Effect Size Eta Squared Calculator

Eta Squared Formula:

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

Eta Squared (η²):

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1. What is Eta Squared Effect Size?

Eta squared (η²) is an effect size measure used in ANOVA that represents the proportion of the total variance in a dependent variable that is associated with the membership of different groups defined by an independent variable.

2. How Does the Calculator Work?

The calculator uses the Eta Squared formula:

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

Where:

\( SS_{effect} \) — Sum of squares for the effect (between groups)
\( SS_{total} \) — Total sum of squares (sum of squares between groups plus sum of squares within groups)

Explanation: Eta squared quantifies the proportion of total variance attributable to a factor, ranging from 0 to 1, with higher values indicating a stronger effect.

3. Importance of Eta Squared Calculation

Details: Eta squared helps researchers determine the practical significance of their findings beyond statistical significance, providing insight into the magnitude of experimental effects in ANOVA studies.

4. Using the Calculator

Tips: Enter the sum of squares for the effect and the total sum of squares from your ANOVA results. Both values must be positive numbers, and SS_effect cannot exceed SS_total.

5. Frequently Asked Questions (FAQ)

Q1: What is considered a small, medium, or large effect size for eta squared?
A: Generally, η² = 0.01 is considered small, η² = 0.06 is medium, and η² = 0.14 is large, though interpretation depends on research context.

Q2: How does eta squared differ from partial eta squared?
A: Eta squared represents the proportion of total variance, while partial eta squared represents the proportion of variance after removing other factors from the total variance.

Q3: When should I use eta squared?
A: Eta squared is appropriate for one-way ANOVA designs. For more complex designs with multiple factors, partial eta squared is often preferred.

Q4: Are there limitations to eta squared?
A: Eta squared can be biased in small samples and tends to overestimate the population effect size. It's also sensitive to the number and nature of factors in the model.

Q5: Can eta squared be negative?
A: No, eta squared values range from 0 to 1, as it represents a proportion of variance explained.