P-Values of the Correlations

Multivariate Analyses

P-Values of the Correlations

The P-Values of the Correlations table contains the p-value of each correlation under the null hypothesis that the correlation is 0, assuming independent and identically distributed (unless weights are specified) observations from a bivariate distribution with at least one variable normally distributed. This table is shown in Figure 40.14. Each p-value in this table can be used to assess the significance of the corresponding correlation coefficient.

The p-value of a correlation r is obtained by treating the statistic

$\hspace*{0.25in} t = \sqrt{n - 2} \frac{r}{\sqrt{1 - r^2} }$

as having a Student's t distribution with n-2 degrees of freedom. The p-value of the correlation r is the probability of obtaining a Student's t statistic greater in absolute value than the absolute value of the observed statistic t.

With partial variables, the p-value of a correlation is obtained by treating the statistic

$\hspace*{0.25in} t = \sqrt{n - n_{p} - 2} \frac{r}{\sqrt{1 - r^2} }$

as having a Student's t distribution with n- n_p-2 degrees of freedom.

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