Effect Size Calculator — Cohen's d
Calculate Cohen's d, Hedge's g, and r effect size for statistical significance testing.
What Is the Effect Size Calculator — Cohen's d?
The Effect Size Calculator computes standardized effect size measures — Cohen's d, r, and eta-squared (η²) — to quantify the practical significance of statistical findings beyond p-values. Enter group means, standard deviations, and sample sizes to get Cohen's d with interpretation.
Formula
How to Use
Enter the mean and standard deviation for each group. Enter the sample sizes. The calculator computes Cohen's d (standardized mean difference), r (correlation coefficient effect size), confidence intervals, and power estimates. Alternatively, convert from t-statistic and degrees of freedom.
Example Calculation
Group 1: M=75, SD=10, n=30. Group 2: M=68, SD=12, n=30. SD_pooled = √((100+144)/2) = √122 = 11.05. Cohen's d = (75−68)/11.05 = 0.63 → Medium effect size.
Understanding Effect Size — Cohen's d
Effect size is a quantitative measure of the magnitude of a statistical phenomenon, independent of sample size. While p-values answer 'Is the effect real?', effect sizes answer 'How big is the effect?' — a crucial distinction for interpreting research findings and planning future studies.
Cohen's d, the most widely used effect size for comparing two means, expresses the difference in units of pooled standard deviation. A d of 0.5 means the groups differ by half a standard deviation — a medium effect that is usually detectable with modest sample sizes. Large effects (d > 0.8) are readily apparent; small effects (d < 0.2) may be real but practically negligible.
Effect sizes are essential in meta-analysis (combining results across studies), power analysis (determining required sample size before a study), and clinical decision-making (where statistical significance alone is insufficient to justify intervention costs and risks). Reporting effect sizes alongside p-values is now required or strongly recommended by major journals and APA guidelines.
Frequently Asked Questions
What are Cohen's benchmarks for effect size?
Cohen's d: Small = 0.2, Medium = 0.5, Large = 0.8. For r: Small = 0.1, Medium = 0.3, Large = 0.5. For η²: Small = 0.01, Medium = 0.06, Large = 0.14. These are rough guidelines — context matters.
Why is effect size important beyond p-values?
A p-value only indicates whether an effect exists given sample size. Effect size measures the magnitude of the effect independently of sample size. A tiny effect can be statistically significant with a large sample but practically meaningless.
What is Hedges' g?
Hedges' g is a corrected version of Cohen's d that adjusts for bias in small samples. For n > 20 per group, d and g are nearly identical.
When should I use eta-squared vs Cohen's d?
Cohen's d is for comparing two group means. Eta-squared (η²) is for ANOVA with three or more groups, measuring the proportion of variance explained by the group factor.
Is this calculator free?
Yes, completely free with no account needed.
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