A major problem in the evaluation of the two approaches by W&H is that it is based on a number that is not available to the scientist. W&H compared the two approaches using the standard deviation of the meta-analytic effect after 5,000 simulations. However, what is available to the scientist is the standard error of one meta-analytic effect size estimate. The standard error of the meta-analytic effect is a function of the sampling error of each study (), the number of published studies (K), and the heterogeneity of the effect as found in the published studies. The underlying effect is homogenous in the publishing everything approach, and the standard error of the meta-analytic effect can be shown to equal . In the selective publishing approach, only studies yielding significantly different effects are published, introducing heterogeneity in effects (see also W&H's Figure 2). This results in a larger standard error of the meta-analytic effect for selective publishing than for publishing everything.
