Effect Sizes

Although most of the individual study statistics were correlation coefficients, the results of several studies had to be converted from a parametric statistic to a correlation. In some of these cases it was possible to calculate r from t, F, d, 2 or a probability value. Procedures for these indirect calculations of r are described by Cohen (1977); Hunter and Schmidt, (1990); Hunter, et al. (1982); Rosenthal (1991a and 1991b); Smith, Glass & Miller (1980); and Wolf (1986). In certain circumstances, the study reported a two-way ANOVA. The relevant F was first converted to eta using an algorithm presented by Haase (1983) and then to r.

Each correlation was weighted by its respective sample size to correct for sampling error. Sampling error refers to the random variation in the estimate of µ due to smaller sample sizes. If one assumes that the estimate of rho, or the relationship within the population, is constant over all studies, then the sample weighted mean r provides a better estimate of rho than the mean unweighted correlation. The sample-weighted r gives more importance to well-conducted large-n studies than to those reports that only have a few subjects, or participants drawn from unrepresentative samples. Ignoring sampling error here would almost guarantee that statistical errors would be made at some point in the analysis (Hunter, et al., 1982). Moreover, if there is little or no variation in rho, weighting serves to improve the general accuracy of the estimate of rho. Even when the variation in rho is large, then if the obtained effect sizes are not related to sample size, the sample-weighted r is still the better estimate of the population relationship (Hunter et al., 1982).