Effect Size Calculator

Compute standardized effect sizes for two-group comparisons and correlation analyses. Obtain Cohen's d, Hedges' g, Glass's Δ, and Pearson's r with 95% confidence intervals and instant interpretive feedback.

Group 1
Group 2
Enter means, standard deviations, and sample sizes for each group. Standard deviations must be positive.
Correlation coefficient between -1 and 1.
Number of paired observations.
? Small effect: M₁=5.0, SD₁=1.5, n₁=30 · M₂=4.7, SD₂=1.6, n₂=30
? Medium effect: M₁=5.0, SD₁=1.5, n₁=30 · M₂=4.0, SD₂=1.8, n₂=30
? Large effect: M₁=5.0, SD₁=1.2, n₁=30 · M₂=3.0, SD₂=1.5, n₂=30
? Correlation r=0.15, n=80
? Correlation r=0.35, n=60
? Correlation r=0.65, n=40
Privacy first: All computations are performed locally in your browser. No data is sent to any server.

What Is Effect Size and Why Does It Matter?

Effect size is a standardized measure that quantifies the magnitude of a phenomenon or the strength of a relationship. Unlike p-values, which simply tell you whether an effect exists (statistical significance), effect sizes tell you how large that effect is — a critical distinction for meaningful scientific inference. Effect sizes are essential for meta-analysis, power analysis, and for interpreting the practical significance of research findings.

Effect size = (observed effect) / (variability)

Standardizing by variability allows comparison across different studies and scales.

The American Psychological Association (APA) and the Publication Manual of the American Psychological Association (7th ed.) strongly recommend reporting effect sizes alongside p-values. In many fields — including psychology, medicine, education, and ecology — effect sizes are now considered essential for transparent and reproducible research.

Effect Size Families

Effect sizes fall into two broad families: d-based (standardized mean differences) and r-based (correlation coefficients). This calculator covers the most widely used metrics from both families:

  • Cohen's d — The standardized mean difference between two groups, using pooled standard deviation.
  • Hedges' g — A bias-corrected version of Cohen's d, recommended for small samples.
  • Glass's Δ — Uses only the control group's standard deviation, useful when treatment groups have unequal variances.
  • Pearson's r — Measures the strength and direction of a linear relationship between two continuous variables.

Cohen's Benchmarks: Interpreting Effect Size Magnitude

Jacob Cohen (1988) proposed the following conventions for interpreting effect sizes in the behavioral sciences. These are general guidelines, not strict rules — context and field-specific norms should always be considered.

Effect Size Small Medium Large
Cohen's d 0.20 0.50 0.80
Pearson's r 0.10 0.30 0.50
r² 0.01 0.09 0.25

Source: Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences (2nd ed.).

How the Calculator Works

Two-Group Comparison Mode: Given means, standard deviations, and sample sizes for two independent groups, the calculator computes:

d = (M₁ − M₂) / SDpooled
SDpooled = √[ ((n₁−1)SD₁² + (n₂−1)SD₂²) / (n₁+n₂−2) ]

Hedges' g applies a small-sample correction factor: g = d × (1 − 3/(4(n₁+n₂)−9)). Glass's Δ uses only the control group SD: Δ = (M₁ − M₂) / SDcontrol.

Confidence intervals for d and g are approximated using the noncentral t distribution method (Cumming & Finch, 2001). For r, the calculator uses Fisher's z transformation to compute the 95% CI.

Why Effect Size Is More Informative Than p-Values

  • p-values depend on sample size: A very small effect can become "statistically significant" with a large sample, while a large effect may be "non-significant" with a small sample.
  • Effect sizes are scale-free: They allow comparison across studies measuring different outcomes or using different instruments.
  • Effect sizes enable meta-analysis: They are the raw material for quantitative syntheses of research evidence.
  • Effect sizes speak to practical significance: A statistically significant result may be practically trivial; effect size helps you judge real-world importance.
Case Study: Cognitive Training Intervention

A researcher tests a new working memory training program. The control group (n=40) has a mean post-test score of 24.5 (SD=4.2), while the treatment group (n=42) scores 28.1 (SD=3.8). The p-value is 0.002 (significant), but the effect size tells a more nuanced story: Cohen's d = 0.91, a large effect, indicating that the training produces a meaningful improvement. Without the effect size, one might overstate or understate the practical value of the intervention. Conversely, a study with d = 0.15 and p = 0.03 would be statistically significant but practically negligible.

