1. Moderator Analyses • Testing a categorical moderator • Testing a continuous moderator • Examining relations among moderators • Testing a multiple regression model

2. Testing a Categorical Moderator • Parallels one-way ANOVA • Between-group heterogeneity Qb • Larger when there are larger differences between group means • Follows a chi-square distribution with p-1 df, where p is the number of groups • Tests whether the moderator explains a significant amount of variability in the effect sizes

3. Testing a Categorical Moderator • Within-group homogeneity Qw • Larger when there is more variability within each of your groups • Follows a chi-square distribution with k-p df, where p is the number of groups and k is the number of effect sizes • Tests whether there is a significant amount of variability in the effect sizes not explained by the moderator

4. Testing a Categorical Moderator • The values of Qb and Qw can be obtained from a weighted ANOVA predicting the effect size from the moderator • Weight is the inverse of the variance • Qb will be the SS associated with the factor • Qe will be the SS error

5. Testing a Continuous Moderator • Can compute regression coefficient and its standard error from a weighted regression predicting the effect size from the moderator • Can then test whether coefficient is significantly different from zero

6. Testing a Continuous Moderator • Standard software packages will use an incorrect weighting procedure • Estimates the coefficient correctly • Standard error will be wrong • Can get the correct standard error using parts of the output

7. Examining Relations Among Moderators • Moderator variables will often be confounded with each other • Methods tend to clump into paradigms rather than being distributed • Useful to determine if there are strong relations among your IVs • Can be tested in the same way as relations with the effect size • Usually only report relations that might question the validity of a significant moderator

8. Multiple Regression Models • Based on weighted regression • All categorical moderators must be dummy-coded for inclusion in the regression model • Can test individual coefficients • Need to correct standard error • Can also test collections of coefficients • Similar to homogeneity test

9. Multiple Regression Models • SSR from the model is equal to Qb, which follows a chi-square distribution with p df • Tests whether your IVs can jointly explain a significant amount of variability in the effect size • SSE from the model is equal to Qe, which follows a chi-square distribution with k-p df • Tests whether there is a significant amount of variability in the effect size not explained by any of your IVs

10. Multiple Regression Models • Used in a slightly different way than in primary research • Often choose moderators for MR model from significant bivariate tests • If moderator not significant in MR model, then it means the moderator must be interpreted cautiously • Still can be used as an omnibus test