What are the conditions for using a Kruskal-Wallis test?

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1. The Kruskal-Wallis test is a non-parametric statistical test used to compare three or more independent groups. The first condition is that the data should be ordinal, interval, or ratio in nature, but it does not need to follow a normal distribution.
2. The second condition is that the groups being compared must be independent of each other. This means that the observations in one group should not influence or be related to the observations in another group.
3. The third condition is that the dependent variable should be measured on at least an ordinal scale. This means the data should have a meaningful order or ranking.
4. The fourth condition is that the sample sizes across the groups do not need to be equal, but they should be reasonably large to ensure the test's robustness.
5. Finally, the Kruskal-Wallis test assumes that the distributions of the dependent variable are similar in shape across the groups, even though the medians may differ. This ensures that the test is comparing medians rather than other distributional characteristics.

Key Concepts

Kruskal-Wallis Test

The Kruskal-Wallis test is a non-parametric statistical method used to compare three or more independent groups. It assesses whether the samples originate from the same distribution, making it suitable when the assumptions of ANOVA are not met, particularly regarding normality and homogeneity of variances.

Independence of Samples

A key condition for the Kruskal-Wallis test is that the samples must be independent. This means that the observations in one group should not influence or be related to the observations in another group, ensuring that the test results are valid and unbiased.

Ordinal or Continuous Data

The Kruskal-Wallis test requires that the data be at least ordinal, meaning that the values can be ranked. It can also be applied to continuous data that do not meet the assumptions of normality, allowing for a broader application in analyzing non-normally distributed datasets.