partial vs semi-partial correlations in MR

[wsu_wright]

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..."

[Jamie Burnett-3]

I think they are both correct David, please note that Tabachnick talks about the unique contribution to the total variance of the DV, whilst Norusis says the unexplained variance in the DV.

Let's say you have a dependent variable Y and two independent variable X1 and X2, Partial correlations looks at the correlation between Y and X1 after accounting for the other IV X2 in both Y and X1, whilst semi-partial correlations show the correlation between Y and X1 after accounting for X2 in X1 only.  This is why Tabachnick talks about total variance in Y when discussing semi-partial correlations and Norusis unexplained variance left in DV when discussing partial correlations.

Does this make sense?

I believe it is the square of the partial correlation that would be best to explain the unique contribution to the explained variance in DV.

Thanks

Jamie

________________________________

From: SPSSX(r) Discussion on behalf of David Wright
Sent: Sun 10/22/2006 4:24 PM
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..."




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[statisticsdoc]

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

For personalized and professional consultation in statistics and research design, visit
www.statisticsdoc.com


-----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..."