306e\u6a19\u6e96\u504f\u5dee\uff09<\/p>\n\n\n\n<p class=\"has-text-align-center\"><br><math data-latex=\"\\dfrac{(n\u22121)S^2}{\\sigma^2}=\\dfrac{\\:1\\:}{\\:\\sigma^2\\:}\\displaystyle \\sum_{i=1}^n (X_i\u2212\\bar{X})^2\"><semantics><mrow><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mrow><mo form=\"prefix\" stretchy=\"false\" lspace=\"0em\" rspace=\"0em\">(<\/mo><mi>n<\/mi><mo>\u2212<\/mo><mn>1<\/mn><mo form=\"postfix\" stretchy=\"false\">)<\/mo><msup><mi>S<\/mi><mn>2<\/mn><\/msup><\/mrow><msup><mi>\u03c3<\/mi><mn>2<\/mn><\/msup><\/mfrac><\/mstyle><mo>=<\/mo><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mrow><mspace width=\"0.2222em\"><\/mspace><mn>1<\/mn><mspace width=\"0.2222em\"><\/mspace><\/mrow><mrow><mspace width=\"0.2222em\"><\/mspace><msup><mi>\u03c3<\/mi><mn>2<\/mn><\/msup><mspace width=\"0.2222em\"><\/mspace><\/mrow><\/mfrac><\/mstyle><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><munderover><mo movablelimits=\"false\">\u2211<\/mo><mrow><mi>i<\/mi><mo>=<\/mo><mn>1<\/mn><\/mrow><mi>n<\/mi><\/munderover><\/mrow><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msub><mi>X<\/mi><mi>i<\/mi><\/msub><mo>\u2212<\/mo><mover><mi>X<\/mi><mo stretchy=\"false\" class=\"tml-capshift\">\u203e<\/mo><\/mover><msup><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><\/mstyle><\/mrow><annotation encoding=\"application\/x-tex\">\\dfrac{(n\u22121)S^2}{\\sigma^2}=\\dfrac{\\:1\\:}{\\:\\sigma^2\\:}\\displaystyle \\sum_{i=1}^n (X_i\u2212\\bar{X})^2<\/annotation><\/semantics><\/math><br><\/p>\n\n\n\n<p>\u3068\u306a\u308b\u3002\u3053\u3053\u3067\u6bcd\u5e73\u5747 <math data-latex=\"\\mu\"><semantics><mi>\u03bc<\/mi><annotation encoding=\"application\/x-tex\">\\mu<\/annotation><\/semantics><\/math> \u304c\u65e2\u77e5\u3067\u3042\u308b\u3053\u3068\u306f\u6975\u3081\u3066\u7a00\u3067\u3042\u308b\u3002\u4eee\u306b\u6bcd\u5e73\u5747 <math data-latex=\"\\mu\"><semantics><mi>\u03bc<\/mi><annotation encoding=\"application\/x-tex\">\\mu<\/annotation><\/semantics><\/math> \u304c\u65e2\u77e5\u3067\u3042\u308c\u3070\u5404 <math data-latex=\"X_i\"><semantics><msub><mi>X<\/mi><mi>i<\/mi><\/msub><annotation encoding=\"application\/x-tex\">X_i<\/annotation><\/semantics><\/math> \u3092\u6a19\u6e96\u5316\u3057<\/p>\n\n\n\n<p class=\"has-text-align-center\"><br><math data-latex=\"Z_i \\:=\\: \\dfrac{\\:X_i - \\mu\\:}{\\:\\sigma\\:}\"><semantics><mrow><msub><mi>Z<\/mi><mi>i<\/mi><\/msub><mspace width=\"0.2222em\"><\/mspace><mo>=<\/mo><mspace width=\"0.2222em\"><\/mspace><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mrow><mspace width=\"0.2222em\"><\/mspace><msub><mi>X<\/mi><mi>i<\/mi><\/msub><mo>\u2212<\/mo><mi>\u03bc<\/mi><mspace width=\"0.2222em\"><\/mspace><\/mrow><mrow><mspace width=\"0.2222em\"><\/mspace><mi>\u03c3<\/mi><mspace width=\"0.2222em\"><\/mspace><\/mrow><\/mfrac><\/mstyle><\/mrow><annotation encoding=\"application\/x-tex\">Z_i \\:=\\: \\dfrac{\\:X_i &#8211; \\mu\\:}{\\:\\sigma\\:}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p>\u3068\u3059\u308b\u3053\u3068\u3067\u3053\u308c\u3089\u306f\u4e92\u3044\u306b\u72ec\u7acb\u306a\u6a19\u6e96\u6b63\u898f\u5206\u5e03\u306b\u5f93\u3046\u3002<\/p>\n\n\n\n<p class=\"has-text-align-center\"><br><math data-latex=\"Z_i \\sim N(0,\\:1)\"><semantics><mrow><msub><mi>Z<\/mi><mi>i<\/mi><\/msub><mo>\u223c<\/mo><mi>N<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>0<\/mn><mo separator=\"true\">,<\/mo><mspace width=\"0.2222em\"><\/mspace><mn>1<\/mn><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">Z_i \\sim N(0,\\:1)<\/annotation><\/semantics><\/math><br><\/p>\n\n\n\n<p>\u3067\u3042\u308b\u3002\u3057\u305f\u304c\u3063\u3066\u305d\u306e\u4e8c\u4e57\u548c\u306f\u4ee5\u4e0b\u306e\u5f0f\u306e\u901a\u308a\u81ea\u7531\u5ea6 <math data-latex=\"n\"><semantics><mi>n<\/mi><annotation encoding=\"application\/x-tex\">n<\/annotation><\/semantics><\/math> \u306e <math data-latex=\"\\chi^2\"><semantics><msup><mi>\u03c7<\/mi><mn>2<\/mn><\/msup><annotation encoding=\"application\/x-tex\">\\chi^2<\/annotation><\/semantics><\/math> \u5206\u5e03\u306b\u5f93\u3046\u3053\u3068\u306b\u306a\u308b\u3002<\/p>\n\n\n\n<p class=\"has-text-align-center\"><br><math data-latex=\"\\displaystyle \\sum_{i=1}^n Z_i^2 \\:=\\:\\dfrac{\\:1\\:}{\\:\\sigma^2\\:}\\displaystyle \\sum_{i=1}^{n} (X_i - \\mu)^2 \\sim \\chi_n^2\"><semantics><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><munderover><mo movablelimits=\"false\">\u2211<\/mo><mrow><mi>i<\/mi><mo>=<\/mo><mn>1<\/mn><\/mrow><mi>n<\/mi><\/munderover><\/mrow><msubsup><mi>Z<\/mi><mi>i<\/mi><mn>2<\/mn><\/msubsup><mspace width=\"0.2222em\"><\/mspace><mo>=<\/mo><mspace width=\"0.2222em\"><\/mspace><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mrow><mspace width=\"0.2222em\"><\/mspace><mn>1<\/mn><mspace width=\"0.2222em\"><\/mspace><\/mrow><mrow><mspace width=\"0.2222em\"><\/mspace><msup><mi>\u03c3<\/mi><mn>2<\/mn><\/msup><mspace width=\"0.2222em\"><\/mspace><\/mrow><\/mfrac><\/mstyle><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><munderover><mo movablelimits=\"false\">\u2211<\/mo><mrow><mi>i<\/mi><mo>=<\/mo><mn>1<\/mn><\/mrow><mi>n<\/mi><\/munderover><\/mrow><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msub><mi>X<\/mi><mi>i<\/mi><\/msub><mo>\u2212<\/mo><mi>\u03bc<\/mi><msup><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><mo>\u223c<\/mo><msubsup><mi>\u03c7<\/mi><mi>n<\/mi><mn>2<\/mn><\/msubsup><\/mstyle><\/mstyle><annotation encoding=\"application\/x-tex\">\\displaystyle \\sum_{i=1}^n Z_i^2 \\:=\\:\\dfrac{\\:1\\:}{\\:\\sigma^2\\:}\\displaystyle \\sum_{i=1}^{n} (X_i &#8211; \\mu)^2 \\sim \\chi_n^2<\/annotation><\/semantics><\/math><br><\/p>\n\n\n\n<p>\u3057\u304b\u3057\u6a19\u672c\u5206\u6563\u306e\u691c\u5b9a\u3067\u4f7f\u7528\u3067\u304d\u308b\u306e\u306f <math data-latex=\"\\mu\"><semantics><mi>\u03bc<\/mi><annotation encoding=\"application\/x-tex\">\\mu<\/annotation><\/semantics><\/math> \u3067\u306f\u306a\u304f <math data-latex=\"\\bar{X}\"><semantics><mover><mi>X<\/mi><mo stretchy=\"false\" class=\"tml-capshift\">\u203e<\/mo><\/mover><annotation encoding=\"application\/x-tex\">\\bar{X}<\/annotation><\/semantics><\/math> \u3067\u3042\u308b\u3002\u3064\u307e\u308a <math data-latex=\"\\mu \\:\\rightarrow\\: \\bar{X}\"><semantics><mrow><mi>\u03bc<\/mi><mspace width=\"0.2222em\"><\/mspace><mo stretchy=\"false\">\u2192<\/mo><mspace width=\"0.2222em\"><\/mspace><mover><mi>X<\/mi><mo stretchy=\"false\" class=\"tml-capshift\">\u203e<\/mo><\/mover><\/mrow><annotation encoding=\"application\/x-tex\">\\mu \\:\\rightarrow\\: \\bar{X}<\/annotation><\/semantics><\/math> \u3068\u3057\u3066\u3082\u305d\u306e\u5206\u6563\u306f <math data-latex=\"\\chi^2\"><semantics><msup><mi>\u03c7<\/mi><mn>2<\/mn><\/msup><annotation encoding=\"application\/x-tex\">\\chi^2<\/annotation><\/semantics><\/math> \u5206\u5e03\u306b\u5f93\u3046\u3053\u3068\u3092\u793a\u3059\u3053\u3068\u304c\u76ee\u6a19\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<p>\u3053\u3053\u3067\u6bcd\u5e73\u5747\u3092\u7528\u3044\u305f\u4e8c\u4e57\u548c\u3092\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5909\u5f62\u3059\u308b\u3002<\/p>\n\n\n\n<p class=\"has-text-align-center\"><br><math data-latex=\"\\displaystyle \\sum_{i=1}^n (X_i - \\mu)^2 \\:=\\: \\displaystyle \\sum_{i=1}^n (X_i - \\bar{X} + \\bar{X}-\\mu)^2 \\:\\:\\:=\\:\\displaystyle \\sum_{i=1}^n (X_i - \\bar{X})^2 + 2 (\\bar{X} - \\mu) \\displaystyle \\sum_{i=1}^n(X_i - \\bar{X})+\\displaystyle \\sum_{i=1}^n (\\bar{X} - \\mu)^2\\:=\\: \\displaystyle \\sum_{i=1}^n (X_i - \\bar{X})^2 + n(\\bar{X} - \\mu)^2\"><semantics><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><munderover><mo movablelimits=\"false\">\u2211<\/mo><mrow><mi>i<\/mi><mo>=<\/mo><mn>1<\/mn><\/mrow><mi>n<\/mi><\/munderover><\/mrow><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msub><mi>X<\/mi><mi>i<\/mi><\/msub><mo>\u2212<\/mo><mi>\u03bc<\/mi><msup><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><mspace width=\"0.2222em\"><\/mspace><mo>=<\/mo><mspace width=\"0.2222em\"><\/mspace><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><munderover><mo movablelimits=\"false\">\u2211<\/mo><mrow><mi>i<\/mi><mo>=<\/mo><mn>1<\/mn><\/mrow><mi>n<\/mi><\/munderover><\/mrow><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msub><mi>X<\/mi><mi>i<\/mi><\/msub><mo>\u2212<\/mo><mover><mi>X<\/mi><mo stretchy=\"false\" class=\"tml-capshift\">\u203e<\/mo><\/mover><mo>+<\/mo><mover><mi>X<\/mi><mo stretchy=\"false\" class=\"tml-capshift\">\u203e<\/mo><\/mover><mo>\u2212<\/mo><mi>\u03bc<\/mi><msup><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><mspace width=\"0.2222em\"><\/mspace><mspace width=\"0.2222em\"><\/mspace><mspace width=\"0.2222em\"><\/mspace><mo>=<\/mo><mspace width=\"0.2222em\"><\/mspace><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><munderover><mo movablelimits=\"false\">\u2211<\/mo><mrow><mi>i<\/mi><mo>=<\/mo><mn>1<\/mn><\/mrow><mi>n<\/mi><\/munderover><\/mrow><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msub><mi>X<\/mi><mi>i<\/mi><\/msub><mo>\u2212<\/mo><mover><mi>X<\/mi><mo stretchy=\"false\" class=\"tml-capshift\">\u203e<\/mo><\/mover><msup><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><mo>+<\/mo><mn>2<\/mn><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mover><mi>X<\/mi><mo stretchy=\"false\" class=\"tml-capshift\">\u203e<\/mo><\/mover><mo>\u2212<\/mo><mi>\u03bc<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><munderover><mo movablelimits=\"false\">\u2211<\/mo><mrow><mi>i<\/mi><mo>=<\/mo><mn>1<\/mn><\/mrow><mi>n<\/mi><\/munderover><\/mrow><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msub><mi>X<\/mi><mi>i<\/mi><\/msub><mo>\u2212<\/mo><mover><mi>X<\/mi><mo stretchy=\"false\" class=\"tml-capshift\">\u203e<\/mo><\/mover><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>+<\/mo><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><munderover><mo movablelimits=\"false\">\u2211<\/mo><mrow><mi>i<\/mi><mo>=<\/mo><mn>1<\/mn><\/mrow><mi>n<\/mi><\/munderover><\/mrow><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mover><mi>X<\/mi><mo stretchy=\"false\" class=\"tml-capshift\">\u203e<\/mo><\/mover><mo>\u2212<\/mo><mi>\u03bc<\/mi><msup><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><mspace width=\"0.2222em\"><\/mspace><mo>=<\/mo><mspace width=\"0.2222em\"><\/mspace><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><munderover><mo movablelimits=\"false\">\u2211<\/mo><mrow><mi>i<\/mi><mo>=<\/mo><mn>1<\/mn><\/mrow><mi>n<\/mi><\/munderover><\/mrow><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msub><mi>X<\/mi><mi>i<\/mi><\/msub><mo>\u2212<\/mo><mover><mi>X<\/mi><mo stretchy=\"false\" class=\"tml-capshift\">\u203e<\/mo><\/mover><msup><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><mo>+<\/mo><mi>n<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mover><mi>X<\/mi><mo stretchy=\"false\" class=\"tml-capshift\">\u203e<\/mo><\/mover><mo>\u2212<\/mo><mi>\u03bc<\/mi><msup><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><\/mstyle><\/mstyle><\/mstyle><\/mstyle><\/mstyle><\/mstyle><annotation encoding=\"application\/x-tex\">\\displaystyle \\sum_{i=1}^n (X_i &#8211; \\mu)^2 \\:=\\: \\displaystyle \\sum_{i=1}^n (X_i &#8211; \\bar{X} + \\bar{X}-\\mu)^2 \\:\\:\\:=\\:\\displaystyle \\sum_{i=1}^n (X_i &#8211; \\bar{X})^2 + 2 (\\bar{X} &#8211; \\mu) \\displaystyle \\sum_{i=1}^n(X_i &#8211; \\bar{X})+\\displaystyle \\sum_{i=1}^n (\\bar{X} &#8211; \\mu)^2\\:=\\: \\displaystyle \\sum_{i=1}^n (X_i &#8211; \\bar{X})^2 + n(\\bar{X} &#8211; \\mu)^2<\/annotation><\/semantics><\/math><br><\/p>\n\n\n\n<p class=\"has-text-align-center\"><br><math data-latex=\"2 (\\bar{X} - \\mu) \\displaystyle \\sum_{i=1}^n(X_i - \\bar{X})\"><semantics><mrow><mn>2<\/mn><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mover><mi>X<\/mi><mo stretchy=\"false\" class=\"tml-capshift\">\u203e<\/mo><\/mover><mo>\u2212<\/mo><mi>\u03bc<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><munderover><mo movablelimits=\"false\">\u2211<\/mo><mrow><mi>i<\/mi><mo>=<\/mo><mn>1<\/mn><\/mrow><mi>n<\/mi><\/munderover><\/mrow><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msub><mi>X<\/mi><mi>i<\/mi><\/msub><mo>\u2212<\/mo><mover><mi>X<\/mi><mo