Eta Squared Calculator

Eta Squared (η²) is a measure of effect size used in the analysis of variance (ANOVA) to indicate the proportion of total variance that is attributed to a specific factor. Understanding this metric helps researchers assess the strength of an effect in experimental studies.

Historical Background

Eta Squared has been widely used in statistical analysis, especially in psychological and educational research, since the mid-20th century. It serves as a valuable measure to interpret the practical significance of findings in addition to their statistical significance.

Calculation Formula

The formula to calculate Eta Squared is as follows:

\[ \eta^2 = \frac{\text{SS}{\text{effect}}}{\text{SS}{\text{total}}} \]

Where:

• SS_effect: Sum of Squares for the effect
• SS_total: Total Sum of Squares

Example Calculation

If SS_effect = 20 and SS_total = 100, then:

\[ \eta^2 = \frac{20}{100} = 0.2 \]

This means that 20% of the total variance can be explained by the effect being studied.

Importance and Usage Scenarios

Eta Squared is crucial in research where the magnitude of an effect needs to be communicated clearly. It is especially useful in fields like psychology, where the size of an effect can provide insights into the practical implications of experimental results.

Common FAQs

1. What is a good Eta Squared value?

   • Values closer to 1 indicate a larger effect size. There is no strict threshold, but generally, η² values of 0.01, 0.06, and 0.14 are considered small, medium, and large effects, respectively.

2. Is Eta Squared the same as R Squared?

   • No, they are different. While both are measures of explained variance, R Squared is typically used in regression analysis, whereas Eta Squared is used in ANOVA.

3. Can Eta Squared be negative?

   • No, since it is a proportion of variance, Eta Squared cannot be negative.