Detecting publication selection bias through excess statistical significance.

We introduce and evaluate three tests for publication selection bias based on excess statistical significance. The proposed tests incorporate heterogeneity explicitly in the formulas for expected and excess statistical significance. We calculate the expected proportion of statistically significant findings in the absence of selective reporting or publication bias based on each study's standard error and meta-analysis estimates of the mean and variance of the true-effect distribution. Comparing the expected to the observed proportion of statistically significant results leads to a simple proportion of statistical significance test (PSST). Alternatively, we propose a direct test of excess statistical significance (TESS). We also combine these two tests of excess statistical significance (TESSPSST). Simulations show that these excess statistical significance tests often outperform the conventional Egger test for publication selection bias and the three-parameter selection model. This article is protected by copyright. All rights reserved.