stretchy=\"false\" class=\"tml-capshift\">\u203e<\/mo><\/mover><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mstyle><\/mrow><annotation encoding=\"application\/x-tex\">2 (\\bar{X} &#8211; \\mu) \\displaystyle \\sum_{i=1}^n(X_i &#8211; \\bar{X})<\/annotation><\/semantics><\/math><br><\/p>\n\n\n\n<p>\u306b\u304a\u3044\u3066\u3001\u6a19\u672c\u5e73\u5747\u306f<\/p>\n\n\n\n<p class=\"has-text-align-center\"><br><math data-latex=\"\\bar{X}\\:=\\: \\dfrac{\\:1\\:}{\\:n\\:}\\displaystyle\\sum_{i=1}^n X_i \\:\\iff\\:n\\bar{X} \\:=\\: \\sum_{i=1}^n X_i\"><semantics><mrow><mover><mi>X<\/mi><mo stretchy=\"false\" class=\"tml-capshift\">\u203e<\/mo><\/mover><mspace width=\"0.2222em\"><\/mspace><mo>=<\/mo><mspace width=\"0.2222em\"><\/mspace><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mrow><mspace width=\"0.2222em\"><\/mspace><mn>1<\/mn><mspace width=\"0.2222em\"><\/mspace><\/mrow><mrow><mspace width=\"0.2222em\"><\/mspace><mi>n<\/mi><mspace width=\"0.2222em\"><\/mspace><\/mrow><\/mfrac><\/mstyle><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><munderover><mo movablelimits=\"false\">\u2211<\/mo><mrow><mi>i<\/mi><mo>=<\/mo><mn>1<\/mn><\/mrow><mi>n<\/mi><\/munderover><\/mrow><msub><mi>X<\/mi><mi>i<\/mi><\/msub><mspace width=\"0.2222em\"><\/mspace><mspace width=\"0.2778em\"><\/mspace><mo stretchy=\"false\">\u27fa<\/mo><mspace width=\"0.2778em\"><\/mspace><mspace width=\"0.2222em\"><\/mspace><mi>n<\/mi><mover><mi>X<\/mi><mo stretchy=\"false\" class=\"tml-capshift\">\u203e<\/mo><\/mover><mspace width=\"0.2222em\"><\/mspace><mo>=<\/mo><mspace width=\"0.2222em\"><\/mspace><mrow><munderover><mo movablelimits=\"false\">\u2211<\/mo><mrow><mi>i<\/mi><mo>=<\/mo><mn>1<\/mn><\/mrow><mi>n<\/mi><\/munderover><\/mrow><msub><mi>X<\/mi><mi>i<\/mi><\/msub><\/mstyle><\/mrow><annotation encoding=\"application\/x-tex\">\\bar{X}\\:=\\: \\dfrac{\\:1\\:}{\\:n\\:}\\displaystyle\\sum_{i=1}^n X_i \\:\\iff\\:n\\bar{X} \\:=\\: \\sum_{i=1}^n X_i<\/annotation><\/semantics><\/math><br><\/p>\n\n\n\n<p>\u3067\u3042\u308a<\/p>\n\n\n\n<p class=\"has-text-align-center\"><br><math data-latex=\"\\displaystyle \\sum_{i=1}^n(X_i - \\bar{X}) \\:=\\: \\sum_{i=1}^n X_i - n\\bar{X}\"><semantics><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><munderover><mo movablelimits=\"false\">\u2211<\/mo><mrow><mi>i<\/mi><mo>=<\/mo><mn>1<\/mn><\/mrow><mi>n<\/mi><\/munderover><\/mrow><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msub><mi>X<\/mi><mi>i<\/mi><\/msub><mo>\u2212<\/mo><mover><mi>X<\/mi><mo stretchy=\"false\" class=\"tml-capshift\">\u203e<\/mo><\/mover><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mspace width=\"0.2222em\"><\/mspace><mo>=<\/mo><mspace width=\"0.2222em\"><\/mspace><mrow><munderover><mo movablelimits=\"false\">\u2211<\/mo><mrow><mi>i<\/mi><mo>=<\/mo><mn>1<\/mn><\/mrow><mi>n<\/mi><\/munderover><\/mrow><msub><mi>X<\/mi><mi>i<\/mi><\/msub><mo>\u2212<\/mo><mi>n<\/mi><mover><mi>X<\/mi><mo stretchy=\"false\" class=\"tml-capshift\">\u203e<\/mo><\/mover><\/mstyle><annotation encoding=\"application\/x-tex\">\\displaystyle \\sum_{i=1}^n(X_i &#8211; \\bar{X}) \\:=\\: \\sum_{i=1}^n X_i &#8211; n\\bar{X}<\/annotation><\/semantics><\/math><br><\/p>\n\n\n\n<p>\u3068\u306a\u308b\u305f\u3081<\/p>\n\n\n\n<p class=\"has-text-align-center\"><br><math data-latex=\"2 (\\bar{X} - \\mu) \\displaystyle \\sum_{i=1}^n(X_i - \\bar{X})\\:=\\:0\"><semantics><mrow><mn>2<\/mn><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mover><mi>X<\/mi><mo stretchy=\"false\" class=\"tml-capshift\">\u203e<\/mo><\/mover><mo>\u2212<\/mo><mi>\u03bc<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><munderover><mo movablelimits=\"false\">\u2211<\/mo><mrow><mi>i<\/mi><mo>=<\/mo><mn>1<\/mn><\/mrow><mi>n<\/mi><\/munderover><\/mrow><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msub><mi>X<\/mi><mi>i<\/mi><\/msub><mo>\u2212<\/mo><mover><mi>X<\/mi><mo stretchy=\"false\" class=\"tml-capshift\">\u203e<\/mo><\/mover><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mspace width=\"0.2222em\"><\/mspace><mo>=<\/mo><mspace width=\"0.2222em\"><\/mspace><mn>0<\/mn><\/mstyle><\/mrow><annotation encoding=\"application\/x-tex\">2 (\\bar{X} &#8211; \\mu) \\displaystyle \\sum_{i=1}^n(X_i &#8211; \\bar{X})\\:=\\:0<\/annotation><\/semantics><\/math><br><\/p>\n\n\n\n<p>\u3067\u3042\u308b\u3002\u3064\u307e\u308a<\/p>\n\n\n\n<p class=\"has-text-align-center\"><br><math data-latex=\"\\displaystyle \\sum_{i=1}^n(X_i - \\mu)^2 \\:=\\: \\sum_{i=1}^n (X_i - \\bar{X})^2 + n(\\bar{X}-\\mu)^2\"><semantics><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><munderover><mo movablelimits=\"false\">\u2211<\/mo><mrow><mi>i<\/mi><mo>=<\/mo><mn>1<\/mn><\/mrow><mi>n<\/mi><\/munderover><\/mrow><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msub><mi>X<\/mi><mi>i<\/mi><\/msub><mo>\u2212<\/mo><mi>\u03bc<\/mi><msup><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><mspace width=\"0.2222em\"><\/mspace><mo>=<\/mo><mspace width=\"0.2222em\"><\/mspace><mrow><munderover><mo movablelimits=\"false\">\u2211<\/mo><mrow><mi>i<\/mi><mo>=<\/mo><mn>1<\/mn><\/mrow><mi>n<\/mi><\/munderover><\/mrow><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msub><mi>X<\/mi><mi>i<\/mi><\/msub><mo>\u2212<\/mo><mover><mi>X<\/mi><mo stretchy=\"false\" class=\"tml-capshift\">\u203e<\/mo><\/mover><msup><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><mo>+<\/mo><mi>n<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mover><mi>X<\/mi><mo stretchy=\"false\" class=\"tml-capshift\">\u203e<\/mo><\/mover><mo>\u2212<\/mo><mi>\u03bc<\/mi><msup><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><\/mstyle><annotation encoding=\"application\/x-tex\">\\displaystyle \\sum_{i=1}^n(X_i &#8211; \\mu)^2 \\:=\\: \\sum_{i=1}^n (X_i &#8211; \\bar{X})^2 + n(\\bar{X}-\\mu)^2<\/annotation><\/semantics><\/math><br><\/p>\n\n\n\n<p>\u3067\u3042\u308a\u3001\u4e0a\u5f0f\u306e\u4e21\u8fba\u3092 <math data-latex=\"\\sigma^2\"><semantics><msup><mi>\u03c3<\/mi><mn>2<\/mn><\/msup><annotation encoding=\"application\/x-tex\">\\sigma^2<\/annotation><\/semantics><\/math> \u3067\u5272\u308b\u3068<\/p>\n\n\n\n<p class=\"has-text-align-center\"><br><math data-latex=\"\\dfrac{\\:1\\:}{\\:\\sigma^2\\:}\\displaystyle\\sum_{i=1}^n(X_i - \\mu)^2 \\:=\\: \\dfrac{\\:1\\:}{\\:\\sigma^2\\:}\\sum_{i=1}^n (X_i - \\bar{X})^2 + \\dfrac{\\:n(\\bar{X}-\\mu)^2\\:}{\\:\\sigma^2\\:}\"><semantics><mrow><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mrow><mspace width=\"0.2222em\"><\/mspace><mn>1<\/mn><mspace width=\"0.2222em\"><\/mspace><\/mrow><mrow><mspace width=\"0.2222em\"><\/mspace><msup><mi>\u03c3<\/mi><mn>2<\/mn><\/msup><mspace width=\"0.2222em\"><\/mspace><\/mrow><\/mfrac><\/mstyle><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><munderover><mo movablelimits=\"false\">\u2211<\/mo><mrow><mi>i<\/mi><mo>=<\/mo><mn>1<\/mn><\/mrow><mi>n<\/mi><\/munderover><\/mrow><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msub><mi>X<\/mi><mi>i<\/mi><\/msub><mo>\u2212<\/mo><mi>\u03bc<\/mi><msup><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><mspace width=\"0.2222em\"><\/mspace><mo>=<\/mo><mspace width=\"0.2222em\"><\/mspace><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mrow><mspace width=\"0.2222em\"><\/mspace><mn>1<\/mn><mspace width=\"0.2222em\"><\/mspace><\/mrow><mrow><mspace width=\"0.2222em\"><\/mspace><msup><mi>\u03c3<\/mi><mn>2<\/mn><\/msup><mspace width=\"0.2222em\"><\/mspace><\/mrow><\/mfrac><\/mstyle><mrow><munderover><mo movablelimits=\"false\">\u2211<\/mo><mrow><mi>i<\/mi><mo>=<\/mo><mn>1<\/mn><\/mrow><mi>n<\/mi><\/munderover><\/mrow><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msub><mi>X<\/mi><mi>i<\/mi><\/msub><mo>\u2212<\/mo><mover><mi>X<\/mi><mo stretchy=\"false\" class=\"tml-capshift\">\u203e<\/mo><\/mover><msup><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><mo>+<\/mo><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mrow><mspace width=\"0.2222em\"><\/mspace><mi>n<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mover><mi>X<\/mi><mo stretchy=\"false\" class=\"tml-capshift\">\u203e<\/mo><\/mover><mo>\u2212<\/mo><mi>\u03bc<\/mi><msup><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><mspace width=\"0.2222em\"><\/mspace><\/mrow><mrow><mspace width=\"0.2222em\"><\/mspace><msup><mi>\u03c3<\/mi><mn>2<\/mn><\/msup><mspace width=\"0.2222em\"><\/mspace><\/mrow><\/mfrac><\/mstyle><\/mstyle><\/mrow><annotation encoding=\"application\/x-tex\">\\dfrac{\\:1\\:}{\\:\\sigma^2\\:}\\displaystyle\\sum_{i=1}^n(X_i &#8211; \\mu)^2 \\:=\\: \\dfrac{\\:1\\:}{\\:\\sigma^2\\:}\\sum_{i=1}^n (X_i &#8211; \\bar{X})^2 + \\dfrac{\\:n(\\bar{X}-\\mu)^2\\:}{\\:\\sigma^2\\:}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p>\u3068\u306a\u308b\u3002\u5de6\u8fba\u306f\u81ea\u7531\u5ea6 <math data-latex=\"n\"><semantics><mi>n<\/mi><annotation encoding=\"application\/x-tex\">n<\/annotation><\/semantics><\/math> \u306e <math data-latex=\"\\chi^2\"><semantics><msup><mi>\u03c7<\/mi><mn>2<\/mn><\/msup><annotation encoding=\"application\/x-tex\">\\chi^2<\/annotation><\/semantics><\/math> \u5206\u5e03\u306b\u5f93\u3044\u3001\u53f3\u8fba\u306e\u7b2c\u4e8c\u9805\u306b\u304a\u3044\u3066\u3082\u305d\u306e\u5e73\u65b9\u6839\u3092\u53d6\u308b\u3068<\/p>\n\n\n\n<p class=\"has-text-align-center\"><br><math data-latex=\"\\dfrac{\\:\\bar{X}-\\mu\\:}{\\:\\sigma\/\\sqrt{n}\\:} \\sim N(0,\\:1)\"><semantics><mrow><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mrow><mspace width=\"0.2222em\"><\/mspace><mover><mi>X<\/mi><mo stretchy=\"false\" class=\"tml-capshift\">\u203e<\/mo><\/mover><mo>\u2212<\/mo><mi>\u03bc<\/mi><mspace width=\"0.2222em\"><\/mspace><\/mrow><mrow><mspace width=\"0.2222em\"><\/mspace><mi>\u03c3<\/mi><mi>\/<\/mi><msqrt><mi>n<\/mi><\/msqrt><mspace width=\"0.2222em\"><\/mspace><\/mrow><\/mfrac><\/mstyle><mo>\u223c<\/mo><mi>N<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>0<\/mn><mo separator=\"true\">,<\/mo><mspace width=\"0.2222em\"><\/mspace><mn>1<\/mn><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">\\dfrac{\\:\\bar{X}-\\mu\\:}{\\:\\sigma\/\\sqrt{n}\\:} \\sim N(0,\\:1)<\/annotation><\/semantics><\/math><br><\/p>\n\n\n\n<p>\u3068\u6a19\u6e96\u6b63\u898f\u5206\u5e03\u306b\u5f93\u3046\u305f\u3081\u3001<\/p>\n\n\n\n<p class=\"has-text-align-center\"><br><math data-latex=\"\\dfrac{\\:n(\\bar{X}-\\mu)^2\\:}{\\:\\sigma^2\\:} \\sim \\chi_1^2\"><semantics><mrow><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mrow><mspace width=\"0.2222em\"><\/mspace><mi>n<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mover><mi>X<\/mi><mo stretchy=\"false\" class=\"tml-capshift\">\u203e<\/mo><\/mover><mo>\u2212<\/mo><mi>\u03bc<\/mi><msup><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><mspace width=\"0.2222em\"><\/mspace><\/mrow><mrow><mspace width=\"0.2222em\"><\/mspace><msup><mi>\u03c3<\/mi><mn>2<\/mn><\/msup><mspace width=\"0.2222em\"><\/mspace><\/mrow><\/mfrac><\/mstyle><mo>\u223c<\/mo><msubsup><mi>\u03c7<\/mi><mn>1<\/mn><mn>2<\/mn><\/msubsup><\/mrow><annotation encoding=\"application\/x-tex\">\\dfrac{\\:n(\\bar{X}-\\mu)^2\\:}{\\:\\sigma^2\\:} \\sim \\chi_1^2<\/annotation><\/semantics><\/math><br><\/p>\n\n\n\n<p>\u3068\u81ea\u7531\u5ea6 1 \u306e <math data-latex=\"\\chi^2\"><semantics><msup><mi>\u03c7<\/mi><mn>2<\/mn><\/msup><annotation encoding=\"application\/x-tex\">\\chi^2<\/annotation><\/semantics><\/math> \u5206\u5e03\u3078\u5f93\u3046\u3002\u3053\u3053\u3067\u6b63\u898f\u6bcd\u96c6\u56e3\u3067\u306f\u3001<math data-latex=\"\\bar{X}\"><semantics><mover><mi>X<\/mi><mo stretchy=\"false\" class=\"tml-capshift\">\u203e<\/mo><\/mover><annotation encoding=\"application\/x-tex\">\\bar{X}<\/annotation><\/semantics><\/math> \u3068 <math data-latex=\"S^2\"><semantics><msup><mi>S<\/mi><mn>2<\/mn><\/msup><annotation encoding=\"application\/x-tex\">S^2<\/annotation><\/semantics><\/math> \u306f\u72ec\u7acb\u3068\u306a\u308b\u306e\u3067\u3001<\/p>\n\n\n\n<p>\u4e8c\u4e57\u548c\u306e\u81ea\u7531\u5ea6\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5206\u89e3\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002<\/p>\n\n\n\n<p class=\"has-text-align-center\"><br><math data-latex=\"\\chi^2_n \\:=\\: \\chi_{n-1}^2 \\:+\\:\\chi_1^2 \ufeff\"><semantics><mrow><msubsup><mi>\u03c7<\/mi><mi>n<\/mi><mn>2<\/mn><\/msubsup><mspace width=\"0.2222em\"><\/mspace><mo>=<\/mo><mspace