Effect Size Measures for Mediation Models

Introduction:

Even though mediation designs have become fairly frequent in research, there is still no universally accepted way to express the magnitude of the mediated effect. The bias and efficiency of five effect size measures for the single mediator model and four effect size measures for the parallel two-mediator model for continuous and binary independent variables were examined in a simulation study in order to provide clear guidelines for substantive researchers.

Methods:

In a study containing 320 combinations of parameters, SAS software (Version 9.2 of the SAS System for Windows) was used to conduct a simulation which calculated bias, relative bias, and standard deviations of effect sizes over 1000 replications. In the first simulation, all three variables (X, M, and Y) were continuous. A macro was designed to loop through all combinations of population sample sizes (10, 50, 100, 500, and 1000) and all possible combinations of values for a, b, and c’ paths (0, 0 .14, 0.39, and 0.59). Means of bias, relative bias, and the standard deviations for each combination over 1000 replications were obtained from the simulation. Standardized bias was subsequently computed from the output of the simulation by dividing the values of bias by the standard deviations corresponding to the same combination of parameter values and sample size. In the second simulation, M and Y remained continuous, while X was a binary variable. The same analyses from the first simulation were repeated at the end of the second simulation. Two comparable simulations were performed for the two-mediator model with zero, small, medium and large mediated effects for binary and continuous X, however, was not examined because it cannot be extended beyond the single mediator model.

Results:

Given the results of the simulations, a general recommendation for the single mediator model with continuous X would be to choose either ab/s_Y, ab(s_X)/s_Y, or  , and when X is binary one would opt for either ab/s_Y or  .  In the two-mediator model one should also select ab/s_Y, ab(s_X)/s_Y for their relative unbiasednes and efficiency. An example will be provided in order to clarify how the results and the interpretations of the effect size measures can guide researchers in their selection.

Conclusions:

Based on the results of the study and the interpretations of each effect size measure, some guidelines for choosing the optimal effect size measures are provided. Ideally, one will choose an effect size that answers the research question directly and has the least bias and most stability in order to obtain accurate findings that are replicable across studies.