第4講統計的検定

無相関の検定

T = \frac{\sqrt{n - 1} r}{\sqrt{1 - r^{2}}} \sim t (n - 2)

$\begin{equation} T = \frac{\sqrt{n-1}r}{\sqrt{1-r^2}} \sim t(n-2) \end{equation}$

$H_{0}:~~\rho = 0~~~~H_{1}:~\rho \ne 0$

| T | > t_{\frac{α}{2}} (n - 2)

$\begin{equation} |T| > t_{\frac{\alpha}{2}}(n-2) \end{equation}$

T = \frac{(n - 1) r^{2}}{1 - r^{2}} \sim F (1, n - 2)

$\begin{equation} T = \frac{(n-1)r^2}{1-r^2} \sim F(1, n-2) \end{equation}$

$H_{0}:~~\rho = 0~~~~H_{1}:~\rho \ne 0$

T > F_{\frac{α}{2}} (1, n - 2)

$\begin{equation} T > F_{\frac{\alpha}{2}}(1, n-2) \end{equation}$