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第4講統計的検定

母相関係数の差の検定

統計量

T = \frac{ζ (r_{1}) - ζ (r_{2})}{\sqrt{\frac{1}{n_{1} - 3} + \frac{1}{n_{2} - 3}}} \sim N (0, 1)

$\begin{equation} T = \frac{\ds \zeta(r_1) - \zeta(r_2)}{\ds\sqrt{\frac{1}{n_1-3}+\frac{1}{n_2-3}}} \sim N(0, 1) \end{equation}$

ζ (r_{1}) = \frac{1}{2} \log \frac{1 + r_{1}}{1 - r_{1}}

$\begin{equation} \zeta(r_1) = \frac{1}{2}\log\frac{1 + r_1}{1 - r_1} \end{equation}$

ζ (r_{2}) = \frac{1}{2} \log \frac{1 + r_{2}}{1 - r_{2}}

$\begin{equation} \zeta(r_2) = \frac{1}{2}\log\frac{1 + r_2}{1 - r_2} \end{equation}$

検定

$H_{0}:~\rho_{1} = \rho_{2}~~~~H_{1}~:~\rho_{1} \ne \rho_{2}$

| T | > z (\frac{α}{2})

$\begin{equation} |T| > z\left(\frac{\alpha}{2}\right) \end{equation}$

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