On testing the significance of squared semipartial correlation coefficient.

#1
On testing the significance of squared semipartial correlation coefficient. Please could you guide me on which test and how the test of significance of squared semipartial correlation coefficient is conducted.
 

j58

Active Member
#2
If I understand the semi-partial correlation correctly, the semi-partial correlation between x and y controlling for the effect of z on y is the correlation between x and the residuals of a regression of y on z. So, one way to test for the significance of this semi-partial correlation coefficient would be to first regress y on z, and then to regress the residuals from that regression on x. The p-value for the regression coefficient of x would be the same as the p-vaule for the semi-partial correlation coeffient, and hence also for its square.
 
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j58

Active Member
#4
Well, if you do it the way I described, most statistical software will test the significance of the regression coefficient by using a t-test.