effect size calculator anova

What is ANOVA effect size?

ANOVA tells you whether group means differ statistically, but significance alone does not show how big that difference is. That is where effect size comes in. ANOVA effect sizes estimate the practical magnitude of your factor’s impact on the outcome.

In plain language, p-values answer “is there evidence of a difference?”, while effect sizes answer “how much of a difference is there?”.

Effect sizes this calculator reports

Eta squared (η²)

Eta squared is the proportion of total variance explained by your effect. If η² = 0.12, then about 12% of the total variance in the dependent variable is associated with the factor.

Partial eta squared (ηp²)

Partial eta squared uses only effect variance and its corresponding error term. In one-way ANOVA, η² and ηp² are often identical. In multifactor ANOVA designs, ηp² is commonly reported for each term.

Omega squared (ω²)

Omega squared is often viewed as a less biased estimate of population effect size than eta squared, especially in small samples. It typically gives slightly smaller values than η².

Cohen’s f

Cohen’s f is a standardized transformation of η² or ηp². Many power analyses use f directly.

How to use this effect size calculator ANOVA tool

• Select your input mode: Sums of Squares or F-statistic.
• Enter values from your ANOVA table.
• Click Calculate Effect Sizes.
• Review η², ηp², ω², and Cohen’s f with interpretation guidance.

Interpretation guidelines

Common rough benchmarks (context still matters):

• For η² / ηp²: small ≈ 0.01, medium ≈ 0.06, large ≈ 0.14
• For Cohen’s f: small ≈ 0.10, medium ≈ 0.25, large ≈ 0.40

These are rules of thumb, not universal truths. In some fields, even a small effect can be highly meaningful.

Reporting ANOVA results with effect size

A clean APA-style example:

There was a significant effect of condition on test scores, F(2, 57) = 5.12, p = .009, ηp² = .15, ω² = .11.

When possible, include confidence intervals for effect sizes and describe practical implications for your domain.

Why effect size should always be reported

• Improves transparency and reproducibility
• Supports meta-analysis and cumulative science
• Helps readers evaluate practical importance
• Avoids over-reliance on p-values alone

Frequently asked questions

Can I calculate effect size from only F and degrees of freedom?

Yes. You can compute ηp² directly from F, df effect, and df error. This calculator also provides an approximate ω² from those values.

What if omega squared is negative?

Negative ω² can occur in small samples or very weak effects. Conventionally, it is interpreted as 0 in practice.

Is this for one-way or factorial ANOVA?

It works for both as long as you enter the correct term-specific values from your ANOVA output.