ABSTRACT
80While synthesizing the effect sizes of two separate studies, the meta-analyst seeks to compare the results to discover the degree of their actual similarity. Given two effect sizes that are not significantly different and therefore combinable on statistical grounds, you may want to determine the effect size of an effect across studies. The first step to take when combining the effect sizes of two studies is to calculate r for each and convert each r value into corresponding Z-scores. If the effect sizes of the two studies are statistically different, it means little sense to average their effect sizes. Although meta-analysts are usually more interested in effect sizes than p-values, they sometimes evaluate the overall level of significance as a way of increasing power. After we compare the results of two separate studies, it is an easy matter to combine the p-levels. In this way, we get an overall estimate of the probability that the two p-levels might have been obtained if the null hypothesis of no relation between X and Y were true.
