Effect Size Calculator
Calculate and visualize effect sizes including Cohen's d, Hedges' g, Glass's delta, eta-squared, omega-squared, and Cohen's f. See animated distribution overlap, step-by-step formulas, CLES probability, and interpretation guidelines for your statistical research.
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About Effect Size Calculator
Understanding Effect Sizes in Research
Effect sizes are essential statistics that quantify the magnitude of a phenomenon, complementing the information provided by p-values. While a p-value tells you whether an effect is statistically significant, the effect size tells you how large that effect is. This distinction is critical for judging practical significance — a statistically significant result with a tiny effect size may have no real-world importance.
How to Calculate Cohen's d
Cohen's d measures the standardized difference between two group means:
$$d = \frac{M_1 - M_2}{SD_{pooled}}$$
where the pooled standard deviation is:
$$SD_{pooled} = \sqrt{\frac{(n_1 - 1) \cdot SD_1^2 + (n_2 - 1) \cdot SD_2^2}{n_1 + n_2 - 2}}$$
A Cohen's d of 0.5 means the two group means differ by half a standard deviation. Hedges' g applies a correction factor \(J = 1 - \frac{3}{4 \cdot df - 1}\) to reduce the upward bias of d in small samples.
Interpreting Effect Size with CLES
The Common Language Effect Size (CLES) translates Cohen's d into an intuitive probability: the chance that a randomly selected individual from Group 1 will score higher than a randomly selected individual from Group 2. It is calculated as:
$$CLES = \Phi\left(\frac{d}{\sqrt{2}}\right)$$
where \(\Phi\) is the standard normal CDF. For example, d = 0.5 corresponds to a CLES of about 64%, meaning there is a 64% chance a random Group 1 member outscores a random Group 2 member.
Eta-Squared vs. Omega-Squared
In ANOVA, eta-squared (η²) represents the proportion of total variance explained by the independent variable:
$$\eta^2 = \frac{SS_{between}}{SS_{total}} = \frac{F \times df_{between}}{F \times df_{between} + df_{within}}$$
However, η² tends to overestimate the population effect. Omega-squared (ω²) provides a less biased estimate:
$$\omega^2 = \frac{df_{between} \times (F - 1)}{df_{between} \times (F - 1) + N}$$
Converting Between Effect Size Measures
| From | To | Formula |
|---|---|---|
| Cohen's d | Point-biserial r | \(r = \frac{d}{\sqrt{d^2 + \frac{(n_1+n_2)^2}{n_1 \cdot n_2}}}\) |
| Correlation r | Cohen's d | \(d = \frac{2r}{\sqrt{1 - r^2}}\) |
| t-test (independent) | Cohen's d | \(d = t \times \sqrt{\frac{1}{n_1} + \frac{1}{n_2}}\) |
| t-test (paired) | Cohen's dz | \(d_z = \frac{t}{\sqrt{n}}\) |
| η² | Cohen's f | \(f = \sqrt{\frac{\eta^2}{1 - \eta^2}}\) |
When to Use Each Effect Size
| Scenario | Recommended | Why |
|---|---|---|
| Two equal-variance groups | Cohen's d or Hedges' g | Standard measure; g is preferred when n < 20 per group |
| Unequal variances | Glass's delta | Uses only the control group SD, unaffected by treatment variance |
| Paired / repeated measures | Cohen's dz | Based on difference scores; accounts for within-subject correlation |
| One-way ANOVA | η² or ω² | η² for descriptive use; ω² for less biased population estimate |
| Correlation analysis | r and r² | r measures strength; r² gives proportion of shared variance |
| Meta-analysis | Hedges' g | Bias correction is essential when pooling across diverse sample sizes |
Frequently Asked Questions
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"Effect Size Calculator" at https://MiniWebtool.com// from MiniWebtool, https://MiniWebtool.com/
by miniwebtool team. Updated: 2026-04-16
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