\u7570\u306a\u308b\u30d9\u30eb\u30cc\u30fc\u30a4\u5206\u5e03\u304b\u3089\u5f97\u3089\u308c\u305f2\u3064\u306e\u6a19\u672c\u5e73\u5747\u306b, \u7d71\u8a08\u7684\u306b\u5dee\u304c\u3042\u308b\u3068\u8a00\u3048\u308b\u304b\u3069\u3046\u304b. <\/p>\n
\u5224\u65ad\u57fa\u6e96\u3092\u300c\u305d\u308c\u305e\u308c\u306e\u6a19\u672c\u5e73\u5747\u306b\u5dee\u304c\u306a\u3044\u3068\u3044\u3046\u5e30\u7121\u4eee\u8aac\u3092\u68c4\u5374\u3067\u304d\u308b\u304b\u3069\u3046\u304b\u300d\u3068\u3057\u305f\u6642, \u3061\u3087\u3046\u3069\u5224\u65ad\u304c\u3067\u304d\u308b(\u3067\u304d\u306a\u3044)\u6642\u70b9\u3092\u8003\u3048\u308b.<\/p>\n
<\/p>\n
\u76ee\u7684<\/p>\n
\\[
\nz = \\frac{\\left|\\mu_{1}-\\mu_{2}\\right|}{\\sqrt{\\mu(1-\\mu)\\left(\\frac{1}{n}+\\frac{1}{m}\\right)}} ~~~ \\mathrm{where} ~~~ \\mu = \\frac{\\mu_{1}m+\\mu_{2}n}{n+m} \\tag{1}
\n\\]<\/p>\n
\u4e0a\u5f0f\u3092 \\(\\mu_{2}\\) \u306b\u3064\u3044\u3066\u89e3\u304f.<\/p>\n
\u524d\u63d0<\/p>\n
\u305d\u308c\u305e\u308c\u306e\u6a19\u672c\u30b5\u30a4\u30ba\u3092 \\(n,~ m\\), \u6a19\u672c\u5e73\u5747\u3092 \\(\\mu_{1},~ \\mu_{2}\\) \u3068\u3059\u308b.<\/p>\n
\u6bd4\u7387\u306e\u5dee\u306b\u3064\u3044\u3066\u306e\u691c\u5b9a\u3092\u8003\u3048\u3066, \u5e30\u7121\u4eee\u8aac \\( \\mu_{1} = \\mu_{2} \\) \u3092\u304a\u304f. \u5e30\u7121\u4eee\u8aac\u304c\u68c4\u5374\u3067\u304d\u308b\u304b\u3069\u3046\u304b\u306e\u5224\u65ad\u306e\u5883\u754c\u3067 (1)\u5f0f\u304c\u6210\u308a\u7acb\u3064.<\/p>\n
\u30fb \\(\\mu_{1} > \\mu_{2}\\) \u306e\u5834\u5408<\/p>\n
\\[
\n\\mu_{1}-\\mu_{2} = z\\sqrt{\\mu(1-\\mu)\\left(\\frac{1}{n}+\\frac{1}{m}\\right)}
\n\\]<\/p>\n
\u4e21\u8fba\u30922\u4e57\u3057\u3066\u6574\u7406\u3059\u308b.<\/p>\n
\\[
\n\\begin{eqnarray}
\n\\left(\\mu_{1}-\\mu_{2}\\right)^{2} & = & z^{2}\\mu(1-\\mu)\\left(\\frac{1}{n}+\\frac{1}{m}\\right) \\\\
\n& = & z^{2} \\left(\\frac{\\mu_{1}m+\\mu_{2}n}{n+m}\\right) \\left(1-\\frac{\\mu_{1}m+\\mu_{2}n}{n+m}\\right) \\left(\\frac{1}{n}+\\frac{1}{m}\\right) \\\\
\n& = & z^{2} \\left(\\frac{1}{n}+\\frac{1}{m}\\right) \\left\\{\\frac{\\mu_{1}m+\\mu_{2}n}{n+m}-\\left(\\frac{\\mu_{1}m+\\mu_{2}n}{n+m}\\right)^{2}\\right\\} \\\\
\n& = & z^{2} \\left(\\frac{1}{n}+\\frac{1}{m}\\right) \\frac{1}{n+m} \\left\\{ \\mu_{1}m+\\mu_{2}n -\\frac{1}{n+m}\\left(\\mu_{1}^{2}m^{2}+2\\mu_{1}\\mu_{2}nm+\\mu_{2}^{2}n^{2}\\right) \\right\\} \\\\
\n& = & z^{2} \\left(\\frac{1}{n}+\\frac{1}{m}\\right) \\frac{1}{n+m} \\left\\{ -\\frac{n^{2}}{n+m}\\mu_{2}^{2} + \\left(n-\\frac{2\\mu_{1}nm}{n+m}\\right)\\mu_{2} + \\mu_{1}m – \\frac{1}{n+m}\\mu_{1}^{2}m^{2} \\right\\}
\n\\end{eqnarray}
\n\\]<\/p>\n
\\[
\n\\mu_{2}^{2} – 2\\mu_{1}\\mu_{2} + \\mu_{1}^{2} = z^{2} \\left(\\frac{1}{n}+\\frac{1}{m}\\right) \\frac{1}{n+m} \\left\\{ -\\frac{n^{2}}{n+m}\\mu_{2}^{2} + \\left(n-\\frac{2\\mu_{1}nm}{n+m}\\right)\\mu_{2} + \\mu_{1}m – \\frac{1}{n+m}\\mu_{1}^{2}m^{2} \\right\\}
\n\\]<\/p>\n
\\[
\n\\left(1 + z^{2}\\left(\\frac{1}{n}+\\frac{1}{m}\\right) \\left(\\frac{n}{n+m}\\right)^{2}\\right)\\mu_{2}^{2} – \\left(2\\mu_{1} + z^{2} \\left(\\frac{1}{n}+\\frac{1}{m}\\right) \\frac{n-\\frac{2\\mu_{1}nm}{n+m}}{n+m} \\right)\\mu_{2} + \\mu_{1}^{2} – z^{2}\\left(\\frac{1}{n}+\\frac{1}{m}\\right)\\frac{1}{n+m}\\left( \\mu_{1}m – \\frac{1}{n+m}\\mu_{1}^{2}m^{2} \\right) = 0
\n\\]<\/p>\n
\\( \\mu_{2} \\) \u306b\u3064\u3044\u3066\u306e2\u6b21\u65b9\u7a0b\u5f0f\u304c\u5f97\u3089\u308c\u305f\u306e\u3067, \u3042\u3068\u306f\u4e0a\u5f0f\u3092\u89e3\u3051\u3070\u3088\u3044.<\/p>\n
\u30fb \\(\\mu_{1} < \\mu_{2}\\) \u306e\u5834\u5408<\/p>\n
\u7565.<\/p>\n
\u95a2\u9023<\/p>\n