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META-ANALYSIS EFFECT SIZE CONVERSIONS TO COHEN’S d

POOLED: Mean d = 0.584
Range: [0.483, 0.747]

CONVERSION FORMULAS USED:
• r → d: d = 2r / √(1-r²)
• OR → d: d = ln(OR) × √3 / π
• F → η²: η² = (df_b × F) / (df_b × F + df_w)
• η² → d: d = 2√η² / √(1-η²)

ASSUMPTIONS:
• r to d: Assumes bivariate normal distribution
• OR to d: Less accurate at extreme base rates (<10% or >90%)
• η² to d: Valid only for two-group comparisons (df_between = 1)

METHODS TEXT FOR YOUR META-ANALYSIS:

Effect sizes were standardized to Cohen’s d using established
conversion formulas (Borenstein et al., 2009; Chinn, 2000; Cohen,
1988). Pearson correlations were converted via d = 2r/√(1-r²),
odds ratios via d = ln(OR)×√3/π, and F-statistics via η² then
d = 2√η²/√(1-η²). All conversions assume bivariate normality and,
for F-statistics, two-group comparisons.