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Keywords:

  • Hedges’d;
  • item response theory;
  • Monte Carlo;
  • publication bias;
  • response ratio;
  • type I error;
  • type II error

Abstract

Variable reporting of results can influence quantitative reviews by limiting the number of studies for analysis, and thereby influencing both the type of analysis and the scope of the review. We performed a Monte Carlo simulation to determine statistical errors for three meta-analytical approaches and related how such errors were affected by numbers of constituent studies. Hedges’d and effect sizes based on item response theory (IRT) had similarly improved error rates with increasing numbers of studies when there was no true effect, but IRT was conservative when there was a true effect. Log response ratio had low precision for detecting null effects as a result of overestimation of effect sizes, but high ability to detect true effects, largely irrespective of number of studies. Traditional meta-analysis based on Hedges’d are preferred; however, quantitative reviews should use various methods in concert to improve representation and inferences from summaries of published data.