ANOVA Eta Squared (η²) Calculator
Enter your ANOVA values below. You can calculate η² using sums of squares, and partial η² using either sums of squares or F with degrees of freedom.
Method 1: From Sums of Squares
You need SS Effect + (SS Total or SS Error).
Method 2: From F Statistic (Partial η²)
You need all three values to compute partial η² from F.
Interpretation guide (Cohen, rough): 0.01 = small, 0.06 = medium, 0.14 = large.
What Is Eta Squared (η²)?
Eta squared is an effect size used in ANOVA to describe how much variance in an outcome is explained by a factor. Unlike a p-value, which only tells you whether an effect is statistically significant, η² helps you understand how big the effect is.
In practical terms, if η² = 0.18, then about 18% of the variance in your dependent variable is associated with the group difference or factor in your model.
Core Formulas
Eta Squared from Sums of Squares
This is often reported in one-way ANOVA. It uses the total variability in the outcome as the denominator.
Partial Eta Squared from Sums of Squares
Partial η² is common in factorial ANOVA and repeated-measures ANOVA because it isolates the effect relative to itself plus residual variance.
Partial Eta Squared from F and Degrees of Freedom
This is useful when a paper reports F-statistics but does not provide sums of squares.
How to Use This Eta Squared Calculator
- Enter ANOVA sums of squares if available.
- If SS Total is missing, enter SS Error instead.
- If you only have test statistics, use F, df1, and df2 to compute partial η².
- Click Calculate to get the effect size and interpretation.
Interpreting Eta Squared Values
Benchmarks are only rules of thumb, but a common guide is:
- Small effect: η² around 0.01
- Medium effect: η² around 0.06
- Large effect: η² around 0.14 or higher
Context matters. In some research areas, a “small” effect may still be meaningful, especially in public health, education, or long-term intervention studies.
Worked Example
Suppose your ANOVA table reports:
- SS Effect = 32
- SS Error = 168
- SS Total = 200
Then:
- η² = 32 / 200 = 0.16
- partial η² = 32 / (32 + 168) = 0.16
That means your factor explains 16% of the variance, usually considered a large effect by standard conventions.
Eta Squared vs Partial Eta Squared vs Omega Squared
Eta Squared (η²)
Easy to calculate and intuitive, but can overestimate population effect size, especially in smaller samples or complex models.
Partial Eta Squared
Widely reported in SPSS and many journal articles. Best interpreted carefully when comparing across different study designs, because denominators differ by model.
Omega Squared (ω²)
Often preferred for less biased estimation in the population. If you are writing a methods-heavy paper, consider reporting both η²/partial η² and ω² when possible.
How to Report in APA Style
A common reporting format is:
F(2, 57) = 5.42, p = .007, partial η² = .16.
If using one-way ANOVA with full sums of squares, reporting η² can be straightforward and transparent.
Common Mistakes to Avoid
- Confusing η² and partial η² (they are not always equal).
- Reporting only p-values without effect size.
- Interpreting benchmarks mechanically without domain context.
- Using rounded ANOVA tables that produce small calculation mismatches.
Final Notes
This eta squared calculator is designed for quick, practical effect size estimation in ANOVA workflows. Use it alongside confidence intervals, assumptions checks, and good reporting practices to provide a complete and responsible statistical interpretation.