Effect sizes of the r-family

There are two common types of effect size in the r-family: correlation coefficients (which are unit free by definition) and regression weights (which can be unstandardized or standardized). Unstandardized regression weights will almost never be meta-analysed because this would require that all studies would use exactly the same measurement instruments (with the same scales) for both the independent and dependent variable. However, in the exceptional case that the user has this type of data, the user could also use the generic workbook 1, assuming that the standard errors are available as well.

Workbook 5 ‘Correlational data.xlsx’ is designed to meta-analyse bivariate correlations. Generally, when people refer to ‘correlations’ they mean this type of correlation, which is sometimes also referred to as Pearson’s correlation.

All workbooks discussed so far (2-5) are used to meta-analyse effect sizes for bivariate effects. However it is very common, in studies with effect sizes of the r-family that the ‘effect’ of a set of multiple independent variables on an independent variable is studied. A problem for meta-analysis is that it is very rare that the same set of independent variables (with the same method of measurement) is used across all studies. This means that the regression weights generated in different studies cannot be compared directly, because they are ‘controlled’ for different sets of other independent variables. The remaining workbooks 6 and 7 provide two slightly different solutions for this situation.

Workbook 6 ‘Partial correlational data.xlsx’ is designed to meta-analyse partial correlations of two variables, that is, the correlation between two variables controlled for other variables. Or more formally, the part of the predictor that is related with the outcome variable after a portion of the effect (the portion that is explained by other additional variables) is partialled out. This effect size can be used when you are interested in the relation between two variables, while controlling for other variables in both the predictor and the dependent variable. The workbook can calculate partial correlations from commonly reported multiple regression results.

Workbook 7 ‘Semi-partial correlational data.xslx’ is designed to meta-analyse the semi-partial correlation between two variables, but removes only the variance explained by additional variables from the outcome and not from the focal predictor. The semi-partial correlation is sometimes referred to as ‘part correlation’. This effect size can be used when you are interested in the relation between two variables, while controlling for other variables in only the predictor. The workbook can calculate semi-partial correlations from commonly reported multiple regression results.