Kruskal-Wallis Test

Definition

The Kruskal-Wallis test is a non-parametric statistical method used to determine if there are statistically significant differences between two or more independent groups or samples. It is an alternative to the one-way ANOVA when the assumptions for the ANOVA are not met, such as when the data is not normally distributed or the variances are not homogeneous.

5 Must Know Facts For Your Next Test

1. The Kruskal-Wallis test is used to compare the medians of three or more independent groups, rather than the means as in the one-way ANOVA.
2. The test statistic for the Kruskal-Wallis test is the H-statistic, which is calculated based on the ranks of the data rather than the actual values.
3. The Kruskal-Wallis test is an extension of the Mann-Whitney U test, which is used to compare two independent groups.
4. If the Kruskal-Wallis test indicates a significant difference between the groups, post-hoc tests can be used to determine which specific groups differ.
5. The Kruskal-Wallis test is more robust to violations of assumptions, such as non-normal distributions and unequal variances, compared to the one-way ANOVA.

Review Questions

• Explain the purpose of the Kruskal-Wallis test and how it differs from the one-way ANOVA.
  • The Kruskal-Wallis test is a non-parametric statistical method used to determine if there are statistically significant differences between the medians of three or more independent groups. Unlike the one-way ANOVA, which compares the means of groups, the Kruskal-Wallis test compares the ranks of the data, making it more robust to violations of assumptions such as non-normal distributions and unequal variances. The Kruskal-Wallis test is an alternative to the one-way ANOVA when the assumptions for the ANOVA are not met.
• Describe the test statistic and decision-making process used in the Kruskal-Wallis test.
  • The test statistic for the Kruskal-Wallis test is the H-statistic, which is calculated based on the ranks of the data. The H-statistic is then compared to a critical value from a chi-square distribution with (k-1) degrees of freedom, where k is the number of groups. If the H-statistic is greater than the critical value, the null hypothesis (that there is no significant difference between the groups) is rejected, and it is concluded that at least one group differs significantly from the others. Post-hoc tests can then be used to determine which specific groups differ.
• Explain how the Kruskal-Wallis test is related to the Mann-Whitney U test and discuss the advantages of using the Kruskal-Wallis test in the context of one-way ANOVA.
  • The Kruskal-Wallis test is an extension of the Mann-Whitney U test, which is used to compare two independent groups. While the Mann-Whitney U test compares the ranks of two groups, the Kruskal-Wallis test compares the ranks of three or more groups. The Kruskal-Wallis test is advantageous in the context of one-way ANOVA because it is more robust to violations of assumptions, such as non-normal distributions and unequal variances. This makes the Kruskal-Wallis test a suitable alternative when the assumptions for the one-way ANOVA are not met, allowing researchers to still assess the differences between groups without the need for the data to follow a specific probability distribution.

Related terms

Non-parametric Test: A statistical test that does not rely on the data following a specific probability distribution, such as the normal distribution.

One-Way ANOVA:

A parametric statistical method used to determine if there are statistically significant differences between the means of three or more independent groups.

Null Hypothesis: The hypothesis that there is no significant difference between the groups being compared in a statistical test.