1. What is Eta Squared?

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:

Where:

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

Explanation: Eta squared quantifies the proportion of total variance attributable to a factor, ranging from 0 to 1 where higher values indicate stronger effects.

3. Importance of Eta Squared Calculation

Details: Eta squared provides information about the practical significance of findings beyond statistical significance, helping researchers understand the magnitude of effects in their studies.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

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

Q2: How does eta squared differ from partial eta squared?
A: Eta squared includes all variance in the denominator, while partial eta squared removes variance from other factors in the model.

Q3: When should I use eta squared?
A: Use eta squared for one-way ANOVA designs or when you want to understand the proportion of total variance explained by a factor.

Q4: Are there limitations to eta squared?
A: Eta squared can be biased in sample estimates and tends to overestimate population effect sizes, especially with small samples.

Q5: Can eta squared be negative?
A: No, eta squared values range from 0 to 1, representing the proportion of variance explained.