effect size calculator

What is an effect size?

An effect size tells you how big a difference is, not just whether that difference is statistically significant. P-values can tell you if an observed effect is unlikely under a null hypothesis, but they do not tell you whether the effect is tiny, meaningful, or huge in practical terms.

For two-group comparisons, one of the most common standardized effect sizes is Cohen’s d, which expresses the mean difference in standard deviation units. This makes results easier to compare across studies with different measurement scales.

Why effect size matters more than you think

• Practical importance: It helps answer whether the effect is useful in the real world.
• Comparability: Standardized metrics allow comparison across different studies and outcomes.
• Meta-analysis: Effect sizes are the foundation of evidence synthesis and cumulative science.
• Power planning: They are essential for sample-size and power calculations before running studies.

Metrics reported by this calculator

1) Cohen’s d

Cohen’s d is computed as the difference between group means divided by the pooled standard deviation (for independent groups). A larger absolute value indicates a larger standardized difference.

2) Hedges’ g

Hedges’ g applies a small-sample correction to Cohen’s d. When sample sizes are modest, g is usually preferred because it is less biased.

3) Glass’s Δ (summary method only)

Glass’s delta uses only Group 2’s standard deviation as the denominator. It can be useful when one group is a control group and you have reason to treat its variability as the baseline.

4) Correlation-style effect size (r)

The calculator also provides an r-style index, which can be easier to interpret for some audiences. It maps the standardized difference to a bounded metric between -1 and 1.

How to use this calculator correctly

1. Choose your input method (raw summary stats or t statistic).
2. Enter values for both groups.
3. Click Calculate Effect Size.
4. Read d, g, confidence interval, and interpretation together.

As always, do not treat interpretation cutoffs as absolute rules. A “small” effect in one field may be highly important in another.

Interpreting Cohen’s d (rule-of-thumb)

• |d| < 0.20: trivial to very small
• 0.20 ≤ |d| < 0.50: small
• 0.50 ≤ |d| < 0.80: medium
• |d| ≥ 0.80: large

These categories are only rough anchors. Context, measurement precision, and downstream consequences should drive your final interpretation.

Example scenario

Suppose a training program yields Group 1 mean = 82, SD = 10, n = 40 and Group 2 mean = 75, SD = 9, n = 38. The resulting d would typically be around the medium-to-large range, suggesting a meaningful improvement relative to baseline variation.

If your p-value is significant and d is practically notable, your findings are both statistically and substantively stronger. If p is significant but d is tiny, the effect may be real yet not very useful.

Reporting template you can copy

“Group 1 outperformed Group 2, d = 0.62, 95% CI [0.18, 1.06], corresponding to a medium effect size. The bias-corrected estimate was g = 0.60.”

Final notes

Effect sizes improve clarity, transparency, and decision-making. Use them alongside p-values, confidence intervals, and domain expertise. If your study design is more complex (paired data, repeated measures, ANCOVA, multilevel data), use estimators tailored to those designs.