Calculate Partial Eta Squared

Partial Eta Squared Formula:

\[ \eta_p^2 = \frac{SS_{effect}}{SS_{effect} + SS_{error}} \]

Partial Eta Squared (η_p²):

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1. What is Partial Eta Squared?

Partial Eta Squared (η_p²) is a measure of effect size used in ANOVA that represents the proportion of variance in the dependent variable that is attributable to a particular independent variable, while controlling for other variables in the model.

2. How Does the Calculator Work?

The calculator uses the partial eta squared formula:

\[ \eta_p^2 = \frac{SS_{effect}}{SS_{effect} + SS_{error}} \]

Where:

\( SS_{effect} \) — Sum of squares for the effect (treatment)
\( SS_{error} \) — Sum of squares for the error (residual)

Explanation: This formula calculates the proportion of total variance that is explained by a specific effect, providing a standardized measure of effect size that is comparable across studies.

3. Importance of Partial Eta Squared

Details: Partial eta squared is crucial for determining the practical significance of research findings beyond statistical significance. It helps researchers understand the magnitude of effects and is particularly useful in power analysis and meta-analysis.

4. Using the Calculator

Tips: Enter the sum of squares for the effect and the sum of squares for the error. Both values must be positive numbers, with SS_error greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is considered a small, medium, and large effect size for partial eta squared?
A: Generally, η_p² = 0.01 is considered small, 0.06 medium, and 0.14 large, though interpretations may vary by research field.

Q2: How does partial eta squared differ from eta squared?
A: Partial eta squared controls for other variables in the model, while eta squared does not. Partial eta squared is preferred in multifactor ANOVA designs.

Q3: Can partial eta squared be negative?
A: No, partial eta squared values range from 0 to 1, where 0 indicates no effect and values closer to 1 indicate stronger effects.

Q4: When should I use partial eta squared?
A: Use partial eta squared in ANOVA designs to report effect sizes, particularly when you have multiple independent variables and want to report the effect size for each factor.

Q5: Are there limitations to partial eta squared?
A: Partial eta squared can be biased in small samples and may overestimate effect sizes. It's also not directly comparable across studies with different designs.