Effect Size Calculator

Select Effect Size Type

• Cohen's d
• Pearson's r
• η² (ANOVA)
• Odds/Risk

Understanding Effect Sizes

What is Effect Size?

Effect size quantifies the magnitude of a phenomenon or difference, independent of sample size. Unlike p-values, which only tell you if an effect exists, effect sizes tell you how large that effect is.

Cohen's d

Interpretation (Cohen, 1988):

• Small: d = 0.2 (noticeable to experts)
• Medium: d = 0.5 (visible to careful observers)
• Large: d = 0.8 (obvious to anyone)

Pearson's r

Interpretation (Cohen, 1988):

• Small: r = 0.10 (explains 1% of variance)
• Medium: r = 0.30 (explains 9% of variance)
• Large: r = 0.50 (explains 25% of variance)

Eta-squared (η²)

Interpretation (Cohen, 1988):

• Small: η² = 0.01 (1% of variance)
• Medium: η² = 0.06 (6% of variance)
• Large: η² = 0.14 (14% of variance)

Odds Ratio (OR) & Risk Ratio (RR)

Interpretation:

• OR/RR = 1: No association
• OR/RR > 1: Increased odds/risk with exposure
• OR/RR < 1: Decreased odds/risk (protective effect)

Why Effect Sizes Matter

• Publication Requirements: Many journals require effect sizes
• Meta-Analysis: Essential for combining studies
• Power Analysis: Needed for sample size calculations
• Practical Significance: Distinguish statistical from practical importance
• Context-Independent: Compare effects across different scales

Common Applications

• Psychology: Treatment effect sizes in clinical trials
• Education: Intervention effectiveness
• Medicine: Drug efficacy, diagnostic accuracy
• Social Sciences: Program evaluation
• Business: Marketing campaign effectiveness