Eta Squared Calculator for ANOVA Effect Size Analysis

Calculator Form

Enter ANOVA Data

Use sums of squares, an F statistic, or a direct eta squared value.

Calculation Mode

Pick the method that matches your ANOVA output.

Decimal Places

Choose output precision from 2 to 6 places.

Interpretation Guide

Used for trivial, small, medium, and large labels.

Sums of Squares Inputs

Effect SS

Error SS

Total SS

Effect df

Error df

Input Hint

F Statistic Inputs

F Statistic

Effect df

Error df

Direct Eta Squared Input

Eta Squared Value

Allowed Range

Meaning

Example Data Table

Worked Example

This example shows a one-factor ANOVA summary and the resulting effect size.

Source	SS	df	MS	F	Eta Squared	Interpretation
Between Groups	24.50	2	12.25	5.41	0.1841	Large
Within Groups	108.60	48	2.2625	—	—	—
Total	133.10	50	—	—	18.41%	Effect explains notable variance.

Formula Used

Eta Squared Formulas

1. From sums of squares:

η² = SS_effect / SS_total

2. From an F statistic and degrees of freedom:

η² = (F × df_effect) / ((F × df_effect) + df_error)

3. Partial eta squared:

Partial η² = SS_effect / (SS_effect + SS_error)

4. Cohen’s f conversion:

f = √(η² / (1 − η²))

Eta squared estimates the proportion of total variance explained by the effect.
Common rough labels are trivial below 0.01, small at 0.01, medium at 0.06, and large at 0.14.
Interpretation should always consider context, sample design, and research field norms.

How to Use

How to Use This Calculator

Select your input mode based on the ANOVA information you already have.
Enter sums of squares, or enter the F statistic with its degrees of freedom.
Choose how many decimal places you want in the output.
Press Calculate Eta Squared to display the result under the header and above the form.
Review eta squared, partial eta squared, explained variance, Cohen’s f, and the interpretation label.
Use the CSV and PDF buttons to export the summary for reporting or documentation.

FAQs

Frequently Asked Questions

1. What does eta squared measure?

Eta squared measures the share of total variance explained by an effect in ANOVA. It helps show how meaningful a factor is beyond simply reporting statistical significance.

2. How is eta squared different from partial eta squared?

Eta squared uses total variance in the denominator. Partial eta squared uses only the effect and its error term. Partial values are often larger because other sources of variation are excluded.

3. Can I calculate eta squared from an F statistic?

Yes. For a standard ANOVA effect, eta squared can be estimated using the F value, effect degrees of freedom, and error degrees of freedom. This is useful when sums of squares are not listed.

4. What counts as a large eta squared value?

A common rule labels 0.14 or higher as large. These thresholds are only rough guides, so field-specific expectations and study design still matter when interpreting impact.

5. Why does the calculator show Cohen’s f too?

Cohen’s f is another effect size format often used in power analysis and study planning. Showing both values makes it easier to move from interpretation into sample size decisions.

6. What if I do not know total sum of squares?

If you know effect SS and error SS, the calculator can estimate total SS by adding them. That works well for standard one-effect ANOVA summaries.

7. Is eta squared enough for reporting effect size?

It is useful, but not always sufficient alone. Many reports also include the F statistic, degrees of freedom, p-value, confidence information, and a practical interpretation of the effect.

8. Can this tool be used for classroom and research work?

Yes. It suits teaching examples, quick ANOVA checks, and reporting support. Always verify that the chosen formula matches your study design and software output.