Effect Size Calculator

Effect size measures how big a difference is, independent of sample size.

How the Math Works

Cohen's d effect size quantifies the standardized difference between two group means by dividing their mean difference by the pooled standard deviation. The pooled SD combines variability from both groups using a weighted average formula, ensuring fair comparison even when sample sizes differ. This unitless metric transforms raw differences into a common scale, where values like 0.2, 0.5, and 0.8 represent small, medium, and large effects respectively. The calculation reveals not just whether groups differ, but how meaningfully they differ relative to their inherent variability.

Practical Applications

Researchers use Cohen's d to evaluate the practical significance of experimental outcomes beyond statistical significance tests. For example, in clinical trials comparing a new drug to a placebo, a small p-value might confirm a statistically detectable difference, but Cohen's d reveals whether this difference is clinically meaningful. Similarly, A/B testing in marketing uses effect size to determine if conversion rate improvements justify implementing design changes. Meta-analyses also rely on Cohen's d to aggregate findings across studies with different sample sizes and measurement scales.

Day-to-Day Use

Effect size calculations help translate abstract statistical results into actionable insights for everyday decisions. Parents might use it to assess whether a new educational app genuinely improves their child's test scores compared to traditional methods. Business leaders apply it to evaluate if customer satisfaction scores from a redesigned website meaningfully exceed the old version. Even in personal health, comparing fitness or diet results between two approaches becomes more insightful when expressed as a standardized effect size, helping distinguish trivial changes from substantial improvements worth pursuing.

Worked example

Means 78 vs 72, pooled SD 10 → d = 0.6 (medium).

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