Kruskal-Wallis Effect Size Calculator

The Kruskal-Wallis test is a non-parametric method for testing whether samples originate from the same distribution. While it provides an H statistic for evaluating the differences, effect size (often reported as eta-squared, \(\eta^2\)) is useful for understanding the magnitude of those differences. This calculator computes the effect size based on the H statistic, total sample size, and the number of groups.

Background and Significance

The Kruskal-Wallis test is typically used when the assumptions of ANOVA are not met. However, like ANOVA, it is important to consider the effect size to understand the practical significance of the results, beyond just the p-value.

Calculation Formula

The effect size for the Kruskal-Wallis test is calculated using the formula:

\[ \eta^2 = \frac{H - (k - 1)}{N - 1} \]

Where:

• \(H\) is the Kruskal-Wallis H statistic.
• \(k\) is the number of groups.
• \(N\) is the total sample size.

Example Calculation

If the H statistic is 12.5, the total sample size (N) is 30, and there are 4 groups (k), the effect size would be:

\[ \eta^2 = \frac{12.5 - (4 - 1)}{30 - 1} = \frac{12.5 - 3}{29} = \frac{9.5}{29} \approx 0.3276 \]

Importance and Usage

Understanding the effect size in the context of the Kruskal-Wallis test helps in determining the importance of group differences. A significant H statistic might indicate a difference, but effect size tells us how meaningful that difference is in a real-world context. This is crucial for interpreting the results of the test in various research scenarios.

Common FAQs

1. What is the Kruskal-Wallis test used for?

   • The Kruskal-Wallis test is used to determine if there are statistically significant differences between two or more groups of an independent variable on a continuous or ordinal dependent variable.

2. What does the effect size tell us?

   • The effect size provides a measure of the magnitude of the difference between groups. It helps in understanding how large or small the observed effect is, which is important for practical interpretation.

3. Can the effect size be negative?

   • No, the effect size (eta-squared) is always a positive value, as it represents a proportion of variance explained by the group differences.