width=\"0.2222em\"><\/mspace><msubsup><mi>\u03c7<\/mi><mrow><mi>n<\/mi><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><mn>2<\/mn><\/msubsup><mspace width=\"0.2222em\"><\/mspace><mo>+<\/mo><mspace width=\"0.2222em\"><\/mspace><msubsup><mi>\u03c7<\/mi><mn>1<\/mn><mn>2<\/mn><\/msubsup><mtext>\ufeff<\/mtext><\/mrow><annotation encoding=\"application\/x-tex\">\\chi^2_n \\:=\\: \\chi_{n-1}^2 \\:+\\:\\chi_1^2 \ufeff<\/annotation><\/semantics><\/math><br><\/p>\n\n\n\n<p>\u3057\u305f\u304c\u3063\u3066\u6b8b\u308a\u306e\u7b2c\u4e00\u9805\u306f\u81ea\u7531\u5ea6 <math data-latex=\"n-1\"><semantics><mrow><mi>n<\/mi><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">n-1<\/annotation><\/semantics><\/math> \u306e <math data-latex=\"\\chi^2\"><semantics><msup><mi>\u03c7<\/mi><mn>2<\/mn><\/msup><annotation encoding=\"application\/x-tex\">\\chi^2<\/annotation><\/semantics><\/math> \u5206\u5e03\u306b\u5f93\u3046\u3053\u3068\u306b\u306a\u308b\u3002<\/p>\n\n\n\n<p>\u3088\u3063\u3066<\/p>\n\n\n\n<p class=\"has-text-align-center\"><br><math data-latex=\"\\dfrac{\\:(n-1)S^2\\:}{\\:\\sigma^2\\:} \\sim \\chi_{n-1}^2\"><semantics><mrow><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mrow><mspace width=\"0.2222em\"><\/mspace><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>n<\/mi><mo>\u2212<\/mo><mn>1<\/mn><mo form=\"postfix\" stretchy=\"false\">)<\/mo><msup><mi>S<\/mi><mn>2<\/mn><\/msup><mspace width=\"0.2222em\"><\/mspace><\/mrow><mrow><mspace width=\"0.2222em\"><\/mspace><msup><mi>\u03c3<\/mi><mn>2<\/mn><\/msup><mspace width=\"0.2222em\"><\/mspace><\/mrow><\/mfrac><\/mstyle><mo>\u223c<\/mo><msubsup><mi>\u03c7<\/mi><mrow><mi>n<\/mi><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><mn>2<\/mn><\/msubsup><\/mrow><annotation encoding=\"application\/x-tex\">\\dfrac{\\:(n-1)S^2\\:}{\\:\\sigma^2\\:} \\sim \\chi_{n-1}^2<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p>\u3068\u306a\u308b\u3002\u672c\u6765\u4e0d\u660e\u3067\u3042\u308b\u6bcd\u5e73\u5747 <math data-latex=\"\\mu\"><semantics><mi>\u03bc<\/mi><annotation encoding=\"application\/x-tex\">\\mu<\/annotation><\/semantics><\/math> \u3092\u6a19\u672c\u5e73\u5747 <math data-latex=\"\\bar{X}\"><semantics><mover><mi>X<\/mi><mo stretchy=\"false\" class=\"tml-capshift\">\u203e<\/mo><\/mover><annotation encoding=\"application\/x-tex\">\\bar{X}<\/annotation><\/semantics><\/math> \u3067\u63a8\u5b9a\u3059\u308b\u305f\u3081\u306b\u3001\u81ea\u7531\u5ea6\u3092 1 \u3064\u4f7f\u3046\u3002\u305d\u306e\u305f\u3081\u3001\u6a19\u672c\u5e73\u5747\u3092\u7528\u3044\u3066\u504f\u5dee\u306e\u4e8c\u4e57\u548c\u3092\u63a8\u5b9a\u3057\u3088\u3046\u3068\u3059\u308b\u3068\u305d\u306e\u81ea\u7531\u5ea6\u306f <math data-latex=\"n-1\"><semantics><mrow><mi>n<\/mi><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">n-1<\/annotation><\/semantics><\/math> \u306b\u306a\u308b\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u6bcd\u5206\u6563\u304c\u672a\u77e5\u306e\u5834\u5408\u306e\u63a8\u5b9a<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\"><math data-latex=\"t\"><semantics><mi>t<\/mi><annotation encoding=\"application\/x-tex\">t<\/annotation><\/semantics><\/math> \u5206\u5e03<\/h3>\n\n\n\n<p>\u6bcd\u5e73\u5747 <math data-latex=\"\\mu\"><semantics><mi>\u03bc<\/mi><annotation encoding=\"application\/x-tex\">\\mu<\/annotation><\/semantics><\/math> \u3092\u691c\u5b9a\u3057\u305f\u3044\u3082\u306e\u3068\u3059\u308b\u3002\u6bcd\u5206\u6563 <math data-latex=\"\\sigma^2\"><semantics><msup><mi>\u03c3<\/mi><mn>2<\/mn><\/msup><annotation encoding=\"application\/x-tex\">\\sigma^2<\/annotation><\/semantics><\/math> \u304c\u65e2\u77e5\u3067\u3042\u308c\u3070\u3001\u6a19\u672c\u5e73\u5747\u306e\u6a19\u6e96\u5316<\/p>\n\n\n\n<p class=\"has-text-align-center\"><br><math data-latex=\"Z\\:=\\: \\dfrac{\\:\\bar{X}- \\mu\\:}{\\:\\sigma\/ \\sqrt{n}\\:}\"><semantics><mrow><mi>Z<\/mi><mspace width=\"0.2222em\"><\/mspace><mo>=<\/mo><mspace width=\"0.2222em\"><\/mspace><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mrow><mspace width=\"0.2222em\"><\/mspace><mover><mi>X<\/mi><mo stretchy=\"false\" class=\"tml-capshift\">\u203e<\/mo><\/mover><mo>\u2212<\/mo><mi>\u03bc<\/mi><mspace width=\"0.2222em\"><\/mspace><\/mrow><mrow><mspace width=\"0.2222em\"><\/mspace><mi>\u03c3<\/mi><mi>\/<\/mi><msqrt><mi>n<\/mi><\/msqrt><mspace width=\"0.2222em\"><\/mspace><\/mrow><\/mfrac><\/mstyle><\/mrow><annotation encoding=\"application\/x-tex\">Z\\:=\\: \\dfrac{\\:\\bar{X}- \\mu\\:}{\\:\\sigma\/ \\sqrt{n}\\:}<\/annotation><\/semantics><\/math><br><\/p>\n\n\n\n<p>\u306f\u6a19\u6e96\u6b63\u898f\u5206\u5e03\u306b\u5f93\u3046\u3002<\/p>\n\n\n\n<p class=\"has-text-align-center\"><br><math data-latex=\"Z\\sim N(0,\\:1)\"><semantics><mrow><mi>Z<\/mi><mo>\u223c<\/mo><mi>N<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>0<\/mn><mo separator=\"true\">,<\/mo><mspace width=\"0.2222em\"><\/mspace><mn>1<\/mn><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">Z\\sim N(0,\\:1)<\/annotation><\/semantics><\/math><br><\/p>\n\n\n\n<p>\u3057\u304b\u3057\u6bcd\u5206\u6563 <math data-latex=\"\\sigma^2\"><semantics><msup><mi>\u03c3<\/mi><mn>2<\/mn><\/msup><annotation encoding=\"application\/x-tex\">\\sigma^2<\/annotation><\/semantics><\/math> \u304c\u65e2\u77e5\u3067\u3042\u308b\u3053\u3068\u306f\u7a00\u3067\u3042\u308a\u3001\u672a\u77e5\u306e <math data-latex=\"\\sigma\"><semantics><mi>\u03c3<\/mi><annotation encoding=\"application\/x-tex\">\\sigma<\/annotation><\/semantics><\/math> \u306e\u4ee3\u308f\u308a\u306b\u6a19\u672c\u6a19\u6e96\u504f\u5dee <math data-latex=\"S\"><semantics><mi>S<\/mi><annotation encoding=\"application\/x-tex\">S<\/annotation><\/semantics><\/math> \u3092\u4f7f\u3046\u5fc5\u8981\u304c\u3042\u308b\u3002<\/p>\n\n\n\n<p class=\"has-text-align-center\"><br><math data-latex=\"T\\:=\\:\\dfrac{\\:\\bar{X}-\\mu\\:}{S\/\\sqrt{n}}\"><semantics><mrow><mi>T<\/mi><mspace width=\"0.2222em\"><\/mspace><mo>=<\/mo><mspace width=\"0.2222em\"><\/mspace><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mrow><mspace width=\"0.2222em\"><\/mspace><mover><mi>X<\/mi><mo stretchy=\"false\" class=\"tml-capshift\">\u203e<\/mo><\/mover><mo>\u2212<\/mo><mi>\u03bc<\/mi><mspace width=\"0.2222em\"><\/mspace><\/mrow><mrow><mi>S<\/mi><mi>\/<\/mi><msqrt><mi>n<\/mi><\/msqrt><\/mrow><\/mfrac><\/mstyle><\/mrow><annotation encoding=\"application\/x-tex\">T\\:=\\:\\dfrac{\\:\\bar{X}-\\mu\\:}{S\/\\sqrt{n}}<\/annotation><\/semantics><\/math><br><\/p>\n\n\n\n<p>\u4e0a\u5f0f\u306b\u304a\u3044\u3066\u3001\u6a19\u672c\u6a19\u6e96\u504f\u5dee <math data-latex=\"S\"><semantics><mi>S<\/mi><annotation encoding=\"application\/x-tex\">S<\/annotation><\/semantics><\/math> \u306b\u306f\u63a8\u5b9a\u8aa4\u5dee\u304c\u542b\u307e\u308c\u308b\u3002\u3057\u305f\u304c\u3063\u3066 <math data-latex=\"T\"><semantics><mi>T<\/mi><annotation encoding=\"application\/x-tex\">T<\/annotation><\/semantics><\/math> \u306f\u6a19\u6e96\u6b63\u898f\u5206\u5e03\u3088\u308a\u3082\u88fe\u304c\u539a\u3044\u5206\u5e03\u306b\u306a\u308b\u3002\u3053\u308c\u304c <math data-latex=\"t\"><semantics><mi>t<\/mi><annotation encoding=\"application\/x-tex\">t<\/annotation><\/semantics><\/math> \u5206\u5e03\u3067\u3042\u308b\u3002<math data-latex=\"\\sigma \\to S\"><semantics><mrow><mi>\u03c3<\/mi><mo>\u2192<\/mo><mi>S<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\sigma \\to S<\/annotation><\/semantics><\/math> \u3068\u7f6e\u304d\u63db\u3048\u308b\u3068\u3001 <math data-latex=\"S\"><semantics><mi>S<\/mi><annotation encoding=\"application\/x-tex\">S<\/annotation><\/semantics><\/math> \u306f\u6a19\u672c\u3054\u3068\u306b\u5024\u304c\u5909\u5316\u3059\u308b\u78ba\u7387\u5909\u6570\u3067\u3042\u308b\u3002\u3057\u305f\u304c\u3063\u3066\u7d71\u8a08\u91cf <math data-latex=\"T\"><semantics><mi>T<\/mi><annotation encoding=\"application\/x-tex\">T<\/annotation><\/semantics><\/math> \u306b\u306f <math data-latex=\"S\"><semantics><mi>S<\/mi><annotation encoding=\"application\/x-tex\">S<\/annotation><\/semantics><\/math> \u3092\u63a8\u5b9a\u3059\u308b\u3053\u3068\u306b\u3088\u308b\u4e0d\u78ba\u5b9f\u6027\u3082\u542b\u307e\u308c\u308b\u3053\u3068\u306b\u306a\u308b\u3002\u4ee5\u4e0b\u3067\u306f\u3053\u306e\u7d71\u8a08\u91cf\u304c\u3069\u3093\u306a\u5206\u5e03\u306b\u5f93\u3046\u304b\u3092\u3001\u524d\u7ae0\u3067\u6271\u3063\u305f <math data-latex=\"\\chi^2\"><semantics><msup><mi>\u03c7<\/mi><mn>2<\/mn><\/msup><annotation encoding=\"application\/x-tex\">\\chi^2<\/annotation><\/semantics><\/math> \u5206\u5e03\u3068\u306e\u95a2\u4fc2\u304b\u3089\u78ba\u8a8d\u3059\u308b\u3002<\/p>\n\n\n\n<p>\u524d\u7ae0\u306b\u304a\u3044\u3066\u6a19\u672c\u5206\u6563\u306b\u3064\u3044\u3066\u306f\u3001<\/p>\n\n\n\n<p class=\"has-text-align-center\"><br><math data-latex=\"\\dfrac{\\:(n-1)S^2\\:}{\\:\\sigma^2\\:} \\sim \\chi_{n-1}^2\"><semantics><mrow><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mrow><mspace width=\"0.2222em\"><\/mspace><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>n<\/mi><mo>\u2212<\/mo><mn>1<\/mn><mo form=\"postfix\" stretchy=\"false\">)<\/mo><msup><mi>S<\/mi><mn>2<\/mn><\/msup><mspace width=\"0.2222em\"><\/mspace><\/mrow><mrow><mspace width=\"0.2222em\"><\/mspace><msup><mi>\u03c3<\/mi><mn>2<\/mn><\/msup><mspace width=\"0.2222em\"><\/mspace><\/mrow><\/mfrac><\/mstyle><mo>\u223c<\/mo><msubsup><mi>\u03c7<\/mi><mrow><mi>n<\/mi><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><mn>2<\/mn><\/msubsup><\/mrow><annotation encoding=\"application\/x-tex\">\\dfrac{\\:(n-1)S^2\\:}{\\:\\sigma^2\\:} \\sim \\chi_{n-1}^2<\/annotation><\/semantics><\/math><br><\/p>\n\n\n\n<p>\u304c\u6210\u308a\u7acb\u3064\u3053\u3068\u304c\u78ba\u8a8d\u3067\u304d\u305f\u3002\u3053\u3053\u3067<\/p>\n\n\n\n<p class=\"has-text-align-center\"><br><math data-latex=\"U\\:=\\: \\dfrac{\\:(n-1)S^2\\:}{\\sigma^2}\"><semantics><mrow><mi>U<\/mi><mspace width=\"0.2222em\"><\/mspace><mo>=<\/mo><mspace width=\"0.2222em\"><\/mspace><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mrow><mspace width=\"0.2222em\"><\/mspace><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>n<\/mi><mo>\u2212<\/mo><mn>1<\/mn><mo form=\"postfix\" stretchy=\"false\">)<\/mo><msup><mi>S<\/mi><mn>2<\/mn><\/msup><mspace width=\"0.2222em\"><\/mspace><\/mrow><msup><mi>\u03c3<\/mi><mn>2<\/mn><\/msup><\/mfrac><\/mstyle><\/mrow><annotation encoding=\"application\/x-tex\">U\\:=\\: \\dfrac{\\:(n-1)S^2\\:}{\\sigma^2}<\/annotation><\/semantics><\/math><br><\/p>\n\n\n\n<p>\u306f\u81ea\u7531\u5ea6 <math data-latex=\"n-1\"><semantics><mrow><mi>n<\/mi><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">n-1<\/annotation><\/semantics><\/math> \u306e <math data-latex=\"\\chi^2\"><semantics><msup><mi>\u03c7<\/mi><mn>2<\/mn><\/msup><annotation encoding=\"application\/x-tex\">\\chi^2<\/annotation><\/semantics><\/math> \u5206\u5e03\u306b\u5f93\u3044<\/p>\n\n\n\n<p class=\"has-text-align-center\"><br><math data-latex=\"U\\sim \\chi^2(n-1)\"><semantics><mrow><mi>U<\/mi><mo>\u223c<\/mo><msup><mi>\u03c7<\/mi><mn>2<\/mn><\/msup><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>n<\/mi><mo>\u2212<\/mo><mn>1<\/mn><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">U\\sim \\chi^2(n-1)<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p>\u3067\u3042\u308b\u3002\u3053\u306e <math data-latex=\"U\"><semantics><mi>U<\/mi><annotation encoding=\"application\/x-tex\">U<\/annotation><\/semantics><\/math> \u3092 <math data-latex=\"n-1\"><semantics><mrow><mi>n<\/mi><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">n-1<\/annotation><\/semantics><\/math> \u3067\u5272\u3063\u305f\u5f8c\u5e73\u65b9\u6839\u3092\u53d6\u308b\u3068<\/p>\n\n\n\n<p class=\"has-text-align-center\"><br><math data-latex=\"\\sqrt{\\dfrac{\\:U\\:}{\\:n-1\\:}} \\:=\\: \\sqrt{\\dfrac{\\:1\\:}{\\:n-1\\:}\\cdot \\dfrac{\\:(n-1)S^2\\:}{\\:\\sigma^2\\:}} \\:=\\: \\sqrt{\\dfrac{\\:S^2\\:}{\\:\\sigma^2\\:}}\\:=\\: \\dfrac{\\:S\\:}{\\:\\sigma\\:}\"><semantics><mrow><msqrt><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mrow><mspace width=\"0.2222em\"><\/mspace><mi>U<\/mi><mspace width=\"0.2222em\"><\/mspace><\/mrow><mrow><mspace width=\"0.2222em\"><\/mspace><mi>n<\/mi><mo>\u2212<\/mo><mn>1<\/mn><mspace width=\"0.2222em\"><\/mspace><\/mrow><\/mfrac><\/mstyle><\/msqrt><mspace