Eta Squared Calculator Anova

Eta Squared Formula:

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

Eta Squared (η²):

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1. What is Eta Squared?

Eta squared (η²) is an effect size measure used in ANOVA (Analysis of Variance) 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 effect (variance explained by the independent variable)
\( SS_{total} \) — Total sum of squares (total variance in the data)

Explanation: Eta squared quantifies the effect size by showing what proportion of the total variance is accounted for by the experimental manipulation or group differences.

3. Importance of Eta Squared Calculation

Details: Calculating effect size is crucial in statistical analysis as it provides information about the magnitude of differences between groups, complementing the statistical significance (p-value) obtained from ANOVA tests.

4. Using the Calculator

Tips: Enter the sum of squares effect and sum of squares total values 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 a small effect, η² = 0.06 a medium effect, and η² = 0.14 a large effect.

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 that a variable explains that is not explained by other variables in the analysis.

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 affected by the number and nature of the variables in the model.

Q5: Can eta squared be negative?
A: No, eta squared values range from 0 to 1, where 0 indicates no effect and values closer to 1 indicate stronger effects.