The influence of nonnormality from primary studies on the standardized mean difference in meta-analysis

In this study we investigated the influence of data nonnormality in the primary studies on meta-analysis of the standardized mean difference (SMD) for a two-independent-group design. The bias, mean squared error, and confidence interval coverage probability of the mean effect sizes under different types of population distributions were compared. Also, the performance of the Q test was examined. The results showed that oppositely skewed distributions (i.e., distributions skewed in different directions) showed poor performance for point and interval estimates of mean effect sizes in meta-analysis, especially when the tails were pointing toward each other. The previously found adverse impacts due to nonnormality in primary studies do not disappear when primary studies with nonnormal data are meta-analyzed, even when the average sample size and number of studies are large. The results also showed that, when the tails were pointing toward each other, the Type I error rates of the Q test were inflated. We suggest that the impact of violating the assumption of normality should not be ignored in meta-analysis.