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I understand the concepts of partial and semi-partial correlation, but I am still not clear on when to use one over the other. Are there specific research questions that would determine that we need to control the third variable for only one vs for both?

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  • $\begingroup$ Please search the site for "semi-partial correlation", "part correlation" $\endgroup$
    – ttnphns
    Aug 1, 2018 at 7:44
  • $\begingroup$ One way to understand a function is to understand what maximizes or minimizes it. I briefly describe that for partial correlation here: stats.stackexchange.com/questions/588968/… $\endgroup$
    – Galen
    Sep 26, 2022 at 5:04

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Partial correlation explains the correlation between two continuous variables (let's say X1 and X2) holding X3 constant for both X1 and X2.

Semipartial correlation measures the strength of linear relationship between variables X1 and X2 holding X3 constant for just X1 or just X2. It is also called part correlation.

Partial correlation holds variable X3 constant for both the other two variables. Whereas, Semipartial correlation holds variable X3 for only one variable (either X1 or X2). Hence, it is called 'semi'partial

In practice the partial and semipartial r are the same in sign and tend to be similar in magnitude.

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  • $\begingroup$ partial correlation is always going to be bigger in magnitude and more statistically significant than semipartial $\endgroup$
    – rep_ho
    Sep 15, 2021 at 8:11

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