How Calculate Proportional Eta Squared

Introduction & Importance

Proportional Eta Squared (η²) is a crucial metric in statistics, measuring the strength and direction of a linear relationship between two variables. Understanding how to calculate proportional eta squared is vital for data analysis and interpretation.

How to Use This Calculator

1. Enter the value of Eta (η) and N (sample size).
2. Click ‘Calculate’.
3. View results and chart below.

Formula & Methodology

The formula for proportional eta squared is η² = SSb / SSt, where SSb is the sum of squares between groups and SSt is the total sum of squares.

Real-World Examples

Example 1

In a study with N=100 participants, η=0.3. Calculate η².

SSb	SSt
300	1000

η² = 300 / 1000 = 0.3

Example 2

In another study with N=50 participants, η=0.25. Calculate η².

SSb	SSt
150	600

η² = 150 / 600 = 0.25

Data & Statistics

η	N	η²
0.2	150	0.04
0.35	75	0.1225

Expert Tips

• η² values range from 0 to 1, with higher values indicating stronger relationships.
• Interpret η² using Cohen’s guidelines: small (0.01), medium (0.09), large (0.25).

Interactive FAQ

What is the difference between η and η²?

η is the effect size, while η² is the proportional reduction in error variance due to the effect.

How is SSb calculated?

SSb = ∑(n_j * (x_j – x_bar)²), where n_j is the sample size for each group, x_j is the group mean, and x_bar is the grand mean.

For more information, see Statistics How To and Social Research Methods.