Effect Size Interpretation, Sample Size Calculation, and Statistical Power in Gerontology

Abstract

Background and Objectives: Researchers typically use Cohen’s guidelines of Pearson’s r = .10, .30, and .50, and Cohen’s d = 0.20, 0.50, and 0.80 to interpret observed effect sizes as small, medium, or large, respectively. However, these guidelines were not based on quantitative estimates, and are only recommended if field-specific estimates are unknown. The current study investigated the distribution of effect sizes in both individual differences research and group differences research in gerontology to provide estimates of effect sizes in the field.Research Design and Methods: Effect sizes (Pearson’s r, Cohen’s d, and Hedges’ g) were extracted from meta-analyses published in ten top-ranked gerontology journals. The 25th, 50th, and 75th percentile ranks were calculated for Pearson’s r (individual differences) and Cohen’s d or Hedges’ g (group differences) values as indicators of small, medium, and large effects. A priori power analyses were conducted for sample size calculations given the observed effect size estimates.Results: Effect sizes of Pearson’s r = .12, .20, and .32 for individual differences research and Hedges’ g = 0.16, 0.38, and 0.76 for group differences research were interpreted as small, medium, and large effects in gerontology. Discussion and Implications: Cohen’s guidelines appear to overestimate effect sizes in gerontology. Researchers are encouraged to use Pearson’s r = .10, .20, and .30, and Cohen’s d or Hedges’ g = 0.15, 0.40, and 0.75 to interpret small, medium, and large effects in gerontology, and recruit larger samples.

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“…Our sample size surpasses the a priori sample size. According to Bartlett, [22] a priori power analysis should be performed if the researcher (s) want to confirm the number of participants required to detect a specific effect in a study. Figure 2 shows the sample size calculation by G∗Power.…”