KruskalWallistestissä

Kruskal-Wallis test is a non-parametric statistical test used to determine if there are statistically significant differences between the medians of three or more independent groups. It is considered the non-parametric equivalent of the one-way ANOVA. The test is named after William Kruskal and W. Allen Wallis, who published it in 1952.

The null hypothesis of the Kruskal-Wallis test is that the medians of all groups are equal. The alternative hypothesis is that at least one group median is different from the others. The test works by ranking all the data from all groups combined, from smallest to largest. Then, it calculates a test statistic based on the sum of the ranks for each group. A large test statistic suggests that the group medians are likely different.

The Kruskal-Wallis test is appropriate when the assumptions of ANOVA, such as normality of residuals and homogeneity of variances, are not met. It can be used with ordinal data or interval/ratio data that is not normally distributed. The interpretation of the results involves comparing the calculated test statistic to a critical value from the chi-squared distribution or by examining the p-value. If the p-value is less than the chosen significance level (e.g., 0.05), the null hypothesis is rejected, indicating a significant difference between at least two group medians. If a significant difference is found, post-hoc tests, such as Dunn's test, can be performed to identify which specific groups differ from each other.