width=\"0.2222em\"><\/mspace><mo>=<\/mo><mspace width=\"0.2222em\"><\/mspace><msqrt><mrow><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mrow><mspace width=\"0.2222em\"><\/mspace><mn>1<\/mn><mspace width=\"0.2222em\"><\/mspace><\/mrow><mrow><mspace width=\"0.2222em\"><\/mspace><mi>n<\/mi><mo>\u2212<\/mo><mn>1<\/mn><mspace width=\"0.2222em\"><\/mspace><\/mrow><\/mfrac><\/mstyle><mo>\u22c5<\/mo><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mrow><mspace width=\"0.2222em\"><\/mspace><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>n<\/mi><mo>\u2212<\/mo><mn>1<\/mn><mo form=\"postfix\" stretchy=\"false\">)<\/mo><msup><mi>S<\/mi><mn>2<\/mn><\/msup><mspace width=\"0.2222em\"><\/mspace><\/mrow><mrow><mspace width=\"0.2222em\"><\/mspace><msup><mi>\u03c3<\/mi><mn>2<\/mn><\/msup><mspace width=\"0.2222em\"><\/mspace><\/mrow><\/mfrac><\/mstyle><\/mrow><\/msqrt><mspace width=\"0.2222em\"><\/mspace><mo>=<\/mo><mspace width=\"0.2222em\"><\/mspace><msqrt><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mrow><mspace width=\"0.2222em\"><\/mspace><msup><mi>S<\/mi><mn>2<\/mn><\/msup><mspace width=\"0.2222em\"><\/mspace><\/mrow><mrow><mspace width=\"0.2222em\"><\/mspace><msup><mi>\u03c3<\/mi><mn>2<\/mn><\/msup><mspace width=\"0.2222em\"><\/mspace><\/mrow><\/mfrac><\/mstyle><\/msqrt><mspace width=\"0.2222em\"><\/mspace><mo>=<\/mo><mspace width=\"0.2222em\"><\/mspace><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mrow><mspace width=\"0.2222em\"><\/mspace><mi>S<\/mi><mspace width=\"0.2222em\"><\/mspace><\/mrow><mrow><mspace width=\"0.2222em\"><\/mspace><mi>\u03c3<\/mi><mspace width=\"0.2222em\"><\/mspace><\/mrow><\/mfrac><\/mstyle><\/mrow><annotation encoding=\"application\/x-tex\">\\sqrt{\\dfrac{\\:U\\:}{\\:n-1\\:}} \\:=\\: \\sqrt{\\dfrac{\\:1\\:}{\\:n-1\\:}\\cdot \\dfrac{\\:(n-1)S^2\\:}{\\:\\sigma^2\\:}} \\:=\\: \\sqrt{\\dfrac{\\:S^2\\:}{\\:\\sigma^2\\:}}\\:=\\: \\dfrac{\\:S\\:}{\\:\\sigma\\:}<\/annotation><\/semantics><\/math><br><\/p>\n\n\n\n<p>\u3053\u3053\u3067\u3001\u6bcd\u6a19\u6e96\u504f\u5dee\u304c\u65e2\u77e5\u306e\u5834\u5408\u306b\u7528\u3044\u305f\u6a19\u6e96\u6b63\u898f\u5909\u6570<\/p>\n\n\n\n<p class=\"has-text-align-center\"><br><math data-latex=\"Z\\:=\\: \\dfrac{\\:\\bar{X}- \\mu\\:}{\\:\\sigma\/ \\sqrt{n}\\:}\"><semantics><mrow><mi>Z<\/mi><mspace width=\"0.2222em\"><\/mspace><mo>=<\/mo><mspace width=\"0.2222em\"><\/mspace><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mrow><mspace width=\"0.2222em\"><\/mspace><mover><mi>X<\/mi><mo stretchy=\"false\" class=\"tml-capshift\">\u203e<\/mo><\/mover><mo>\u2212<\/mo><mi>\u03bc<\/mi><mspace width=\"0.2222em\"><\/mspace><\/mrow><mrow><mspace width=\"0.2222em\"><\/mspace><mi>\u03c3<\/mi><mi>\/<\/mi><msqrt><mi>n<\/mi><\/msqrt><mspace width=\"0.2222em\"><\/mspace><\/mrow><\/mfrac><\/mstyle><\/mrow><annotation encoding=\"application\/x-tex\">Z\\:=\\: \\dfrac{\\:\\bar{X}- \\mu\\:}{\\:\\sigma\/ \\sqrt{n}\\:}<\/annotation><\/semantics><\/math><br><\/p>\n\n\n\n<p>\u3092\u5148\u307b\u3069\u6c42\u3081\u305f <math data-latex=\"S\/\\sigma\"><semantics><mrow><mi>S<\/mi><mi>\/<\/mi><mi>\u03c3<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">S\/\\sigma<\/annotation><\/semantics><\/math> \u3067\u5272\u308b\u3068<\/p>\n\n\n\n<p class=\"has-text-align-center\"><br><math data-latex=\"\\dfrac{\\:Z\\:}{\\:\\sqrt{U\/(n-1)}\\:} \\:=\\: \\dfrac{\\:\\dfrac{\\:\\bar{X}- \\mu\\:}{\\:\\sigma\/\\sqrt{n}\\:}\\:}{\\:\\dfrac{\\:S\\:}{\\:\\sigma\\:}\\:}=\\dfrac{\\:\\bar{X}- \\mu\\:}{\\:\\sigma\/\\sqrt{n}\\:}\\cdot \\dfrac{\\:\\sigma\\:}{\\:S\\:} \\:=\\:\\dfrac{\\:\\bar{X}- \\mu\\:}{\\:S\/\\sqrt{n}\\:}\"><semantics><mrow><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mrow><mspace width=\"0.2222em\"><\/mspace><mi>Z<\/mi><mspace width=\"0.2222em\"><\/mspace><\/mrow><mrow><mspace width=\"0.2222em\"><\/mspace><msqrt><mrow><mi>U<\/mi><mi>\/<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>n<\/mi><mo>\u2212<\/mo><mn>1<\/mn><mo form=\"postfix\" stretchy=\"false\" lspace=\"0em\" rspace=\"0em\">)<\/mo><\/mrow><\/msqrt><mspace width=\"0.2222em\"><\/mspace><\/mrow><\/mfrac><\/mstyle><mspace width=\"0.2222em\"><\/mspace><mo>=<\/mo><mspace width=\"0.2222em\"><\/mspace><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mrow><mspace width=\"0.2222em\"><\/mspace><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mrow><mspace width=\"0.2222em\"><\/mspace><mover><mi>X<\/mi><mo stretchy=\"false\" class=\"tml-capshift\">\u203e<\/mo><\/mover><mo>\u2212<\/mo><mi>\u03bc<\/mi><mspace width=\"0.2222em\"><\/mspace><\/mrow><mrow><mspace width=\"0.2222em\"><\/mspace><mi>\u03c3<\/mi><mi>\/<\/mi><msqrt><mi>n<\/mi><\/msqrt><mspace width=\"0.2222em\"><\/mspace><\/mrow><\/mfrac><\/mstyle><mspace width=\"0.2222em\"><\/mspace><\/mrow><mrow><mspace width=\"0.2222em\"><\/mspace><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mrow><mspace width=\"0.2222em\"><\/mspace><mi>S<\/mi><mspace width=\"0.2222em\"><\/mspace><\/mrow><mrow><mspace width=\"0.2222em\"><\/mspace><mi>\u03c3<\/mi><mspace width=\"0.2222em\"><\/mspace><\/mrow><\/mfrac><\/mstyle><mspace width=\"0.2222em\"><\/mspace><\/mrow><\/mfrac><\/mstyle><mo>=<\/mo><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mrow><mspace width=\"0.2222em\"><\/mspace><mover><mi>X<\/mi><mo stretchy=\"false\" class=\"tml-capshift\">\u203e<\/mo><\/mover><mo>\u2212<\/mo><mi>\u03bc<\/mi><mspace width=\"0.2222em\"><\/mspace><\/mrow><mrow><mspace width=\"0.2222em\"><\/mspace><mi>\u03c3<\/mi><mi>\/<\/mi><msqrt><mi>n<\/mi><\/msqrt><mspace width=\"0.2222em\"><\/mspace><\/mrow><\/mfrac><\/mstyle><mo>\u22c5<\/mo><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mrow><mspace width=\"0.2222em\"><\/mspace><mi>\u03c3<\/mi><mspace width=\"0.2222em\"><\/mspace><\/mrow><mrow><mspace width=\"0.2222em\"><\/mspace><mi>S<\/mi><mspace width=\"0.2222em\"><\/mspace><\/mrow><\/mfrac><\/mstyle><mspace width=\"0.2222em\"><\/mspace><mo>=<\/mo><mspace width=\"0.2222em\"><\/mspace><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mrow><mspace width=\"0.2222em\"><\/mspace><mover><mi>X<\/mi><mo stretchy=\"false\" class=\"tml-capshift\">\u203e<\/mo><\/mover><mo>\u2212<\/mo><mi>\u03bc<\/mi><mspace width=\"0.2222em\"><\/mspace><\/mrow><mrow><mspace width=\"0.2222em\"><\/mspace><mi>S<\/mi><mi>\/<\/mi><msqrt><mi>n<\/mi><\/msqrt><mspace width=\"0.2222em\"><\/mspace><\/mrow><\/mfrac><\/mstyle><\/mrow><annotation encoding=\"application\/x-tex\">\\dfrac{\\:Z\\:}{\\:\\sqrt{U\/(n-1)}\\:} \\:=\\: \\dfrac{\\:\\dfrac{\\:\\bar{X}- \\mu\\:}{\\:\\sigma\/\\sqrt{n}\\:}\\:}{\\:\\dfrac{\\:S\\:}{\\:\\sigma\\:}\\:}=\\dfrac{\\:\\bar{X}- \\mu\\:}{\\:\\sigma\/\\sqrt{n}\\:}\\cdot \\dfrac{\\:\\sigma\\:}{\\:S\\:} \\:=\\:\\dfrac{\\:\\bar{X}- \\mu\\:}{\\:S\/\\sqrt{n}\\:}<\/annotation><\/semantics><\/math><br><\/p>\n\n\n\n<p>\u3068\u306a\u308b\u3002\u53f3\u8fba\u306f\u672a\u77e5\u306e\u6a19\u6e96\u504f\u5dee <math data-latex=\"\\sigma\"><semantics><mi>\u03c3<\/mi><annotation encoding=\"application\/x-tex\">\\sigma<\/annotation><\/semantics><\/math> \u3092\u6a19\u672c\u6a19\u6e96\u504f\u5dee <math data-latex=\"S\"><semantics><mi>S<\/mi><annotation encoding=\"application\/x-tex\">S<\/annotation><\/semantics><\/math> \u306b\u7f6e\u304d\u63db\u3048\u305f\u7d71\u8a08\u91cf <math data-latex=\"T\"><semantics><mi>T<\/mi><annotation encoding=\"application\/x-tex\">T<\/annotation><\/semantics><\/math> \u306b\u4e00\u81f4\u3059\u308b\u3002<\/p>\n\n\n\n<p>\u6b63\u898f\u6bcd\u96c6\u56e3\u3067\u306f\u3001\u6a19\u672c\u5e73\u5747 <math data-latex=\"\\bar{X}\"><semantics><mover><mi>X<\/mi><mo stretchy=\"false\" class=\"tml-capshift\">\u203e<\/mo><\/mover><annotation encoding=\"application\/x-tex\">\\bar{X}<\/annotation><\/semantics><\/math> \u3068\u6a19\u672c\u5206\u6563 <math data-latex=\"S^2\"><semantics><msup><mi>S<\/mi><mn>2<\/mn><\/msup><annotation encoding=\"application\/x-tex\">S^2<\/annotation><\/semantics><\/math> \u306f\u72ec\u7acb\u3067\u3042\u308b\u3002\u3057\u305f\u304c\u3063\u3066<\/p>\n\n\n\n<p class=\"has-text-align-center\"><br><math data-latex=\"Z\\sim N(0,\\:1)\"><semantics><mrow><mi>Z<\/mi><mo>\u223c<\/mo><mi>N<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>0<\/mn><mo separator=\"true\">,<\/mo><mspace width=\"0.2222em\"><\/mspace><mn>1<\/mn><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">Z\\sim N(0,\\:1)<\/annotation><\/semantics><\/math><br><\/p>\n\n\n\n<p>\u3068<\/p>\n\n\n\n<p class=\"has-text-align-center\"><br><math data-latex=\"U\\sim \\chi^2(n-1)\"><semantics><mrow><mi>U<\/mi><mo>\u223c<\/mo><msup><mi>\u03c7<\/mi><mn>2<\/mn><\/msup><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>n<\/mi><mo>\u2212<\/mo><mn>1<\/mn><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">U\\sim \\chi^2(n-1)<\/annotation><\/semantics><\/math><br><\/p>\n\n\n\n<p>\u3082\u72ec\u7acb\u3067\u3042\u308a<\/p>\n\n\n\n<p class=\"has-text-align-center\"><br><math data-latex=\"T\\:=\\:\\dfrac{\\:Z\\:}{\\:\\sqrt{U\/(n- 1)}\\:} \\:=\\: \\dfrac{\\:\\bar{X}- \\mu\\:}{\\:S\/\\sqrt{n}\\:}\"><semantics><mrow><mi>T<\/mi><mspace width=\"0.2222em\"><\/mspace><mo>=<\/mo><mspace width=\"0.2222em\"><\/mspace><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mrow><mspace width=\"0.2222em\"><\/mspace><mi>Z<\/mi><mspace width=\"0.2222em\"><\/mspace><\/mrow><mrow><mspace width=\"0.2222em\"><\/mspace><msqrt><mrow><mi>U<\/mi><mi>\/<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>n<\/mi><mo>\u2212<\/mo><mn>1<\/mn><mo form=\"postfix\" stretchy=\"false\" lspace=\"0em\" rspace=\"0em\">)<\/mo><\/mrow><\/msqrt><mspace width=\"0.2222em\"><\/mspace><\/mrow><\/mfrac><\/mstyle><mspace width=\"0.2222em\"><\/mspace><mo>=<\/mo><mspace width=\"0.2222em\"><\/mspace><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mrow><mspace width=\"0.2222em\"><\/mspace><mover><mi>X<\/mi><mo stretchy=\"false\" class=\"tml-capshift\">\u203e<\/mo><\/mover><mo>\u2212<\/mo><mi>\u03bc<\/mi><mspace width=\"0.2222em\"><\/mspace><\/mrow><mrow><mspace width=\"0.2222em\"><\/mspace><mi>S<\/mi><mi>\/<\/mi><msqrt><mi>n<\/mi><\/msqrt><mspace width=\"0.2222em\"><\/mspace><\/mrow><\/mfrac><\/mstyle><\/mrow><annotation encoding=\"application\/x-tex\">T\\:=\\:\\dfrac{\\:Z\\:}{\\:\\sqrt{U\/(n- 1)}\\:} \\:=\\: \\dfrac{\\:\\bar{X}- \\mu\\:}{\\:S\/\\sqrt{n}\\:}<\/annotation><\/semantics><\/math><br><\/p>\n\n\n\n<p>\u306f\u81ea\u7531\u5ea6 <math data-latex=\"n-1\"><semantics><mrow><mi>n<\/mi><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">n-1<\/annotation><\/semantics><\/math> \u306e <math data-latex=\"t\"><semantics><mi>t<\/mi><annotation encoding=\"application\/x-tex\">t<\/annotation><\/semantics><\/math> \u5206\u5e03\u306b\u5f93\u3046\u3002<\/p>\n\n\n\n<p class=\"has-text-align-center\"><br><math data-latex=\"\\dfrac{\\:\\bar{X}- \\mu\\:}{\\:S\/\\sqrt{n}\\:} \\sim t(n-1)\"><semantics><mrow><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mrow><mspace width=\"0.2222em\"><\/mspace><mover><mi>X<\/mi><mo stretchy=\"false\" class=\"tml-capshift\">\u203e<\/mo><\/mover><mo>\u2212<\/mo><mi>\u03bc<\/mi><mspace width=\"0.2222em\"><\/mspace><\/mrow><mrow><mspace width=\"0.2222em\"><\/mspace><mi>S<\/mi><mi>\/<\/mi><msqrt><mi>n<\/mi><\/msqrt><mspace width=\"0.2222em\"><\/mspace><\/mrow><\/mfrac><\/mstyle><mo>\u223c<\/mo><mi>t<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>n<\/mi><mo>\u2212<\/mo><mn>1<\/mn><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">\\dfrac{\\:\\bar{X}- \\mu\\:}{\\:S\/\\sqrt{n}\\:} \\sim t(n-1)<\/annotation><\/semantics><\/math><br><\/p>\n\n\n\n<p>\u4ee5\u4e0a\u304b\u3089 <math data-latex=\"t\"><semantics><mi>t<\/mi><annotation encoding=\"application\/x-tex\">t<\/annotation><\/semantics><\/math> \u5206\u5e03\u306f\u3001\u6bcd\u6a19\u6e96\u504f\u5dee <math data-latex=\"\\sigma\"><semantics><mi>\u03c3<\/mi><annotation encoding=\"application\/x-tex\">\\sigma<\/annotation><\/semantics><\/math> \u304c\u672a\u77e5\u3067\u3042\u308b\u305f\u3081\u306b\u6a19\u672c\u304b\u3089\u6c42\u3081\u305f <math data-latex=\"S\"><semantics><mi>S<\/mi><annotation encoding=\"application\/x-tex\">S<\/annotation><\/semantics><\/math> \u3092\u7528\u3044\u3066\u6a19\u6e96\u5316\u3092\u884c\u3044\u3001\u305d\u306e\u6642\u306b\u767a\u751f\u3059\u308b\u5206\u5e03\u3067\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u308b\u3002<\/p>\n\n\n\n<p>\u6bcd\u6a19\u6e96\u504f\u5dee\u304c\u65e2\u77e5\u306e\u6642\u3001\u7d71\u8a08\u91cf\u306f\u6a19\u6e96\u6b63\u898f\u5206\u5e03\u306b\u5f93\u3046\u3002\u4e00\u65b9\u3001<math