What test should be used for 3 or more independent samples of ordinal data?

When dealing with three or more independent samples of ordinal data, the correct statistical test to use is the Kruskal Wallis 1-way ANOVA. This non-parametric test is specifically designed to compare the medians of different groups and is appropriate for ordinal data, which does not assume a normal distribution.

Ordinal data represents categories with a meaningful order but does not provide information about the exact differences between those categories. The Kruskal Wallis test ranks all the observations from all groups together and determines whether there are statistically significant differences between the medians of the groups.

Using the Kruskal Wallis test ensures that the analysis accounts for the ranked nature of the data, making it a robust choice when the assumptions necessary for parametric tests, such as the t-test or ANOVA, are not met. Thus, for the situation presented—comparing three or more independent samples of ordinal data—the Kruskal Wallis 1-way ANOVA is the appropriate method.