表 8.4 两个正态总体方差的假设检验的拒绝域

两个正态总体方差的假设检验的拒绝域 (显著性水平为 $α$ )

序号	$H_{0}$	$H_{1}$	$μ_{1}, μ_{2}$ 已知	$μ_{1}, μ_{2}$ 未知
I	$σ_{1}^{2} = σ_{2}^{2}$	$σ_{1}^{2} \neq = σ_{2}^{2}$	$\frac{i = 1 \sum m ( x _{i} - μ _{1} ) ^{2} / m}{j = 1 \sum n ( y _{j} - μ _{2} ) ^{2} / n} \leq F_{\frac{α}{2}} (m, n) 或 \frac{i = 1 \sum m ( x _{i} - μ _{1} ) ^{2} / m}{i = 1 \sum n ( y _{i} - μ _{2} ) ^{2} / n} \geq F_{1 - \frac{α}{2}} (m, n)$	$\frac{S _{1 m}^{* 2}}{S _{2 n}^{* 2}} \leq F_{\frac{α}{2}} (m - 1, n - 1)$ 或
				$\frac{S _{1 m}^{* 2}}{S _{2 n}^{* 2}} \geq F_{1 - \frac{α}{2}} (m - 1, n - 1)$
II	$σ_{1}^{2} = σ_{2}^{2}$	$σ_{1}^{2} > σ_{2}^{2}$	$\frac{i = 1 \sum m ( x _{i} - μ _{1} ) ^{2} / m}{j = 1 \sum n ( y _{j} - μ _{2} ) ^{2} / n} \geq F_{1 - α} (m, n)$	$\frac{S _{1 m}^{* 2}}{S _{2 n}^{* 2}} \geq F_{1 - α} (m - 1, n - 1)$
III	$σ_{1}^{2} \leq σ_{2}^{2}$	$σ_{1}^{2} > σ_{2}^{2}$
IV	$σ_{1}^{2} = σ_{2}^{2}$	$σ_{1}^{2} < σ_{2}^{2}$	$\frac{i = 1 \sum m ( x _{i} - μ _{1} ) ^{2} / m}{j = 1 \sum n ( y _{j} - μ _{2} ) ^{2} / n} \leq F_{α} (m, n)$	$\frac{S _{1 m}^{* 2}}{S _{2 n}^{* 2}} \leq F_{α} (m - 1, n - 1)$
V	$σ_{1}^{2} \geq σ_{2}^{2}$	$σ_{1}^{2} < σ_{2}^{2}$	$\frac{i = 1 \sum m ( x _{i} - μ _{1} ) ^{2} / m}{j = 1 \sum n ( y _{j} - μ _{2} ) ^{2} / n} \leq F_{α} (m, n)$	$\frac{S _{1 m}^{* 2}}{S _{2 n}^{* 2}} \leq F_{α} (m - 1, n - 1)$

Youliang Zhong