data-latex=\"S\"><semantics><mi>S<\/mi><annotation encoding=\"application\/x-tex\">S<\/annotation><\/semantics><\/math> \u306f\u6a19\u672c\u3054\u3068\u306b\u5909\u52d5\u3059\u308b\u305f\u3081\u3001\u305d\u306e\u4e0d\u78ba\u5b9f\u6027\u304c\u52a0\u308f\u308a\u3001 <math data-latex=\"t\"><semantics><mi>t<\/mi><annotation encoding=\"application\/x-tex\">t<\/annotation><\/semantics><\/math> \u5206\u5e03\u306f\u6a19\u6e96\u6b63\u898f\u5206\u5e03\u3088\u308a\u3082\u88fe\u306e\u539a\u3044\u5f62\u306b\u306a\u308b\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" width=\"1024\" height=\"521\" src=\"https:\/\/since2020.jp\/media\/wp-content\/uploads\/2026\/07\/image-5-1024x521.png\" alt=\"\" class=\"wp-image-9233\" srcset=\"https:\/\/since2020.jp\/media\/wp-content\/uploads\/2026\/07\/image-5-1024x521.png 1024w, https:\/\/since2020.jp\/media\/wp-content\/uploads\/2026\/07\/image-5-300x153.png 300w, https:\/\/since2020.jp\/media\/wp-content\/uploads\/2026\/07\/image-5-768x391.png 768w, https:\/\/since2020.jp\/media\/wp-content\/uploads\/2026\/07\/image-5-1536x782.png 1536w, https:\/\/since2020.jp\/media\/wp-content\/uploads\/2026\/07\/image-5.png 1552w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p>\u56f32: \u6b63\u898f\u4e71\u6570\u3068 <math data-latex=\"\\chi^2\"><semantics><msup><mi>\u03c7<\/mi><mn>2<\/mn><\/msup><annotation encoding=\"application\/x-tex\">\\chi^2<\/annotation><\/semantics><\/math> \u578b\u306e\u4e8c\u4e57\u548c\u304b\u3089\u4f5c\u3063\u305f <math data-latex=\"t\"><semantics><mi>t<\/mi><annotation encoding=\"application\/x-tex\">t<\/annotation><\/semantics><\/math> \u5206\u5e03\u3001\u304a\u3088\u3073SciPy\u306e <math data-latex=\"t\"><semantics><mi>t<\/mi><annotation encoding=\"application\/x-tex\">t<\/annotation><\/semantics><\/math> \u7406\u8ad6\u5bc6\u5ea6<\/p>\n\n\n\n<p>\u3053\u3053\u3067 <math data-latex=\"\\chi^2\"><semantics><msup><mi>\u03c7<\/mi><mn>2<\/mn><\/msup><annotation encoding=\"application\/x-tex\">\\chi^2<\/annotation><\/semantics><\/math> \u5206\u5e03\u306e\u671f\u5f85\u5024\u3068\u5206\u6563\u306f<\/p>\n\n\n\n<p class=\"has-text-align-center\"><br><math data-latex=\"E[U]\\:=\\:\\nu,\\:\\:\\:Var(U) \\:=\\: 2\\nu\"><semantics><mrow><mi>E<\/mi><mo form=\"prefix\" stretchy=\"false\">[<\/mo><mi>U<\/mi><mo form=\"postfix\" stretchy=\"false\">]<\/mo><mspace width=\"0.2222em\"><\/mspace><mo>=<\/mo><mspace width=\"0.2222em\"><\/mspace><mi>\u03bd<\/mi><mo separator=\"true\">,<\/mo><mspace width=\"0.2222em\"><\/mspace><mspace width=\"0.2222em\"><\/mspace><mspace width=\"0.2222em\"><\/mspace><mi>V<\/mi><mi>a<\/mi><mi>r<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>U<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mspace width=\"0.2222em\"><\/mspace><mo>=<\/mo><mspace width=\"0.2222em\"><\/mspace><mn>2<\/mn><mi>\u03bd<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">E[U]\\:=\\:\\nu,\\:\\:\\:Var(U) \\:=\\: 2\\nu<\/annotation><\/semantics><\/math><br><\/p>\n\n\n\n<p>\u3067\u3042\u3063\u305f\u3002\u3053\u3053\u3067 <math data-latex=\"U\"><semantics><mi>U<\/mi><annotation encoding=\"application\/x-tex\">U<\/annotation><\/semantics><\/math> \u3092\u81ea\u7531\u5ea6 <math data-latex=\"\\nu\"><semantics><mi>\u03bd<\/mi><annotation encoding=\"application\/x-tex\">\\nu<\/annotation><\/semantics><\/math> \u3067\u5272\u3063\u305f\u5024\u306b\u3064\u3044\u3066\u306f<\/p>\n\n\n\n<p class=\"has-text-align-center\"><br><math data-latex=\"E[U\/\\nu] \\:=\\: \\dfrac{\\:E[U]\\:}{\\:\\nu\\:}\\:=\\: 1\"><semantics><mrow><mi>E<\/mi><mo form=\"prefix\" stretchy=\"false\">[<\/mo><mi>U<\/mi><mi>\/<\/mi><mi>\u03bd<\/mi><mo form=\"postfix\" stretchy=\"false\">]<\/mo><mspace width=\"0.2222em\"><\/mspace><mo>=<\/mo><mspace width=\"0.2222em\"><\/mspace><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mrow><mspace width=\"0.2222em\"><\/mspace><mi>E<\/mi><mo form=\"prefix\" stretchy=\"false\">[<\/mo><mi>U<\/mi><mo form=\"postfix\" stretchy=\"false\">]<\/mo><mspace width=\"0.2222em\"><\/mspace><\/mrow><mrow><mspace width=\"0.2222em\"><\/mspace><mi>\u03bd<\/mi><mspace width=\"0.2222em\"><\/mspace><\/mrow><\/mfrac><\/mstyle><mspace width=\"0.2222em\"><\/mspace><mo>=<\/mo><mspace width=\"0.2222em\"><\/mspace><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">E[U\/\\nu] \\:=\\: \\dfrac{\\:E[U]\\:}{\\:\\nu\\:}\\:=\\: 1<\/annotation><\/semantics><\/math><br><\/p>\n\n\n\n<p>\u307e\u305f\u5206\u6563\u306f<\/p>\n\n\n\n<p class=\"has-text-align-center\"><br><math data-latex=\"\\mathrm{Var}\\biggl(\\dfrac{\\:U\\:}{\\:\\nu\\:}\\biggr) \\:=\\: \\dfrac{\\:1\\:}{\\:\\nu^2\\:}\\mathrm{Var(U)} \\:=\\: \\dfrac{\\:2\\:}{\\:\\nu\\:}\"><semantics><mrow><mrow><mtext><\/mtext><mi>Var<\/mi><\/mrow><mo fence=\"true\" symmetric=\"true\" minsize=\"2.4em\" maxsize=\"2.4em\">(<\/mo><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mrow><mspace width=\"0.2222em\"><\/mspace><mi>U<\/mi><mspace width=\"0.2222em\"><\/mspace><\/mrow><mrow><mspace width=\"0.2222em\"><\/mspace><mi>\u03bd<\/mi><mspace width=\"0.2222em\"><\/mspace><\/mrow><\/mfrac><\/mstyle><mo fence=\"true\" symmetric=\"true\" minsize=\"2.4em\" maxsize=\"2.4em\">)<\/mo><mspace width=\"0.2222em\"><\/mspace><mo>=<\/mo><mspace width=\"0.2222em\"><\/mspace><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mrow><mspace width=\"0.2222em\"><\/mspace><mn>1<\/mn><mspace width=\"0.2222em\"><\/mspace><\/mrow><mrow><mspace width=\"0.2222em\"><\/mspace><msup><mi>\u03bd<\/mi><mn>2<\/mn><\/msup><mspace width=\"0.2222em\"><\/mspace><\/mrow><\/mfrac><\/mstyle><mrow><mrow><mi mathvariant=\"normal\">V<\/mi><\/mrow><mrow><mi mathvariant=\"normal\">a<\/mi><\/mrow><mrow><mi mathvariant=\"normal\">r<\/mi><\/mrow><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mrow><mi mathvariant=\"normal\">U<\/mi><\/mrow><mo form=\"postfix\" stretchy=\"false\" lspace=\"0em\" rspace=\"0em\">)<\/mo><\/mrow><mspace width=\"0.2222em\"><\/mspace><mo>=<\/mo><mspace width=\"0.2222em\"><\/mspace><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mrow><mspace width=\"0.2222em\"><\/mspace><mn>2<\/mn><mspace width=\"0.2222em\"><\/mspace><\/mrow><mrow><mspace width=\"0.2222em\"><\/mspace><mi>\u03bd<\/mi><mspace width=\"0.2222em\"><\/mspace><\/mrow><\/mfrac><\/mstyle><\/mrow><annotation encoding=\"application\/x-tex\">\\mathrm{Var}\\biggl(\\dfrac{\\:U\\:}{\\:\\nu\\:}\\biggr) \\:=\\: \\dfrac{\\:1\\:}{\\:\\nu^2\\:}\\mathrm{Var(U)} \\:=\\: \\dfrac{\\:2\\:}{\\:\\nu\\:}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p>\u3064\u307e\u308a <math data-latex=\"U\/\\nu\"><semantics><mrow><mi>U<\/mi><mi>\/<\/mi><mi>\u03bd<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">U\/\\nu<\/annotation><\/semantics><\/math> \u306f\u3070\u3089\u3064\u304d\u3092\u542b\u3081\u3066<\/p>\n\n\n\n<p class=\"has-text-align-center\"><br><math data-latex=\"\\dfrac{\\:U\\:}{\\:\\nu\\:} \\:=\\: 1 \\:\\pm\\: \\dfrac{\\:2\\:}{\\:\\nu\\:}\"><semantics><mrow><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mrow><mspace width=\"0.2222em\"><\/mspace><mi>U<\/mi><mspace width=\"0.2222em\"><\/mspace><\/mrow><mrow><mspace width=\"0.2222em\"><\/mspace><mi>\u03bd<\/mi><mspace width=\"0.2222em\"><\/mspace><\/mrow><\/mfrac><\/mstyle><mspace width=\"0.2222em\"><\/mspace><mo>=<\/mo><mspace width=\"0.2222em\"><\/mspace><mn>1<\/mn><mspace width=\"0.2222em\"><\/mspace><mo>\u00b1<\/mo><mspace width=\"0.2222em\"><\/mspace><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mrow><mspace width=\"0.2222em\"><\/mspace><mn>2<\/mn><mspace width=\"0.2222em\"><\/mspace><\/mrow><mrow><mspace width=\"0.2222em\"><\/mspace><mi>\u03bd<\/mi><mspace width=\"0.2222em\"><\/mspace><\/mrow><\/mfrac><\/mstyle><\/mrow><annotation encoding=\"application\/x-tex\">\\dfrac{\\:U\\:}{\\:\\nu\\:} \\:=\\: 1 \\:\\pm\\: \\dfrac{\\:2\\:}{\\:\\nu\\:}<\/annotation><\/semantics><\/math><br><\/p>\n\n\n\n<p>\u3068\u8868\u3059\u3053\u3068\u3067\u6574\u5408\u6027\u304c\u3068\u308c\u3001\u81ea\u7531\u5ea6\u304c\u5927\u304d\u304f\u306a\u308b\u3068\u5909\u52d5\u304c\u5c0f\u3055\u304f\u306a\u308a<\/p>\n\n\n\n<p class=\"has-text-align-center\"><br><math data-latex=\"\\nu\\to\\infty \\:\\:\\Rightarrow\\:\\: \\dfrac{\\:U\\:}{\\:\\nu\\:} \\to 1\"><semantics><mrow><mi>\u03bd<\/mi><mo>\u2192<\/mo><mi>\u221e<\/mi><mspace width=\"0.2222em\"><\/mspace><mspace width=\"0.2222em\"><\/mspace><mo stretchy=\"false\">\u21d2<\/mo><mspace width=\"0.2222em\"><\/mspace><mspace width=\"0.2222em\"><\/mspace><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mrow><mspace width=\"0.2222em\"><\/mspace><mi>U<\/mi><mspace width=\"0.2222em\"><\/mspace><\/mrow><mrow><mspace width=\"0.2222em\"><\/mspace><mi>\u03bd<\/mi><mspace width=\"0.2222em\"><\/mspace><\/mrow><\/mfrac><\/mstyle><mo>\u2192<\/mo><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\nu\\to\\infty \\:\\:\\Rightarrow\\:\\: \\dfrac{\\:U\\:}{\\:\\nu\\:} \\to 1<\/annotation><\/semantics><\/math><br><\/p>\n\n\n\n<p>\u4e0a\u5f0f\u306e\u3088\u3046\u306b\u3084\u304c\u3066 1 \u306b\u53ce\u675f\u3059\u308b\u3002\u3057\u305f\u304c\u3063\u3066<\/p>\n\n\n\n<p class=\"has-text-align-center\"><br><math data-latex=\"\\sqrt{\\dfrac{\\:U\\:}{\\:\\nu\\:}} \\to 1\"><semantics><mrow><msqrt><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mrow><mspace width=\"0.2222em\"><\/mspace><mi>U<\/mi><mspace width=\"0.2222em\"><\/mspace><\/mrow><mrow><mspace width=\"0.2222em\"><\/mspace><mi>\u03bd<\/mi><mspace width=\"0.2222em\"><\/mspace><\/mrow><\/mfrac><\/mstyle><\/msqrt><mo>\u2192<\/mo><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\sqrt{\\dfrac{\\:U\\:}{\\:\\nu\\:}} \\to 1<\/annotation><\/semantics><\/math><br><\/p>\n\n\n\n<p>\u3067\u3042\u308b\u3002\u3053\u3053\u3067 <math data-latex=\"t\"><semantics><mi>t<\/mi><annotation encoding=\"application\/x-tex\">t<\/annotation><\/semantics><\/math> \u7d71\u8a08\u91cf\u306f<\/p>\n\n\n\n<p class=\"has-text-align-center\"><br><math data-latex=\"T\\:=\\: \\dfrac{\\:Z\\:}{\\:\\sqrt{U\/\\nu}\\:}\"><semantics><mrow><mi>T<\/mi><mspace width=\"0.2222em\"><\/mspace><mo>=<\/mo><mspace width=\"0.2222em\"><\/mspace><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mrow><mspace width=\"0.2222em\"><\/mspace><mi>Z<\/mi><mspace width=\"0.2222em\"><\/mspace><\/mrow><mrow><mspace width=\"0.2222em\"><\/mspace><msqrt><mrow><mi>U<\/mi><mi>\/<\/mi><mi>\u03bd<\/mi><\/mrow><\/msqrt><mspace width=\"0.2222em\"><\/mspace><\/mrow><\/mfrac><\/mstyle><\/mrow><annotation encoding=\"application\/x-tex\">T\\:=\\: \\dfrac{\\:Z\\:}{\\:\\sqrt{U\/\\nu}\\:}<\/annotation><\/semantics><\/math><br><\/p>\n\n\n\n<p>\u3067\u3042\u308a\u3001\u81ea\u7531\u5ea6\u304c\u5927\u304d\u304f\u306a\u308b\u3068\u5206\u6bcd\u306f 1 \u306b\u8fd1\u3065\u304f\u3053\u3068\u304b\u3089<\/p>\n\n\n\n<p class=\"has-text-align-center\"><br><math data-latex=\"T\\:=\\: \\dfrac{\\:Z\\:}{\\:\\sqrt{U\/\\nu}\\:} \\:\\approx\\: \\dfrac{\\:Z\\:}{\\:1\\:} \\:=\\: Z\"><semantics><mrow><mi>T<\/mi><mspace width=\"0.2222em\"><\/mspace><mo>=<\/mo><mspace width=\"0.2222em\"><\/mspace><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mrow><mspace width=\"0.2222em\"><\/mspace><mi>Z<\/mi><mspace width=\"0.2222em\"><\/mspace><\/mrow><mrow><mspace width=\"0.2222em\"><\/mspace><msqrt><mrow><mi>U<\/mi><mi>\/<\/mi><mi>\u03bd<\/mi><\/mrow><\/msqrt><mspace width=\"0.2222em\"><\/mspace><\/mrow><\/mfrac><\/mstyle><mspace width=\"0.2222em\"><\/mspace><mo>\u2248<\/mo><mspace width=\"0.2222em\"><\/mspace><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mrow><mspace width=\"0.2222em\"><\/mspace><mi>Z<\/mi><mspace width=\"0.2222em\"><\/mspace><\/mrow><mrow><mspace width=\"0.2222em\"><\/mspace><mn>1<\/mn><mspace width=\"0.2222em\"><\/mspace><\/mrow><\/mfrac><\/mstyle><mspace width=\"0.2222em\"><\/mspace><mo>=<\/mo><mspace width=\"0.2222em\"><\/mspace><mi>Z<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">T\\:=\\: \\dfrac{\\:Z\\:}{\\:\\sqrt{U\/\\nu}\\:} \\:\\approx\\: \\dfrac{\\:Z\\:}{\\:1\\:} \\:=\\: Z<\/annotation><\/semantics><\/math><br><\/p>\n\n\n\n<p>\u3068\u306a\u308b\u3002<math data-latex=\"Z\"><semantics><mi>Z<\/mi><annotation encoding=\"application\/x-tex\">Z<\/annotation><\/semantics><\/math> \u306f\u305d\u306e\u5b9a\u7fa9\u304b\u3089<\/p>\n\n\n\n<p