Effect Size Calculator: Cohen's d, Hedges g, Eta Squared, and Omega Squared
Use this effect size calculator for Cohen's d, Hedges g, Glass delta, eta squared, partial eta squared, omega squared, Cohen's f, Cohen's f squared, R-squared, and effect-size interpretation. It is built for t-tests, ANOVA, correlation, regression, research reports, and statistics homework.
- Cohen's d calculator Calculate Cohen's d, Hedges g, Glass delta, pooled standard deviation, and common language effect size.
- Paired or one-sample Calculate standardized mean difference from a mean difference, standard deviation of differences, and sample size.
- ANOVA effect size Calculate eta squared, partial eta squared, omega squared, Cohen's f, and Cohen's f squared from SS or F.
- R-squared and r Convert r or R-squared into explained variance, Cohen's f squared, and an approximate d equivalent.
Calculate Effect Size
Choose the type of result you have. The calculator supports independent groups, paired or one-sample mean differences, ANOVA sums of squares, ANOVA F statistics, and correlation or regression effect sizes.
Inputs
Results
The two-group standardized mean difference is d = 0.6311, a medium effect by common rough guidelines.
Use these labels as rough reporting language, not as a substitute for subject-matter interpretation.
| Formula | d = (82 - 75) / 11.0912 = 0.6311 |
|---|---|
| Correction | Hedges g = 0.9884 * d = 0.6238 |
| Interpretation | The pooled standard deviation is 11.0912, and Glass delta using group 2 SD is 0.7000. |
Effect Size Formulas
Different statistical tests use different effect sizes. Match the effect size to the test and the assignment instructions.
| Cohen's d | d = (mean1 - mean2) / pooled SD |
|---|---|
| Hedges g | g = J * d, where J is a small-sample correction |
| Glass delta | delta = (mean1 - mean2) / control group SD |
| Eta squared | eta squared = SS effect / SS total |
| Partial eta squared from F | partial eta squared = (F * df effect) / (F * df effect + df error) |
| Omega squared | omega squared = (SS effect - df effect * MS error) / (SS total + MS error) |
| Cohen's f | f = sqrt(eta squared / (1 - eta squared)) |
Common Mistakes
- Reporting only the p-value and forgetting to describe the size of the effect.
- Using Cohen's d when the assignment asks for eta squared, omega squared, or R-squared.
- Entering an ANOVA F value without checking that the effect and error degrees of freedom match the same test.
- Treating small, medium, and large labels as universal rules instead of rough context-dependent guidelines.
- Using group standard deviations from the wrong groups or mixing sample and population standard deviations.
Effect Size Calculator Examples
These examples match the calculator defaults and give students a quick way to check whether their result is in the right range.
| Case | Input | Result |
|---|---|---|
| Two independent groups | Mean 1 = 82, Mean 2 = 75, SDs = 12 and 10, n = 35 and 32 | Cohen's d = 0.6311, Hedges g = 0.6238, Glass delta = 0.7000 |
| Paired samples | Mean difference = 6, SD of differences = 9, n = 28 | Cohen's dz = 0.6667, Hedges g = 0.6480, t equivalent = 3.5277 |
| ANOVA table | SS effect = 240, SS error = 960, df effect = 2, df error = 57 | Eta squared = 0.2000, omega squared = 0.1696, Cohen's f = 0.5000 |
| Correlation or regression | Correlation r = 0.35 | R-squared = 0.1225, Cohen's f squared = 0.1396, d equivalent = 0.7473 |
When This Calculator Helps
Statistics homework
Use it when your instructor asks for practical significance, Cohen's d, Hedges g, eta squared, omega squared, Cohen's f, R-squared, or effect-size interpretation.
Research reports
Use it to add effect-size language to t-test, ANOVA, correlation, and regression results so the write-up explains both significance and magnitude.
How To Report Effect Size
A strong answer usually explains the test result, the effect size, and what the magnitude means in the context of the assignment.
- Name the statistical test first, such as independent t-test, paired t-test, ANOVA, correlation, or regression.
- Report the effect-size statistic that matches the test, not just the p-value.
- Add a short interpretation in plain English, using small, medium, and large only as rough guidance.
- Connect the effect size back to the assignment question, data context, and practical importance.
Effect Size FAQs
What is an effect size?
An effect size describes how large a difference, association, or model effect is. It helps explain practical importance beyond whether a test is statistically significant.
Which effect size should I use?
Use Cohen's d or Hedges g for mean differences, eta squared or omega squared for ANOVA, and r or R-squared for correlation and regression-style questions.
What is the difference between Cohen's d and Hedges g?
Hedges g applies a small-sample correction to Cohen's d. The correction matters more when sample sizes are small.
Are small, medium, and large labels always correct?
No. They are rough conventions. A small effect can matter in some fields, and a large effect can be less meaningful if the design or measurement is weak.
Can I calculate effect size from an ANOVA F statistic?
Yes. If you have F, df effect, and df error, use the ANOVA F input to estimate partial eta squared, partial omega squared, Cohen's f, and Cohen's f squared.
Is effect size required in APA-style statistics writing?
Many statistics and research assignments expect an effect size alongside the test result, p-value, and interpretation. Always follow your rubric if it names a specific effect size.
Related Statistics Resources
If your effect-size question is attached to a hypothesis test or ANOVA table, these pages are useful next steps.
Need Help Interpreting Effect Size?
Statskan can help you choose the correct effect size, calculate it from your output, and write the interpretation clearly for a statistics assignment, research report, or software output.