On a Proper Meta-Analytic Model for Correlations

Combining statistical information across studies is a standard research tool in applied psychology. The most common approach in applied psychology is the fixed effects model. The fixed-effects approach assumes that individual study characteristics such as treatment conditions, study context, or individual differences do not influence study effect sizes. That is, that the majority of the differences between the effect sizes of different studies can be explained by sampling error alone. We critique the fixed-effects methodology for correlations and propose an advancement, the random-effects model, that ameliorates problems imposed by fixed-effects models. The random-effects approach explicitly incorporates between-study differences in data analysis and provides estimates of how those study characteristics influence the relationships among constructs of interest. Because they can model the influence of study characteristics, we assert that random-effects models have advantages for psychological research. Parameter estimates of both models are compared and evidence in favor of the random-effects approach is presented.