Effect Size Guidelines, Sample Size Calculations, 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. This 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 10 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.

Keywords: Effect size; Sample size; Statistical power; Statistical significance.

Figure 1.

Meta-analysis inclusion flow chart for effect size distribution analysis.

Figure 2.

(A) The distributions of correlations (Pearson’s r). The dashed red lines represent the 25th, 50th, and 75th percentiles, which correspond to small (Pearson’s r = .12), medium (Pearson’s r = .20), and large (Pearson’s r = .32) effects. (B) The distributions of Hedges’ g. The dashed red lines represent the 25th, 50th, and 75th percentiles, which correspond to small (Hedges’ g = 0.16), medium (Hedges’ g = 0.38), and large (Hedges’ g = 0.76) effects. The purple lines in each panel represent the a priori power achieved by the median sample size of the included studies across effect sizes.

Figure 3.

(A) One-sided contour-enhanced funnel plot for individual differences research. (B) One-sided contour-enhanced funnel plot for group differences research. (C) One-sided contour-enhanced funnel plot for group differences research in biomedical gerontology. (D) One-sided contour-enhanced funnel plot for group differences research in psychosocial gerontology.

Figure 4.

Density plots illustrating the distribution of Hedges’ g, based on study categorization as biomedical (pink) or psychosocial (turquoise). The distributions display the larger average effect size of the psychosocial studies.