class=\"has-text-align-center\"><br><math data-latex=\"Z \\sim N(0,\\:1)\"><semantics><mrow><mi>Z<\/mi><mo>\u223c<\/mo><mi>N<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>0<\/mn><mo separator=\"true\">,<\/mo><mspace width=\"0.2222em\"><\/mspace><mn>1<\/mn><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">Z \\sim N(0,\\:1)<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p>\u3067\u3042\u308b\u304b\u3089\u3001<math data-latex=\"t\"><semantics><mi>t<\/mi><annotation encoding=\"application\/x-tex\">t<\/annotation><\/semantics><\/math> \u5206\u5e03\u306f\u81ea\u7531\u5ea6\u304c\u5927\u304d\u304f\u306a\u308b\u306b\u3064\u308c\u3066\u6a19\u6e96\u6b63\u898f\u5206\u5e03\u306b\u8fd1\u3065\u304f\u3053\u3068\u304c\u308f\u304b\u308b\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u5206\u6563\u6bd4\u691c\u5b9a<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\"><math data-latex=\"F\"><semantics><mi>F<\/mi><annotation encoding=\"application\/x-tex\">F<\/annotation><\/semantics><\/math> \u5206\u5e03<\/h3>\n\n\n\n<p>\u4e8c\u3064\u306e\u6b63\u898f\u6bcd\u96c6\u56e3\u304b\u3089\u72ec\u7acb\u306b\u6a19\u672c\u3092\u53d6\u308b\u3002<\/p>\n\n\n\n<p class=\"has-text-align-center\"><br><math data-latex=\"X_1,\\:X_2,\\:\\cdots,\\:X_{n1} \\overset{\\text\\small\\textrm{i.i.d}}{\\sim}N(\\mu_1,\\:\\sigma_1^2),\\hspace{2em}Y_1,\\:Y_2,\\:\\cdots,Y_{n2}\\overset{\\text\\small\\textrm{i.i.d}}{\\sim} N(\\mu_2,\\:\\sigma_2^2)\"><semantics><mrow><msub><mi>X<\/mi><mn>1<\/mn><\/msub><mo separator=\"true\">,<\/mo><mspace width=\"0.2222em\"><\/mspace><msub><mi>X<\/mi><mn>2<\/mn><\/msub><mo separator=\"true\">,<\/mo><mspace width=\"0.2222em\"><\/mspace><mo>\u22ef<\/mo><mspace width=\"0.1667em\"><\/mspace><mo separator=\"true\">,<\/mo><mspace width=\"0.2222em\"><\/mspace><msub><mi>X<\/mi><mrow><mi>n<\/mi><mn>1<\/mn><\/mrow><\/msub><mrow><mover><mo>\u223c<\/mo><mrow><mstyle mathsize=\"0.9000em\"><\/mstyle><mtext>i.i.d<\/mtext><\/mrow><\/mover><\/mrow><mi>N<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msub><mi>\u03bc<\/mi><mn>1<\/mn><\/msub><mo separator=\"true\">,<\/mo><mspace width=\"0.2222em\"><\/mspace><msubsup><mi>\u03c3<\/mi><mn>1<\/mn><mn>2<\/mn><\/msubsup><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo separator=\"true\">,<\/mo><mspace width=\"2em\"><\/mspace><msub><mi>Y<\/mi><mn>1<\/mn><\/msub><mo separator=\"true\">,<\/mo><mspace width=\"0.2222em\"><\/mspace><msub><mi>Y<\/mi><mn>2<\/mn><\/msub><mo separator=\"true\">,<\/mo><mspace width=\"0.2222em\"><\/mspace><mo>\u22ef<\/mo><mspace width=\"0.1667em\"><\/mspace><mo separator=\"true\">,<\/mo><msub><mi>Y<\/mi><mrow><mi>n<\/mi><mn>2<\/mn><\/mrow><\/msub><mrow><mover><mo>\u223c<\/mo><mrow><mstyle mathsize=\"0.9000em\"><\/mstyle><mtext>i.i.d<\/mtext><\/mrow><\/mover><\/mrow><mi>N<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msub><mi>\u03bc<\/mi><mn>2<\/mn><\/msub><mo separator=\"true\">,<\/mo><mspace width=\"0.2222em\"><\/mspace><msubsup><mi>\u03c3<\/mi><mn>2<\/mn><mn>2<\/mn><\/msubsup><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">X_1,\\:X_2,\\:\\cdots,\\:X_{n1} \\overset{\\text\\small\\textrm{i.i.d}}{\\sim}N(\\mu_1,\\:\\sigma_1^2),\\hspace{2em}Y_1,\\:Y_2,\\:\\cdots,Y_{n2}\\overset{\\text\\small\\textrm{i.i.d}}{\\sim} N(\\mu_2,\\:\\sigma_2^2)<\/annotation><\/semantics><\/math><br><\/p>\n\n\n\n<p>\u305d\u308c\u305e\u308c\u306e\u4e0d\u504f\u5206\u6563\u3092 <math data-latex=\"S_1^2,\\:S_2^2\"><semantics><mrow><msubsup><mi>S<\/mi><mn>1<\/mn><mn>2<\/mn><\/msubsup><mo separator=\"true\">,<\/mo><mspace width=\"0.2222em\"><\/mspace><msubsup><mi>S<\/mi><mn>2<\/mn><mn>2<\/mn><\/msubsup><\/mrow><annotation encoding=\"application\/x-tex\">S_1^2,\\:S_2^2<\/annotation><\/semantics><\/math> \u3068\u3059\u308b\u3068\u3001\u524d\u3005\u7bc0\u306e\u5185\u5bb9\u304b\u3089<\/p>\n\n\n\n<p class=\"has-text-align-center\"><br><math data-latex=\"U_1\\:=\\:\\dfrac{\\:(n_1 - 1) S_1^2\\:}{\\:\\sigma_1^2\\:} \\sim \\chi^2(n_1 -1),\\hspace{2em}U_2\\:=\\:\\dfrac{\\:(n_2 - 1) S_2^2\\:}{\\:\\sigma_2^2\\:} \\sim \\chi^2(n_2 -1)\"><semantics><mrow><msub><mi>U<\/mi><mn>1<\/mn><\/msub><mspace width=\"0.2222em\"><\/mspace><mo>=<\/mo><mspace width=\"0.2222em\"><\/mspace><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mrow><mspace width=\"0.2222em\"><\/mspace><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msub><mi>n<\/mi><mn>1<\/mn><\/msub><mo>\u2212<\/mo><mn>1<\/mn><mo form=\"postfix\" stretchy=\"false\">)<\/mo><msubsup><mi>S<\/mi><mn>1<\/mn><mn>2<\/mn><\/msubsup><mspace width=\"0.2222em\"><\/mspace><\/mrow><mrow><mspace width=\"0.2222em\"><\/mspace><msubsup><mi>\u03c3<\/mi><mn>1<\/mn><mn>2<\/mn><\/msubsup><mspace width=\"0.2222em\"><\/mspace><\/mrow><\/mfrac><\/mstyle><mo>\u223c<\/mo><msup><mi>\u03c7<\/mi><mn>2<\/mn><\/msup><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msub><mi>n<\/mi><mn>1<\/mn><\/msub><mo>\u2212<\/mo><mn>1<\/mn><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo separator=\"true\">,<\/mo><mspace width=\"2em\"><\/mspace><msub><mi>U<\/mi><mn>2<\/mn><\/msub><mspace width=\"0.2222em\"><\/mspace><mo>=<\/mo><mspace width=\"0.2222em\"><\/mspace><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mrow><mspace width=\"0.2222em\"><\/mspace><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msub><mi>n<\/mi><mn>2<\/mn><\/msub><mo>\u2212<\/mo><mn>1<\/mn><mo form=\"postfix\" stretchy=\"false\">)<\/mo><msubsup><mi>S<\/mi><mn>2<\/mn><mn>2<\/mn><\/msubsup><mspace width=\"0.2222em\"><\/mspace><\/mrow><mrow><mspace width=\"0.2222em\"><\/mspace><msubsup><mi>\u03c3<\/mi><mn>2<\/mn><mn>2<\/mn><\/msubsup><mspace width=\"0.2222em\"><\/mspace><\/mrow><\/mfrac><\/mstyle><mo>\u223c<\/mo><msup><mi>\u03c7<\/mi><mn>2<\/mn><\/msup><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msub><mi>n<\/mi><mn>2<\/mn><\/msub><mo>\u2212<\/mo><mn>1<\/mn><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">U_1\\:=\\:\\dfrac{\\:(n_1 &#8211; 1) S_1^2\\:}{\\:\\sigma_1^2\\:} \\sim \\chi^2(n_1 -1),\\hspace{2em}U_2\\:=\\:\\dfrac{\\:(n_2 &#8211; 1) S_2^2\\:}{\\:\\sigma_2^2\\:} \\sim \\chi^2(n_2 -1)<\/annotation><\/semantics><\/math><br><\/p>\n\n\n\n<p>\u3067\u3042\u308a\u3001\u4e8c\u3064\u306f\u72ec\u7acb\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<p>\u305d\u308c\u305e\u308c\u306e <math data-latex=\"\\chi^2\"><semantics><msup><mi>\u03c7<\/mi><mn>2<\/mn><\/msup><annotation encoding=\"application\/x-tex\">\\chi^2<\/annotation><\/semantics><\/math> \u5909\u6570\uff08<math data-latex=\"U_1, \\:U_2\"><semantics><mrow><msub><mi>U<\/mi><mn>1<\/mn><\/msub><mo separator=\"true\">,<\/mo><mspace width=\"0.2222em\"><\/mspace><msub><mi>U<\/mi><mn>2<\/mn><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">U_1, \\:U_2<\/annotation><\/semantics><\/math>\uff09\u3092\u81ea\u7531\u5ea6\u3067\u5272\u308b\u3068<\/p>\n\n\n\n<p class=\"has-text-align-center\"><br><math data-latex=\"\\dfrac{\\:U_1\\:}{n_1-1}\\:=\\:\\dfrac{\\:S_1^2\\:}{\\:\\sigma_1^2\\:}\\\\\\dfrac{\\:U_2\\:}{n_2-1}\\:=\\:\\dfrac{\\:S_2^2\\:}{\\:\\sigma_2^2\\:}\"><semantics><mtable columnalign=\"left\" rowspacing=\"0em\"><mtr><mtd style=\"text-align:left\"><mrow><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mrow><mspace width=\"0.2222em\"><\/mspace><msub><mi>U<\/mi><mn>1<\/mn><\/msub><mspace width=\"0.2222em\"><\/mspace><\/mrow><mrow><msub><mi>n<\/mi><mn>1<\/mn><\/msub><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><\/mfrac><\/mstyle><mspace width=\"0.2222em\"><\/mspace><mo>=<\/mo><mspace width=\"0.2222em\"><\/mspace><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mrow><mspace width=\"0.2222em\"><\/mspace><msubsup><mi>S<\/mi><mn>1<\/mn><mn>2<\/mn><\/msubsup><mspace width=\"0.2222em\"><\/mspace><\/mrow><mrow><mspace width=\"0.2222em\"><\/mspace><msubsup><mi>\u03c3<\/mi><mn>1<\/mn><mn>2<\/mn><\/msubsup><mspace width=\"0.2222em\"><\/mspace><\/mrow><\/mfrac><\/mstyle><\/mrow><mo><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left\"><mrow><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mrow><mspace width=\"0.2222em\"><\/mspace><msub><mi>U<\/mi><mn>2<\/mn><\/msub><mspace width=\"0.2222em\"><\/mspace><\/mrow><mrow><msub><mi>n<\/mi><mn>2<\/mn><\/msub><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><\/mfrac><\/mstyle><mspace width=\"0.2222em\"><\/mspace><mo>=<\/mo><mspace width=\"0.2222em\"><\/mspace><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mrow><mspace width=\"0.2222em\"><\/mspace><msubsup><mi>S<\/mi><mn>2<\/mn><mn>2<\/mn><\/msubsup><mspace width=\"0.2222em\"><\/mspace><\/mrow><mrow><mspace width=\"0.2222em\"><\/mspace><msubsup><mi>\u03c3<\/mi><mn>2<\/mn><mn>2<\/mn><\/msubsup><mspace width=\"0.2222em\"><\/mspace><\/mrow><\/mfrac><\/mstyle><\/mrow><\/mtd><\/mtr><\/mtable><annotation encoding=\"application\/x-tex\">\\dfrac{\\:U_1\\:}{n_1-1}\\:=\\:\\dfrac{\\:S_1^2\\:}{\\:\\sigma_1^2\\:}\\\\\\dfrac{\\:U_2\\:}{n_2-1}\\:=\\:\\dfrac{\\:S_2^2\\:}{\\:\\sigma_2^2\\:}<\/annotation><\/semantics><\/math><br><\/p>\n\n\n\n<p>\u3068\u306a\u308b\u3002\u3053\u3053\u30672\u3064\u306e\u91cf\u306e\u6bd4\u3092\u53d6\u308b\u3068\u3053\u308c\u304c <math data-latex=\"F\"><semantics><mi>F<\/mi><annotation encoding=\"application\/x-tex\">F<\/annotation><\/semantics><\/math> \u7d71\u8a08\u91cf\u3068\u306a\u308b\u3002<\/p>\n\n\n\n<p class=\"has-text-align-center\"><br><math data-latex=\"F\\:=\\: \\dfrac{\\:U_1\/(n_1-1)\\:}{\\:U_2\/(n_2 -1)\\:}\\:=\\: \\dfrac{\\:S_1^2\\:}{\\:S_2^2\\:}\\cdot \\dfrac{\\:\\sigma_2^2\\:}{\\:\\sigma_1^2\\:}\"><semantics><mrow><mi>F<\/mi><mspace width=\"0.2222em\"><\/mspace><mo>=<\/mo><mspace width=\"0.2222em\"><\/mspace><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mrow><mspace width=\"0.2222em\"><\/mspace><msub><mi>U<\/mi><mn>1<\/mn><\/msub><mi>\/<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msub><mi>n<\/mi><mn>1<\/mn><\/msub><mo>\u2212<\/mo><mn>1<\/mn><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mspace width=\"0.2222em\"><\/mspace><\/mrow><mrow><mspace width=\"0.2222em\"><\/mspace><msub><mi>U<\/mi><mn>2<\/mn><\/msub><mi>\/<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msub><mi>n<\/mi><mn>2<\/mn><\/msub><mo>\u2212<\/mo><mn>1<\/mn><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mspace width=\"0.2222em\"><\/mspace><\/mrow><\/mfrac><\/mstyle><mspace width=\"0.2222em\"><\/mspace><mo>=<\/mo><mspace width=\"0.2222em\"><\/mspace><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mrow><mspace width=\"0.2222em\"><\/mspace><msubsup><mi>S<\/mi><mn>1<\/mn><mn>2<\/mn><\/msubsup><mspace width=\"0.2222em\"><\/mspace><\/mrow><mrow><mspace width=\"0.2222em\"><\/mspace><msubsup><mi>S<\/mi><mn>2<\/mn><mn>2<\/mn><\/msubsup><mspace width=\"0.2222em\"><\/mspace><\/mrow><\/mfrac><\/mstyle><mo>\u22c5<\/mo><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mrow><mspace width=\"0.2222em\"><\/mspace><msubsup><mi>\u03c3<\/mi><mn>2<\/mn><mn>2<\/mn><\/msubsup><mspace width=\"0.2222em\"><\/mspace><\/mrow><mrow><mspace width=\"0.2222em\"><\/mspace><msubsup><mi>\u03c3<\/mi><mn>1<\/mn><mn>2<\/mn><\/msubsup><mspace width=\"0.2222em\"><\/mspace><\/mrow><\/mfrac><\/mstyle><\/mrow><annotation encoding=\"application\/x-tex\">F\\:=\\: \\dfrac{\\:U_1\/(n_1-1)\\:}{\\:U_2\/(n_2 -1)\\:}\\:=\\: \\dfrac{\\:S_1^2\\:}{\\:S_2^2\\:}\\cdot \\dfrac{\\:\\sigma_2^2\\:}{\\:\\sigma_1^2\\:}<\/annotation><\/semantics><\/math><br><\/p>\n\n\n\n<p>\u3053\u306e\u7d71\u8a08\u91cf\u306f\u4e8c\u3064\u306e\u81ea\u7531\u5ea6<\/p>\n\n\n\n<p class=\"has-text-align-center\"><br><math data-latex=\"\\nu_1 \\:=\\: n_1 -1,\\hspace{2em}\\nu_2 \\:=\\: n_2 -1\"><semantics><mrow><msub><mi>\u03bd<\/mi><mn>1<\/mn><\/msub><mspace width=\"0.2222em\"><\/mspace><mo>=<\/mo><mspace width=\"0.2222em\"><\/mspace><msub><mi>n<\/mi><mn>1<\/mn><\/msub><mo>\u2212<\/mo><mn>1<\/mn><mo separator=\"true\">,<\/mo><mspace width=\"2em\"><\/mspace><msub><mi>\u03bd<\/mi><mn>2<\/mn><\/msub><mspace width=\"0.2222em\"><\/mspace><mo>=<\/mo><mspace width=\"0.2222em\"><\/mspace><msub><mi>n<\/mi><mn>2<\/mn><\/msub><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\nu_1 \\:=\\: n_1 -1,\\hspace{2em}\\nu_2 \\:=\\: n_2 -1<\/annotation><\/semantics><\/math><br><\/p>\n\n\n\n<p>\u3092\u6301\u3064 <math data-latex=\"F\"><semantics><mi>F<\/mi><annotation encoding=\"application\/x-tex\">F<\/annotation><\/semantics><\/math> \u5206\u5e03\u306b\u5f93\u3046\u3002<\/p>\n\n\n\n<p