A Monte-Carlo estimation of effect size distortion due to significance testing

A Monte-Carlo study was done with true effect sizes in deviation units ranging from 0 to 2 and a variety of sample sizes. The purpose was to assess the amount of bias created by considering only effect sizes that passed a statistical cut-off criterion of alpha = .05. The deviation values obtained at the .05 level jointly determined by the set effect sizes and sample sizes are presented. This table is useful when summarizing sets of studies to judge whether published results reflect an accurate appraisal of an underlying effect or a distorted estimate expected because significant studies are published and nonsignificant results are not. The table shows that the magnitudes of error are substantial with small sample sizes and inherently small effect sizes. Thus, reviews based on published literature could be misleading and especially so if true effect sizes were close to zero. A researcher should be particularly cautious of small sample sizes showing large effect sizes when larger samples indicate diminishing smaller effects.