12.5：章节公式回顾

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12.1 两个方差的检验

$H_{0} : \frac{\sigma_{1}^{2}}{\sigma_{2}^{2}}=\delta_{0}\nonumber$

$H_{a} : \frac{\sigma_{1}^{2}}{\sigma_{2}^{2}} \neq \delta_{0}\nonumber$

如果 $\delta_{0}=1$ 那么

$H_{0} : \sigma_{1}^{2}=\sigma_{2}^{2}\nonumber$

$H_{a} : \sigma_{1}^{2} \neq \sigma_{2}\nonumber$

测试统计数据为：

$F_{c}=\frac{S_{1}^{2}}{S_{2}^{2}}\nonumber$

$S S_{\mathrm{between}}=\sum\left[\frac{\left(s_{j}\right)^{2}}{n_{j}}\right]-\frac{\left(\sum s_{j}\right)^{2}}{n}$

$S S_{\mathrm{total}}=\sum x^{2}-\frac{\left(\sum x\right)^{2}}{n}$

$S S_{\text {within}}=S S_{\text {total}}-S S_{\text {between}}$

$d f_{\mathrm{between}}=d f(n u m)=k-1$

$d f_{\text {within}}=d f(\text {denom})=n-k$

$M S_{\text {between}}=\frac{S S_{\text {between}}}{d f_{\text {between}}}$

$M S_{\text {within}}=\frac{S S_{\text {within}}}{d f_{\text {within}}}$

$F=\frac{M S_{\text {between}}}{M S_{\text {within}}}$