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} }](images/multeq32.gif)
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} }](images/multeq33.gif)
as having a Student's t distribution
with n- np-2 degrees of freedom.
Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.