\u5728\u6bd4\u8f83\u4e24\u4e2a\u65b9\u5dee\u9f50\u6027\u4e00\u81f4\u7ec4\u7684\u5747\u503c\u65f6\uff0c\u6c42\u89e3t\u503c\u7684\u7b97\u5f0f\u6709\u4e24\u79cd\u3002\u5206\u522b\u662f\uff1a<\/p>\n\\((1) t=\\frac{\\bar{X_1}-\\bar{X_2}}{\\sqrt{\\frac{(n_1-1)S_1^2+(n_2-1)S_2^2}{n_1+n_2-2}(\\frac{1}{n_1}+\\frac{1}{n_2})}}\\)\n
<\/p>\n\\((2) t=\\frac{\\bar{X_1}-\\bar{X_2}}{\\sqrt{\\frac{\\sum{X_1}^2-\\frac{(\\sum{X_1})^2}{n_1}+\\sum{X_2}^2-\\frac{(\\sum{X_2})^2}{n_2}}{n_1+n_2-2}(\\frac{1}{n_1}+\\frac{1}{n_2})}}\\)\n
\u4e8c\u8005\u5176\u5b9e\u662f\u4e00\u6837\u7684\u3002\u8f6c\u5316\u8fc7\u7a0b\u4e00\u6837\uff0c\u6211\u4eec\u53ea\u9700\u8981\u8bc1\u660e\\(\\sum{X}^2-\\frac{(\\sum{X})^2}{n}=(n-1)S^2\\)\u5373\u53ef\u3002\u8fc7\u7a0b\u5982\u4e0b\uff1a<\/p>\n\\((n-1)S^2=(n-1)\\frac{\\sum{(X-\\bar{X})^2}}{n-1}=\\sum{(X-\\bar{X})}^2\\)\n\\(=\\sum{(\\frac{nX-\\sum{X}}{n})^2}\\)\n
\u8fdb\u800c<\/p>\n\\(=\\sum{(\\frac{n^2X^2+(\\sum{X})^2-2nX\\sum{X}{n^2}}{n^2})}\\)\n\\(=\\sum{X^2+(\\frac{(\\sum{X})^2-2nX\\sum{X}{n^2}}{n^2})}\\)\n\\(=\\sum{X}^2+\\frac{(\\sum{X})^2-2n(\\sum{X})^2}{n^2}=\\sum{X}^2-\\frac{(\\sum{X})^2}{n}\\)\n","protected":false},"excerpt":{"rendered":"
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