Kruskal-Wallis-test

The Kruskal-Wallis, or H test, is a non-parametric alternative to one-way ANOVA. It effectively tests the null hypothesis that three or more populations have identical medians.

Consider the dataset on a supermarket's red, green, and black grapes sales.

How can one determine if the three samples originate from populations with the same median sales?

For testing this claim, all samples are initially merged to assign ranks. Then, the sum of ranks for each sample is calculated independently.

The test statistic, H, is derived using a formula that quantifies the variance among the rank sums.

In this scenario, the H value follows the chi-square distribution, with the degrees of freedom being one less than the total number of samples, which is two.

At this level of degrees of freedom, the critical value is determined from its corresponding table at a chosen significance level, such as 0.05.

Given that the calculated H value is lower than the critical value, the null hypothesis, suggesting that the samples come from populations with equivalent medians, cannot be rejected.