Re: partial vs semi-partial correlations in MR

Posted by statisticsdoc on Oct 23, 2006; 4:23am
URL: http://spssx-discussion.165.s1.nabble.com/partial-vs-semi-partial-correlations-in-MR-tp1071617p1071618.html

Stephen Brand
www.statisticsdoc.com

David,

The partial and semi-partial correlation answer different questions.  The partial correlation between X and Y partialling out Z is the correlation between the residuals of X and the residuals of Y after Z has been utilized to predict each.  In a semipartial correlation, we residualize X for Z but not Y.  The following link explains the distinction in more detail.

http://luna.cas.usf.edu/~mbrannic/files/regression/Partial.html

Both Tabachnick & Fidell and Norusis are correct, but are addressing different questions.  The square of the the semipartial correlation shows the unique contribution of a predictor variable, after adjusting for all of the other predictors, to the prediction of a criterion variable Y, but Y is not adjusted for any of the predictor variables.  The semipartial correlation is appropriate for understanding the contributions of predictors in a regression model.  The squared partial addresses the shared variance between predictor and criterion when both are adjusted for one or more variables.  In the larger scheme of things, whether you use a semi-partial or a partial correlation depends on your research questions.

HTH,

Stephen Brand

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-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]]On Behalf Of
David Wright
Sent: Sunday, October 22, 2006 11:25 AM
To: [hidden email]
Subject: partial vs semi-partial correlations in MR


Just when I get this figured out I read more & get confused.  Partial vs semi-partial correlations in multiple regsression-- which is the better measure squared to identify the unique contribution to the explained variance in the DV?

In Tabachnick & Fidell (2007, 5th ed, pp145-146) they note the "squared semi-partial correlations expresses the unique contribution of the IV to the total variance of the DV."  Whereas Norusis (spss 14 statistical procedures companion,  p248) states "The square of the partial correlation coefficient tells you waht proportion of the unexplained variance in the DV is explained..."