Kruskal-Wallis Test Calculator

Perform a Kruskal-Wallis H test to determine if there is a significant difference among independent samples.

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About Kruskal-Wallis Test Calculator

The Kruskal-Wallis Test Calculator performs the Kruskal-Wallis H test, a nonparametric method for testing whether samples originate from the same distribution.

What is the Kruskal-Wallis Test?

The Kruskal-Wallis H test is a rank-based nonparametric test used to determine if there are statistically significant differences between two or more independent groups. It is an extension of the Mann-Whitney U test when you have more than two groups.

The test statistic \( H \) is calculated based on the ranks of the combined data from all samples.

How to Calculate the Kruskal-Wallis H Statistic

The Kruskal-Wallis H statistic is calculated using the following formula:

\( H = \frac{12}{N(N+1)} \sum_{i=1}^{k} n_i (R_i - \bar{R})^2 \)

Where:
\( N \) = Total number of observations across all groups
\( k \) = Number of groups
\( n_i \) = Number of observations in group \( i \)
\( R_i \) = Sum of ranks for group \( i \)
\( \bar{R} \) = Average of all ranks

Interpreting the Results

A large \( H \) value suggests a difference among the groups.
The p-value indicates the probability of observing the data if the null hypothesis (no difference) is true.
A p-value ≤ 0.05 typically suggests a significant difference among the groups.

Use Cases of the Kruskal-Wallis Test

The Kruskal-Wallis test is widely used in various fields:

Medicine: Comparing treatment effects across multiple groups when data are not normally distributed.
Psychology: Assessing differences in responses among several independent groups.
Agriculture: Evaluating the effects of different fertilizers on crop yields.