A Note on the Use of Partial Correlation Coefficients in Meta-Analyses

Meta-analyses in economics, business, and the social sciences commonly use partial correlation coefficients (PCCs) when the original estimated effects cannot be combined. This can occur, for example, when the primary studies use different measures for the dependent and independent variables, even though they are all concerned with estimating the same conceptual effect. This note demonstrates that analyses based on PCCs can produce different results than those based on the original, estimated effects. This can affect conclusions about the overall mean effect, the factors responsible for differences in estimated effects across studies, and the existence of publication selection bias. I first derive the theoretical relationship between Fixed Effects/Weighted Least Squares estimates of the overall mean effect when using the original estimated effects and their PCC transformations. I then provide two empirical examples from recently published studies. The first empirical analysis is an example where the use of PCCs does not change the main conclusions. The second analysis is an example where the conclusions are substantially impacted. I explain why the use of PCCs had different effects in the two examples.