Calculator
Formula used
For two independent groups, the pooled standard deviation is: Sp = √(((n1−1)s1² + (n2−1)s2²) / (n1+n2−2)).
Cohen’s d is computed as: d = (M1 − M2) / Sp (with the chosen direction).
Hedges’ g applies a small-sample correction: g = J · d, where J = 1 − 3 / (4(n1+n2) − 9).
An approximate standard error is: SE ≈ √((n1+n2)/(n1·n2) + g²/(2(n1+n2−2))), and the confidence interval is g ± z·SE.
How to use this calculator
- Select an input mode that matches your available data.
- Set direction to control whether results are positive or negative.
- Enter sample sizes for both groups in every mode.
- Provide means and SDs, paste raw values, or enter t or d.
- Click Calculate to view g, SE, and CI.
Example data table
| Scenario | n1 | Mean 1 | SD 1 | n2 | Mean 2 | SD 2 | Hedges' g (≈) |
|---|---|---|---|---|---|---|---|
| Training vs. Control (sample) | 30 | 55 | 10 | 28 | 50 | 12 | 0.4480 |
Why Hedges’ g matters in small samples
Standardized mean differences help compare outcomes measured on different scales. However, Cohen’s d can be slightly biased upward when total sample size is modest. Hedges’ g applies a correction factor, J, to reduce that small-sample bias. In practice, this matters for pilots, classroom studies, A/B experiments with limited traffic, and subgroup analyses where n is constrained. Using g improves comparability across studies and reduces inflation in pooled estimates, across cohorts and time periods.
Inputs you can trust for reproducible estimates
This calculator supports four input routes so you can reuse whatever a paper reports. Summary statistics are ideal when means and standard deviations are available. Raw values allow direct verification and automatically recompute means, SDs, and sample sizes. If only an independent-groups t statistic is reported, d is derived using the common conversion with n1 and n2. When a prior effect size is known, you can apply the correction directly to d.
Bias correction and pooled variability
For independent groups, the pooled standard deviation combines within-group variance using (n1−1)s1² and (n2−1)s2². This approach assumes similar variability across groups and is widely used in meta-analysis. The correction J = 1 − 3/(4(n1+n2) − 9) approaches 1 as sample sizes grow, so g and d converge for larger studies. Direction controls the sign so your report stays consistent.
Confidence intervals for decision-ready reporting
Point estimates alone hide uncertainty. The calculator provides an approximate standard error and confidence interval for g using common z values (90%, 95%, 99%). Wider intervals often signal limited power or high dispersion. When the interval crosses zero, the observed difference may be compatible with no effect, even if the point estimate looks meaningful. Exporting results supports transparent reporting and quick peer review.
Interpreting magnitude with context and benchmarks
Magnitude labels such as negligible, small, medium, and large are only heuristics. Real-world importance depends on the outcome, costs, and domain norms. For example, a small standardized gain can still be valuable in safety, reliability, or public health settings. Use the direction option to align with your hypothesis, and consider sensitivity checks when group SDs differ strongly or when outliers drive raw-data results.
FAQs
What is the difference between Cohen’s d and Hedges’ g?
Hedges’ g is Cohen’s d multiplied by a small-sample correction factor (J). When total sample size is small, g is slightly smaller and less biased; for large samples, g and d are nearly identical.
Which input mode should I use?
Use summary statistics when you have means and SDs. Paste raw values for verification and automatic recomputation. Use t-statistic when a paper reports t and group sizes. Use d when an effect size is already provided.
Does this assume equal variances across groups?
The pooled SD approach matches the common equal-variance formulation for independent groups. If group dispersions differ greatly, consider alternative effect sizes or robust methods, and report sensitivity results alongside Hedges’ g.
How do I set the sign of the effect size?
Choose the direction dropdown to define whether results represent Group 1 minus Group 2 or the reverse. Enable the absolute-value option if you only need magnitude without directional interpretation.
How is the confidence interval computed here?
The calculator uses an approximate standard error for g and a normal critical value (90%, 95%, or 99%) to form g ± z·SE. This is practical for quick reporting; specialized meta-analysis may use refined methods.
What do the CSV and PDF downloads include?
Downloads capture your latest computed metrics, including inputs, pooled SD (when applicable), correction factor, g, SE, and the confidence interval. Files are generated on demand from the most recent submission in your session.