class=\"has-text-align-center\"><br><math data-latex=\"F\\sim F(\\nu_1,\\:\\nu_2)\"><semantics><mrow><mi>F<\/mi><mo>\u223c<\/mo><mi>F<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msub><mi>\u03bd<\/mi><mn>1<\/mn><\/msub><mo separator=\"true\">,<\/mo><mspace width=\"0.2222em\"><\/mspace><msub><mi>\u03bd<\/mi><mn>2<\/mn><\/msub><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">F\\sim F(\\nu_1,\\:\\nu_2)<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u6bcd\u5206\u6563\u306e\u6bd4\u306e\u691c\u5b9a<\/h3>\n\n\n\n<p>2\u3064\u306e\u6bcd\u5206\u6563\u304c\u7b49\u3057\u3044\u304b\u3069\u3046\u304b\u3092\u8abf\u3079\u305f\u3044\u3068\u3059\u308b\u3002\u3053\u306e\u3068\u304d\u5e30\u7121\u4eee\u8aac\u3092<\/p>\n\n\n\n<p class=\"has-text-align-center\"><br><math data-latex=\"H_0:\\sigma_1^2 \\:=\\: \\sigma_2^2\"><semantics><mrow><msub><mi>H<\/mi><mn>0<\/mn><\/msub><mo lspace=\"0.2222em\" rspace=\"0.2222em\">:<\/mo><msubsup><mi>\u03c3<\/mi><mn>1<\/mn><mn>2<\/mn><\/msubsup><mspace width=\"0.2222em\"><\/mspace><mo>=<\/mo><mspace width=\"0.2222em\"><\/mspace><msubsup><mi>\u03c3<\/mi><mn>2<\/mn><mn>2<\/mn><\/msubsup><\/mrow><annotation encoding=\"application\/x-tex\">H_0:\\sigma_1^2 \\:=\\: \\sigma_2^2<\/annotation><\/semantics><\/math><br><\/p>\n\n\n\n<p>\u3068\u304a\u304f\u3002\u3053\u306e\u4eee\u8aac\u306e\u5143\u3067\u306f<\/p>\n\n\n\n<p class=\"has-text-align-center\"><br><math data-latex=\"\\dfrac{\\:\\sigma_2^2\\:}{\\:\\sigma_1^2\\:}\\:=\\: 1\"><semantics><mrow><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mrow><mspace width=\"0.2222em\"><\/mspace><msubsup><mi>\u03c3<\/mi><mn>2<\/mn><mn>2<\/mn><\/msubsup><mspace width=\"0.2222em\"><\/mspace><\/mrow><mrow><mspace width=\"0.2222em\"><\/mspace><msubsup><mi>\u03c3<\/mi><mn>1<\/mn><mn>2<\/mn><\/msubsup><mspace width=\"0.2222em\"><\/mspace><\/mrow><\/mfrac><\/mstyle><mspace width=\"0.2222em\"><\/mspace><mo>=<\/mo><mspace width=\"0.2222em\"><\/mspace><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\dfrac{\\:\\sigma_2^2\\:}{\\:\\sigma_1^2\\:}\\:=\\: 1<\/annotation><\/semantics><\/math><br><\/p>\n\n\n\n<p>\u3067\u3042\u308b\u304b\u3089\u3001<math data-latex=\"F\"><semantics><mi>F<\/mi><annotation encoding=\"application\/x-tex\">F<\/annotation><\/semantics><\/math> \u7d71\u8a08\u91cf\u306f<\/p>\n\n\n\n<p class=\"has-text-align-center\"><br><math data-latex=\"F\\:=\\: \\dfrac{\\:S_1^2\\:}{\\:S_2^2\\:}\"><semantics><mrow><mi>F<\/mi><mspace width=\"0.2222em\"><\/mspace><mo>=<\/mo><mspace width=\"0.2222em\"><\/mspace><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mrow><mspace width=\"0.2222em\"><\/mspace><msubsup><mi>S<\/mi><mn>1<\/mn><mn>2<\/mn><\/msubsup><mspace width=\"0.2222em\"><\/mspace><\/mrow><mrow><mspace width=\"0.2222em\"><\/mspace><msubsup><mi>S<\/mi><mn>2<\/mn><mn>2<\/mn><\/msubsup><mspace width=\"0.2222em\"><\/mspace><\/mrow><\/mfrac><\/mstyle><\/mrow><annotation encoding=\"application\/x-tex\">F\\:=\\: \\dfrac{\\:S_1^2\\:}{\\:S_2^2\\:}<\/annotation><\/semantics><\/math><br><\/p>\n\n\n\n<p>\u3068\u306a\u308b\u3002\u3057\u305f\u304c\u3063\u3066<\/p>\n\n\n\n<p class=\"has-text-align-center\"><br><math data-latex=\"\\dfrac{\\:S_1^2\\:}{\\:S_2^2\\:}\\sim F(n_1-1, \\: n_2 -1)\"><semantics><mrow><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mrow><mspace width=\"0.2222em\"><\/mspace><msubsup><mi>S<\/mi><mn>1<\/mn><mn>2<\/mn><\/msubsup><mspace width=\"0.2222em\"><\/mspace><\/mrow><mrow><mspace width=\"0.2222em\"><\/mspace><msubsup><mi>S<\/mi><mn>2<\/mn><mn>2<\/mn><\/msubsup><mspace width=\"0.2222em\"><\/mspace><\/mrow><\/mfrac><\/mstyle><mo>\u223c<\/mo><mi>F<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msub><mi>n<\/mi><mn>1<\/mn><\/msub><mo>\u2212<\/mo><mn>1<\/mn><mo separator=\"true\">,<\/mo><mspace width=\"0.2222em\"><\/mspace><msub><mi>n<\/mi><mn>2<\/mn><\/msub><mo>\u2212<\/mo><mn>1<\/mn><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">\\dfrac{\\:S_1^2\\:}{\\:S_2^2\\:}\\sim F(n_1-1, \\: n_2 -1)<\/annotation><\/semantics><\/math><br><\/p>\n\n\n\n<p>\u3067\u3042\u308b\u3002\u3064\u307e\u308a <math data-latex=\"F\"><semantics><mi>F<\/mi><annotation encoding=\"application\/x-tex\">F<\/annotation><\/semantics><\/math> \u5206\u5e03\u306f2\u3064\u306e\u6a19\u672c\u5206\u6563\u306e\u6bd4\u304c\u3001\u6bcd\u5206\u6563\u304c\u7b49\u3057\u3044\u3068\u3044\u3046\u4eee\u5b9a\u306e\u3082\u3068\u3067\u3069\u306e\u7a0b\u5ea6\u5909\u52d5\u3059\u308b\u304b\u3092\u8868\u3059\u5206\u5e03\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" width=\"1024\" height=\"556\" src=\"https:\/\/since2020.jp\/media\/wp-content\/uploads\/2026\/07\/image-6-1024x556.png\" alt=\"\" class=\"wp-image-9234\" srcset=\"https:\/\/since2020.jp\/media\/wp-content\/uploads\/2026\/07\/image-6-1024x556.png 1024w, https:\/\/since2020.jp\/media\/wp-content\/uploads\/2026\/07\/image-6-300x163.png 300w, https:\/\/since2020.jp\/media\/wp-content\/uploads\/2026\/07\/image-6-768x417.png 768w, https:\/\/since2020.jp\/media\/wp-content\/uploads\/2026\/07\/image-6-1536x834.png 1536w, https:\/\/since2020.jp\/media\/wp-content\/uploads\/2026\/07\/image-6.png 1580w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p>\u56f33: \u4e8c\u3064\u306e\u72ec\u7acb\u306a\u5e73\u5747\u4e8c\u4e57\u306e\u6bd4\u3067\u4f5c\u3063\u305f <math data-latex=\"F\"><semantics><mi>F<\/mi><annotation encoding=\"application\/x-tex\">F<\/annotation><\/semantics><\/math> \u5206\u5e03\u304a\u3088\u3073\u3001SciPy\u306e <math data-latex=\"F\"><semantics><mi>F<\/mi><annotation encoding=\"application\/x-tex\">F<\/annotation><\/semantics><\/math> \u7406\u8ad6\u5bc6\u5ea6<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">$t$ \u5206\u5e03\u3068\u306e\u95a2\u4fc2<\/h3>\n\n\n\n<p>\u81ea\u7531\u5ea6 <math data-latex=\"\\nu\"><semantics><mi>\u03bd<\/mi><annotation encoding=\"application\/x-tex\">\\nu<\/annotation><\/semantics><\/math> \u306e <math data-latex=\"t\"><semantics><mi>t<\/mi><annotation encoding=\"application\/x-tex\">t<\/annotation><\/semantics><\/math> \u5206\u5e03\u306b\u5f93\u3046\u78ba\u7387\u5909\u6570 <math data-latex=\"T\"><semantics><mi>T<\/mi><annotation encoding=\"application\/x-tex\">T<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"has-text-align-center\"><br><math data-latex=\"T \\sim t_\\nu\"><semantics><mrow><mi>T<\/mi><mo>\u223c<\/mo><msub><mi>t<\/mi><mi>\u03bd<\/mi><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">T \\sim t_\\nu<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p>\u304c\u3042\u308b\u3068\u304d\u3001\u3053\u308c\u3092\u4e8c\u4e57\u3059\u308b\u3068<\/p>\n\n\n\n<p class=\"has-text-align-center\"><br><math data-latex=\"T^2\\sim F(1,\\:\\nu)\"><semantics><mrow><msup><mi>T<\/mi><mn>2<\/mn><\/msup><mo>\u223c<\/mo><mi>F<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>1<\/mn><mo separator=\"true\">,<\/mo><mspace width=\"0.2222em\"><\/mspace><mi>\u03bd<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">T^2\\sim F(1,\\:\\nu)<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p>\u3068\u306a\u308b\u3002<math data-latex=\"T\"><semantics><mi>T<\/mi><annotation encoding=\"application\/x-tex\">T<\/annotation><\/semantics><\/math> \u306f<\/p>\n\n\n\n<p class=\"has-text-align-center\"><br><math data-latex=\"T\\:=\\: \\dfrac{\\:Z\\:}{\\:\\sqrt{U\/\\nu}\\:}\"><semantics><mrow><mi>T<\/mi><mspace width=\"0.2222em\"><\/mspace><mo>=<\/mo><mspace width=\"0.2222em\"><\/mspace><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mrow><mspace width=\"0.2222em\"><\/mspace><mi>Z<\/mi><mspace width=\"0.2222em\"><\/mspace><\/mrow><mrow><mspace width=\"0.2222em\"><\/mspace><msqrt><mrow><mi>U<\/mi><mi>\/<\/mi><mi>\u03bd<\/mi><\/mrow><\/msqrt><mspace width=\"0.2222em\"><\/mspace><\/mrow><\/mfrac><\/mstyle><\/mrow><annotation encoding=\"application\/x-tex\">T\\:=\\: \\dfrac{\\:Z\\:}{\\:\\sqrt{U\/\\nu}\\:}<\/annotation><\/semantics><\/math><br><\/p>\n\n\n\n<p>\u3068\u8868\u305b\u308b\u305f\u3081\u3001\u4e8c\u4e57\u3059\u308b\u3068<\/p>\n\n\n\n<p class=\"has-text-align-center\"><br><math data-latex=\"T^2\\:=\\: \\dfrac{\\:Z^2\\:}{\\:{U\/\\nu}\\:}\"><semantics><mrow><msup><mi>T<\/mi><mn>2<\/mn><\/msup><mspace width=\"0.2222em\"><\/mspace><mo>=<\/mo><mspace width=\"0.2222em\"><\/mspace><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mrow><mspace width=\"0.2222em\"><\/mspace><msup><mi>Z<\/mi><mn>2<\/mn><\/msup><mspace width=\"0.2222em\"><\/mspace><\/mrow><mrow><mspace width=\"0.2222em\"><\/mspace><mrow><mi>U<\/mi><mi>\/<\/mi><mi>\u03bd<\/mi><\/mrow><mspace width=\"0.2222em\"><\/mspace><\/mrow><\/mfrac><\/mstyle><\/mrow><annotation encoding=\"application\/x-tex\">T^2\\:=\\: \\dfrac{\\:Z^2\\:}{\\:{U\/\\nu}\\:}<\/annotation><\/semantics><\/math><br><\/p>\n\n\n\n<p>\u3068\u306a\u308b\u3002\u6a19\u6e96\u6b63\u898f\u5909\u6570 <math data-latex=\"Z\"><semantics><mi>Z<\/mi><annotation encoding=\"application\/x-tex\">Z<\/annotation><\/semantics><\/math> \u306e\u4e8c\u4e57\u306f\u81ea\u7531\u5ea6 1 \u306e <math data-latex=\"\\chi^2\"><semantics><msup><mi>\u03c7<\/mi><mn>2<\/mn><\/msup><annotation encoding=\"application\/x-tex\">\\chi^2<\/annotation><\/semantics><\/math> \u5206\u5e03\u306b\u5f93\u3044<\/p>\n\n\n\n<p class=\"has-text-align-center\"><br><math data-latex=\"Z^2\\sim \\chi_1^2\"><semantics><mrow><msup><mi>Z<\/mi><mn>2<\/mn><\/msup><mo>\u223c<\/mo><msubsup><mi>\u03c7<\/mi><mn>1<\/mn><mn>2<\/mn><\/msubsup><\/mrow><annotation encoding=\"application\/x-tex\">Z^2\\sim \\chi_1^2<\/annotation><\/semantics><\/math><br><\/p>\n\n\n\n<p>\u3067\u3042\u308b\u305f\u3081\u3001<\/p>\n\n\n\n<p class=\"has-text-align-center\"><br><math data-latex=\"T^2\\:=\\: \\dfrac{\\:\\chi_1^2\/1\\:}{\\:\\chi_\\nu^2\/\\nu\\:}\"><semantics><mrow><msup><mi>T<\/mi><mn>2<\/mn><\/msup><mspace width=\"0.2222em\"><\/mspace><mo>=<\/mo><mspace width=\"0.2222em\"><\/mspace><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mrow><mspace width=\"0.2222em\"><\/mspace><msubsup><mi>\u03c7<\/mi><mn>1<\/mn><mn>2<\/mn><\/msubsup><mi>\/<\/mi><mn>1<\/mn><mspace width=\"0.2222em\"><\/mspace><\/mrow><mrow><mspace width=\"0.2222em\"><\/mspace><msubsup><mi>\u03c7<\/mi><mi>\u03bd<\/mi><mn>2<\/mn><\/msubsup><mi>\/<\/mi><mi>\u03bd<\/mi><mspace width=\"0.2222em\"><\/mspace><\/mrow><\/mfrac><\/mstyle><\/mrow><annotation encoding=\"application\/x-tex\">T^2\\:=\\: \\dfrac{\\:\\chi_1^2\/1\\:}{\\:\\chi_\\nu^2\/\\nu\\:}<\/annotation><\/semantics><\/math><br><\/p>\n\n\n\n<p>\u3068\u306a\u308b\u3002\u3053\u308c\u306f\u5206\u5b50\u306e\u81ea\u7531\u5ea6 1\u3001\u5206\u6bcd\u306e\u81ea\u7531\u5ea6\u304c <math data-latex=\"\\nu\"><semantics><mi>\u03bd<\/mi><annotation encoding=\"application\/x-tex\">\\nu<\/annotation><\/semantics><\/math> \u3067\u3042\u308b <math data-latex=\"F\"><semantics><mi>F<\/mi><annotation encoding=\"application\/x-tex\">F<\/annotation><\/semantics><\/math> \u5206\u5e03\u306e\u5b9a\u7fa9\u305d\u306e\u3082\u306e\u3068\u306a\u3063\u3066\u3044\u308b\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u307e\u3068\u3081<\/h2>\n\n\n\n<p>\u6700\u5f8c\u306b\u3001\u5206\u5e03\u306e\u95a2\u4fc2\u3092\u4e00\u3064\u306e\u6d41\u308c\u3068\u3057\u3066\u6574\u7406\u3059\u308b\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u6a19\u6e96\u6b63\u898f\u5206\u5e03<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center\"><br><math data-latex=\"Z \\sim N(0,\\:1)\"><semantics><mrow><mi>Z<\/mi><mo>\u223c<\/mo><mi>N<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>0<\/mn><mo separator=\"true\">,<\/mo><mspace width=\"0.2222em\"><\/mspace><mn>1<\/mn><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">Z \\sim N(0,\\:1)<\/annotation><\/semantics><\/math><br><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u72ec\u7acb\u306a\u6a19\u6e96\u6b63\u898f\u4e71\u6570\u3092\u4e8c\u4e57\u3057\u3066\u8db3\u3059\u3068\u3001<math data-latex=\"\\chi^2\"><semantics><msup><mi>\u03c7<\/mi><mn>2<\/mn><\/msup><annotation encoding=\"application\/x-tex\">\\chi^2<\/annotation><\/semantics><\/math> \u5206\u5e03\u306b\u306a\u308b\u3002<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center\"><br><math data-latex=\"\\displaystyle\\sum_{i=1}^{\\nu} Z_i^2 \\sim \\chi^2(\\nu)\"><semantics><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mrow><munderover><mo