Common Misconceptions About Effect Size

  • "Effect size is only for significant results" — Effect size should be reported regardless of statistical significance. It provides valuable information even when p > 0.05.
  • "A large effect size means the result is important" — Magnitude must be interpreted in context. A large effect in one domain may be trivial in another.
  • "Cohen's d is always the best choice" — Hedges' g is preferred for small samples; Glass's Δ is better when group variances differ substantially.
  • "Effect sizes are not affected by sample size" — While effect sizes are standardized, they can still have sampling variability. Confidence intervals capture this uncertainty.

Applications Across Disciplines

  • Psychology & Psychiatry: Quantifying treatment effects in clinical trials, comparing cognitive performance between groups.
  • Medicine & Epidemiology: Estimating risk differences, standardized mean differences in biomarker studies.
  • Education: Measuring the impact of pedagogical interventions, comparing test scores.
  • Economics & Business: Evaluating policy interventions, A/B testing in marketing.
  • Ecology & Environmental Science: Comparing species abundance, assessing climate change impacts.

Practical Guidelines for Reporting Effect Sizes

Based on recommendations from the APA Task Force on Statistical Inference (Wilkinson & APA, 1999) and the Publication Manual of the APA (7th ed.):

  1. Always report the effect size and the confidence interval.
  2. Specify which effect size metric you are using (e.g., Cohen's d, not just "effect size").
  3. Interpret the magnitude using field-specific benchmarks or contextual reasoning.
  4. In meta-analyses, use Hedges' g to correct for small-sample bias.
  5. When variances are unequal, consider using Glass's Δ or the Welch version of Cohen's d.

Rooted in statistical best practices – This tool implements formulas from Cohen (1988), Hedges (1981), and Glass (1976), with confidence interval methods from Cumming & Finch (2001) and the Handbook of Research Synthesis and Meta-Analysis (Cooper et al., 2019). The calculator has been cross-validated against established statistical packages including R's effsize and psych packages. Reviewed by the GetZenQuery tech team, last updated June 2026.

Frequently Asked Questions

Cohen's d uses the pooled standard deviation as the denominator. Hedges' g applies a correction factor to remove small-sample bias. For large samples, d and g are virtually identical; for small samples (n < 20 per group), Hedges' g is preferred.

Glass's Δ uses only the control group's standard deviation in the denominator. This is useful when the treatment group has substantially different variance (e.g., due to intervention effects). It is also commonly used in single-case designs and when the control group is considered the "standard" population.

Cohen's benchmarks (0.2, 0.5, 0.8 for d; 0.1, 0.3, 0.5 for r) are general guidelines. However, interpretation should be context-dependent. In some fields (e.g., medicine), a "small" effect may still be clinically meaningful. Consult meta-analyses and systematic reviews in your field for discipline-specific norms.

This calculator is designed for independent groups. For paired-samples designs, we recommend using the paired version of Cohen's d, which uses the standard deviation of the difference scores. A dedicated paired-samples effect size calculator is available separately in our Paired Effect Size Calculator.

The 95% confidence interval gives the range of values that is likely to contain the true population effect size with 95% confidence. A narrower interval indicates more precise estimation. If the interval does not include zero, you can conclude that the effect is statistically significant at α = 0.05.

Excellent resources include: Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences; Cumming, G. (2012). Understanding The New Statistics; and the Handbook of Research Synthesis and Meta-Analysis (Cooper et al., 2019). Online, see the Psychometrica effect size calculator and RealStats.
References: Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences (2nd ed.). Hillsdale, NJ: Erlbaum. | Hedges, L. V. (1981). Distribution theory for Glass's estimator of effect size and related estimators. Journal of Educational Statistics, 6(2), 107–128. | Glass, G. V. (1976). Primary, secondary, and meta-analysis of research. Educational Researcher, 5(10), 3–8. | Cumming, G., & Finch, S. (2001). A primer on the understanding, use, and calculation of confidence intervals. Journal of Educational and Behavioral Statistics, 26(1), 1–24.