Sample Sizes and Effect Sizes are Negatively Correlated in Meta-Analyses: Evidence and Implications of a Publication Bias Against NonSignificant Findings

Meta-analysis involves cumulating effects across studies in order to qualitatively summarize existing literatures. A recent finding suggests that the effect sizes reported in meta-analyses may be negatively correlated with study sample sizes. This prediction was tested with a sample of 51 published meta-analyses summarizing the results of 3,602 individual studies. The correlation between effect size and sample size was negative in almost 80 percent of the meta-analyses examined, and the negative correlation was not limited to a particular type of research or substantive area. This result most likely stems from a bias against publishing findings that are not statistically significant. The primary implication is that meta-analyses may systematically overestimate population effect sizes. It is recommended that researchers routinely examine the n–r scatter plot and correlation, or some other indication of publication bias and report this information in meta-analyses.