movablelimits=\"false\">\u2211<\/mo><mrow><mi>i<\/mi><mo>=<\/mo><mn>1<\/mn><\/mrow><mi>\u03bd<\/mi><\/munderover><\/mrow><msubsup><mi>Z<\/mi><mi>i<\/mi><mn>2<\/mn><\/msubsup><mo>\u223c<\/mo><msup><mi>\u03c7<\/mi><mn>2<\/mn><\/msup><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>\u03bd<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mstyle><annotation encoding=\"application\/x-tex\">\\displaystyle\\sum_{i=1}^{\\nu} Z_i^2 \\sim \\chi^2(\\nu)<\/annotation><\/semantics><\/math><br><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u6a19\u6e96\u6b63\u898f\u4e71\u6570\u3092\u3001\u72ec\u7acb\u306a <math data-latex=\"\\chi^2\"><semantics><msup><mi>\u03c7<\/mi><mn>2<\/mn><\/msup><annotation encoding=\"application\/x-tex\">\\chi^2<\/annotation><\/semantics><\/math> \u4e71\u6570\u304b\u3089\u4f5c\u3063\u305f\u63a8\u5b9a\u6a19\u6e96\u504f\u5dee\u3067\u5272\u308b\u3068\u3001<math data-latex=\"t\"><semantics><mi>t<\/mi><annotation encoding=\"application\/x-tex\">t<\/annotation><\/semantics><\/math> \u5206\u5e03\u306b\u306a\u308b\u3002<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center\"><br><math data-latex=\"\\dfrac{\\:Z\\:}{\\:\\sqrt{U\/\\nu}\\:} \\sim t(\\nu)\"><semantics><mrow><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mrow><mspace width=\"0.2222em\"><\/mspace><mi>Z<\/mi><mspace width=\"0.2222em\"><\/mspace><\/mrow><mrow><mspace width=\"0.2222em\"><\/mspace><msqrt><mrow><mi>U<\/mi><mi>\/<\/mi><mi>\u03bd<\/mi><\/mrow><\/msqrt><mspace width=\"0.2222em\"><\/mspace><\/mrow><\/mfrac><\/mstyle><mo>\u223c<\/mo><mi>t<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>\u03bd<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">\\dfrac{\\:Z\\:}{\\:\\sqrt{U\/\\nu}\\:} \\sim t(\\nu)<\/annotation><\/semantics><\/math><br><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u72ec\u7acb\u306a\u4e8c\u3064\u306e <math data-latex=\"\\chi^2\"><semantics><msup><mi>\u03c7<\/mi><mn>2<\/mn><\/msup><annotation encoding=\"application\/x-tex\">\\chi^2<\/annotation><\/semantics><\/math> \u4e71\u6570\u3092\u81ea\u7531\u5ea6\u3067\u5272\u308a\u3001\u305d\u306e\u6bd4\u3092\u53d6\u308b\u3068\u3001<math data-latex=\"F\"><semantics><mi>F<\/mi><annotation encoding=\"application\/x-tex\">F<\/annotation><\/semantics><\/math> \u5206\u5e03\u306b\u306a\u308b\u3002<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center\"><br><math data-latex=\"\\dfrac{\\:U_1\/\\nu_1\\:}{\\:U_2\/\\nu_2\\:} \\sim F(\\nu_1,\\:\\nu_2)\"><semantics><mrow><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mrow><mspace width=\"0.2222em\"><\/mspace><msub><mi>U<\/mi><mn>1<\/mn><\/msub><mi>\/<\/mi><msub><mi>\u03bd<\/mi><mn>1<\/mn><\/msub><mspace width=\"0.2222em\"><\/mspace><\/mrow><mrow><mspace width=\"0.2222em\"><\/mspace><msub><mi>U<\/mi><mn>2<\/mn><\/msub><mi>\/<\/mi><msub><mi>\u03bd<\/mi><mn>2<\/mn><\/msub><mspace width=\"0.2222em\"><\/mspace><\/mrow><\/mfrac><\/mstyle><mo>\u223c<\/mo><mi>F<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msub><mi>\u03bd<\/mi><mn>1<\/mn><\/msub><mo separator=\"true\">,<\/mo><mspace width=\"0.2222em\"><\/mspace><msub><mi>\u03bd<\/mi><mn>2<\/mn><\/msub><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">\\dfrac{\\:U_1\/\\nu_1\\:}{\\:U_2\/\\nu_2\\:} \\sim F(\\nu_1,\\:\\nu_2)<\/annotation><\/semantics><\/math><br><\/p>\n\n\n\n<p>\u3057\u305f\u304c\u3063\u3066\u3001<math data-latex=\"\\chi^2\"><semantics><msup><mi>\u03c7<\/mi><mn>2<\/mn><\/msup><annotation encoding=\"application\/x-tex\">\\chi^2<\/annotation><\/semantics><\/math> \u5206\u5e03\u3001<math data-latex=\"t\"><semantics><mi>t<\/mi><annotation encoding=\"application\/x-tex\">t<\/annotation><\/semantics><\/math> \u5206\u5e03\u3001<math data-latex=\"F\"><semantics><mi>F<\/mi><annotation encoding=\"application\/x-tex\">F<\/annotation><\/semantics><\/math> \u5206\u5e03\u306f\u6b63\u898f\u5206\u5e03\u3092\u51fa\u767a\u70b9\u306b\u3057\u3066\u3001\u300c\u4e8c\u4e57\u548c\u300d\u300c\u63a8\u5b9a\u5206\u6563\u306b\u3088\u308b\u6a19\u6e96\u5316\u300d\u300c\u5e73\u5747\u4e8c\u4e57\u306e\u6bd4\u300d\u3068\u3044\u3046\u64cd\u4f5c\u3092\u8ffd\u3048\u3070\u3001\u691c\u5b9a\u3067\u306a\u305c\u305d\u306e\u5206\u5e03\u304c\u51fa\u3066\u304f\u308b\u306e\u304b\u304c\u81ea\u7136\u306b\u898b\u3048\u3066\u304f\u308b\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" width=\"1024\" height=\"122\" src=\"https:\/\/since2020.jp\/media\/wp-content\/uploads\/2026\/07\/image-7-1024x122.png\" alt=\"\" class=\"wp-image-9235\" srcset=\"https:\/\/since2020.jp\/media\/wp-content\/uploads\/2026\/07\/image-7-1024x122.png 1024w, https:\/\/since2020.jp\/media\/wp-content\/uploads\/2026\/07\/image-7-300x36.png 300w, https:\/\/since2020.jp\/media\/wp-content\/uploads\/2026\/07\/image-7-768x92.png 768w, https:\/\/since2020.jp\/media\/wp-content\/uploads\/2026\/07\/image-7.png 1030w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">\u4ed8\u9332<\/h2>\n\n\n\n<p>3\u3064\u306e\u56f3\u306e\u63cf\u753b\u306b\u4f7f\u3063\u305fPython\u30b3\u30fc\u30c9\u3092\u4ee5\u4e0b\u306b\u793a\u3059\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>\"\"\"\nGenerate only the three simulation figures: chi-square, t, and F.\n\nThe figures are built from normal random numbers first, then theoretical\nSciPy densities are overlaid for comparison.\n\"\"\"\n\nfrom pathlib import Path\n\nimport matplotlib\n\nmatplotlib.use(\"Agg\")\n\nimport matplotlib.pyplot as plt\nimport numpy as np\nfrom scipy import stats\n\n\nROOT = Path(__file__).resolve().parents&#091;1]\n# Figures\u306b\u4fdd\u5b58\u3059\u308b\u524d\u63d0\nOUTPUT_DIR = ROOT \/ \"Figures\"\nOUTPUT_DIR.mkdir(exist_ok=True)\n\nRNG = np.random.default_rng(20260717)\nN = 100_000\n\nplt.rcParams.update(\n    {\n        \"font.family\": &#091;\"YuGothic\", \"Hiragino Sans\", \"DejaVu Sans\"],\n        \"axes.unicode_minus\": False,\n        \"figure.dpi\": 140,\n        \"savefig.dpi\": 220,\n        \"axes.spines.top\": False,\n        \"axes.spines.right\": False,\n    }\n)\n\n\ndef save(fig, name):\n    for suffix in (\"png\", \"pdf\"):\n        fig.savefig(\n            OUTPUT_DIR \/ f\"{name}.{suffix}\",\n            bbox_inches=\"tight\",\n            facecolor=\"white\",\n            edgecolor=\"white\",\n        )\n    plt.close(fig)\n\n\ndef style(ax):\n    ax.grid(True, axis=\"y\", color=\"#d9dee7\", linewidth=0.8, alpha=0.8)\n    ax.tick_params(labelsize=8)\n\n\ndef chi_square_figure():\n    dfs = &#091;1, 2, 5, 30]\n    fig, axes = plt.subplots(2, 2, figsize=(10.5, 6.4))\n    fig.suptitle(\"\u6a19\u6e96\u6b63\u898f\u4e71\u6570\u306e\u4e8c\u4e57\u548c\u304b\u3089\u4f5c\u308b $\\\\chi^2$ \u5206\u5e03\", fontsize=14)\n\n    for ax, df in zip(axes.ravel(), dfs):\n        z = RNG.normal(size=(N, df))\n        simulated = np.sum(z**2, axis=1)\n        xmax = stats.chi2.ppf(0.995, df)\n        x = np.linspace(0.001, xmax, 600)\n\n        ax.hist(simulated, bins=90, range=(0, xmax), density=True, color=\"#7aa6c2\", alpha=0.58)\n        ax.plot(x, stats.chi2.pdf(x, df), color=\"#b23b3b\", lw=2.1)\n        ax.set_title(f\"\u81ea\u7531\u5ea6 $\\\\nu={df}$\", fontsize=11)\n        ax.set_xlabel(\"$x$\")\n        ax.set_ylabel(\"density\")\n        style(ax)\n\n    fig.legend(&#091;\"SciPy \u7406\u8ad6\u5bc6\u5ea6\", \"\u6b63\u898f\u4e71\u6570\u304b\u3089\u4f5c\u6210\"], loc=\"lower center\", ncol=2, frameon=False)\n    fig.tight_layout(rect=(0, 0.06, 1, 0.95))\n    save(fig, \"three_distribution_chi_square\")\n\n\ndef t_figure():\n    dfs = &#091;1, 3, 10, 30]\n    fig, axes = plt.subplots(2, 2, figsize=(10.5, 6.4), sharex=True, sharey=True)\n    fig.suptitle(\"\u6a19\u6e96\u6b63\u898f\u3092\u63a8\u5b9a\u5206\u6563\u3067\u6a19\u6e96\u5316\u3059\u308b\u3068 $t$ \u5206\u5e03\u306b\u306a\u308b\", fontsize=14)\n    x = np.linspace(-5.5, 5.5, 900)\n\n    for ax, df in zip(axes.ravel(), dfs):\n        z = RNG.normal(size=N)\n        u = np.sum(RNG.normal(size=(N, df)) ** 2, axis=1)\n        simulated = z \/ np.sqrt(u \/ df)\n\n        ax.hist(simulated, bins=120, range=(-5.5, 5.5), density=True, color=\"#83b799\", alpha=0.55)\n        ax.plot(x, stats.t.pdf(x, df), color=\"#b23b3b\", lw=2.1)\n        ax.plot(x, stats.norm.pdf(x), color=\"#30343f\", lw=1.6, ls=\"--\")\n        ax.set_title(f\"\u81ea\u7531\u5ea6 $\\\\nu={df}$\", fontsize=11)\n        ax.set_xlabel(\"$t$\")\n        ax.set_ylabel(\"density\")\n        style(ax)\n\n    fig.legend(\n        &#091;\"SciPy t \u5bc6\u5ea6\", \"\u6a19\u6e96\u6b63\u898f\u5bc6\u5ea6\", \"\u6b63\u898f\u4e71\u6570\u304b\u3089\u4f5c\u6210\"],\n        loc=\"lower center\",\n        ncol=3,\n        frameon=False,\n    )\n    fig.tight_layout(rect=(0, 0.06, 1, 0.95))\n    save(fig, \"three_distribution_t\")\n\n\ndef f_figure():\n    df_pairs = &#091;(1, 5), (5, 5), (10, 20), (30, 30)]\n    fig, axes = plt.subplots(2, 2, figsize=(10.5, 6.4))\n    fig.suptitle(\"\u4e8c\u3064\u306e\u72ec\u7acb\u306a\u5e73\u5747\u4e8c\u4e57\u306e\u6bd4\u304b\u3089\u4f5c\u308b $F$ \u5206\u5e03\", fontsize=14)\n\n    for ax, (df1, df2) in zip(axes.ravel(), df_pairs):\n        u1 = np.sum(RNG.normal(size=(N, df1)) ** 2, axis=1)\n        u2 = np.sum(RNG.normal(size=(N, df2)) ** 2, axis=1)\n        simulated = (u1 \/ df1) \/ (u2 \/ df2)\n        xmax = stats.f.ppf(0.995, df1, df2)\n        x = np.linspace(0.001, xmax, 700)\n\n        ax.hist(simulated, bins=120, range=(0, xmax), density=True, color=\"#d7a86e\", alpha=0.55)\n        ax.plot(x, stats.f.pdf(x, df1, df2), color=\"#b23b3b\", lw=2.1)\n        ax.axvline(1, color=\"#30343f\", lw=1.2, ls=\":\")\n        ax.set_title(f\"\u81ea\u7531\u5ea6 $(\\\\nu_1,\\\\nu_2)=({df1},{df2})$\", fontsize=11)\n        ax.set_xlabel(\"$f$\")\n        ax.set_ylabel(\"density\")\n        style(ax)\n\n    fig.legend(&#091;\"SciPy F \u5bc6\u5ea6\", \"$F=1$\", \"\u6b63\u898f\u4e71\u6570\u304b\u3089\u4f5c\u6210\"], loc=\"lower center\", ncol=3, frameon=False)\n    fig.tight_layout(rect=(0, 0.06, 1, 0.95))\n    save(fig, \"three_distribution_f\")\n\n\nif __name__ == \"__main__\":\n    chi_square_figure()\n    t_figure()\n    f_figure()\n    print(f\"Generated three distribution figures in {OUTPUT_DIR}\")\n<\/code><\/pre>\n","protected":false},"excerpt":{"rendered":"<p>3\u3064\u306e\u5206\u5e03\u3092\u516c\u5f0f\u3068\u3057\u3066\u899a\u3048\u3066\u3044\u307e\u305b\u3093\u304b\uff1f \u7d71\u8a08\u5b66\u3092\u5b66\u3073\u59cb\u3081\u308b\u3068\u3001\u6b63\u898f\u5206\u5e03\u3001\u4e8c\u9805\u5206\u5e03\u3001\u30dd\u30a2\u30bd\u30f3\u5206\u5e03\u306a\u3069\u6bd4\u8f03\u7684\u65e9\u3044\u6bb5\u968e\u3067\u76ee\u306b\u3059\u308b\u78ba\u7387\u5206\u5e03\u304c\u3042\u308b\u3002\u305d\u306e\u5f8c\u3001\u7d71\u8a08\u7684\u63a8\u6e2c\u3084\u4eee\u8a2d\u691c\u5b9a\u3092\u5b66\u3076\u9803\u306b\u306f\u4ee5\u4e0b\u306e3\u3064\u306e\u5206\u5e03\u304c\u767b\u5834\u3059\u308b\u3002 \u3053\u308c\u3089\u3092\u521d [&hellip;]<\/p>\n","protected":false},"author":100,"featured_media":3438,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"content-type":"","swell_btn_cv_data":"","footnotes":"","_wp_rev_ctl_limit":""},"categories":[1249],"tags":[331,522,57],"class_list":["post-9219","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-knowledge","tag-python","tag-522","tag-57"],"_links":{"self":[{"href":"https:\/\/since2020.jp\/media\/wp-json\/wp\/v2\/posts\/9219","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/since2020.jp\/media\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/since2020.jp\/media\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/since2020.jp\/media\/wp-json\/wp\/v2\/users\/100"}],"replies":[{"embeddable":true,"href":"https:\/\/since2020.jp\/media\/wp-json\/wp\/v2\/comments?post=9219"}],"version-history":[{"count":8,"href":"https:\/\/since2020.jp\/media\/wp-json\/wp\/v2\/posts\/9219\/revisions"}],"predecessor-version":[{"id":9236,"href":"https:\/\/since2020.jp\/media\/wp-json\/wp\/v2\/posts\/9219\/revisions\/9236"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/since2020.jp\/media\/wp-json\/wp\/v2\/media\/3438"}],"wp:attachment":[{"href":"https:\/\/since2020.jp\/media\/wp-json\/wp\/v2\/media?parent=9219"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/since2020.jp\/media\/wp-json\/wp\/v2\/categories?post=9219"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/since2020.jp\/media\/wp-json\/wp\/v2\/tags?post=9219"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}