Eta Squared Calculator

Reviewed By: Patrick Myers (BSME)

Enter the sum of squares for the effect and the total sum of squares into the calculator to determine the eta squared.

Calculate eta squared (η²) and partial eta squared (ηp²) from ANOVA output. Use the sums of squares tab when you have SS values, or the F-statistic tab when you have F and degrees of freedom.

Common formulas

η² = SS_effect / SS_total

ηp² = SS_effect / (SS_effect + SS_error)

ηp² = (F × df_effect) / ((F × df_effect) + df_error)

Cohen’s f = √(η² / (1 − η²)) or √(ηp² / (1 − ηp²))

From Sums of Squares

From F and df

Best when you have ANOVA table sums of squares. Enter the values you have and this returns η², partial η², percent variance explained, Cohen’s f, and an interpretation.

SS for Effect

SS for Error

SS Total

If SS Total is left blank, the calculator uses SS Effect + SS Error.

Best when your software reports an F-statistic and degrees of freedom. This returns partial eta squared directly, then estimates Cohen’s f and variance explained.

F-statistic

df Effect

df Error

Results

Eta Squared (η²)

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Partial Eta Squared (ηp²)

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Variance Explained

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Cohen’s f

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Interpretation

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Method Used

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Related Calculators

Eta Squared Formula

The following formula is used to calculate Eta Squared.

η² = SS_{effect} / SS_{total}

Variables:

η² is the Eta Squared
SS_effect is the sum of squares for the effect
SS_total is the total sum of squares

To calculate Eta Squared, divide the sum of squares for the effect by the total sum of squares. This will give you the proportion of variance in the dependent variable that can be predicted from the independent variable(s).

What is an Eta Squared?

Eta Squared is a statistical measure used in the context of an analysis of variance (ANOVA), which indicates the proportion of the total variance in a dependent variable that can be attributed to the variations in an independent variable. It is a measure of effect size and is used to determine the strength of the relationship between variables. The value of Eta Squared ranges from 0 to 1, where 0 indicates no effect and 1 indicates a perfect effect.

How to Calculate Eta Squared?

The following steps outline how to calculate the Eta Squared (η²).

First, determine the sum of squares for the effect (SS_effect).
Next, determine the total sum of squares (SS_total).
Next, gather the formula from above = η² = SS_effect / SS_total.
Finally, calculate the Eta Squared (η²).
After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem :

Use the following variables as an example problem to test your knowledge.

SS_effect = 120

SS_total = 200