The formula to calculate the Kruskal Wallis Effect Size (η²) is:
\[ η² = \frac{H}{N - 1} \]
Where:
Let's say the Kruskal Wallis statistic (\( H \)) is 10, and the total sample size (\( N \)) is 50. Using the formula:
\[ η² = \frac{10}{50 - 1} \]
We get:
\[ η² = \frac{10}{49} \approx 0.20 \]
So, the Kruskal Wallis Effect Size (\( η² \)) is approximately 0.20.
The Kruskal Wallis effect size (η²) is a measure of the strength of association or effect in non-parametric data when comparing three or more independent groups. It is used when the assumptions of ANOVA are not met. The effect size is a way to quantify the size of the difference between groups, and it is an important aspect of hypothesis testing that complements the p-value.