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An excerpt from Will's recent post:
But my original question, about which partial correlation to use, is still unanswered! You can calculate the correlation as a semi-partial, which means effectively that the magnitude of the effect is interpreted using the SD of the original dependent variable. Or you can calculate it as a (full) partial, which means you effectively use the SD of the residual variation in the dependent variable after all the other predictors have been taken into account. The partial will be larger than the semi-partial, because the partial is the expected correlation for subjects all with the same SES, diet etc etc. Is it the right one to use? Dunno. It looks bigger, so if you want a big correlation, use the partial, not the semi-partial? But if you want your answer to be little or no effect, use the semi-partial, not the partial? That's not good science.
Attached is a 5-page Microsoft Word document that may help to explain the concept of partial and semi-partial correlations in the context of the health, physical activity, and socioeconomic status example discussed by Will Hopkins. [Attachment deleted by moderator. Use the link below to download the attachment.] I created this document from the examples I use when teaching the concept of partial and semi-partial correlations. Also included are the equations for calculating these correlations. The same Word document is available at http://www.uta.edu/faculty/jcramer/downloads.
Joel
Joel Cramer
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