What nonparametric test is used to analyze more than two mean scores on a single variable?

The Kruskal-Wallis Test is the correct choice for analyzing more than two mean scores on a single variable when the assumptions required for parametric tests (like the ANOVA) are not met. This nonparametric test is used when you have one independent variable with three or more groups, and it compares the ranks of the data rather than the actual data values. This approach is particularly beneficial in situations where the data may not be normally distributed or when the sample sizes are unequal, which can violate the assumptions of parametric testing.

The Kruskal-Wallis Test ranks all the observations from all groups together and examines whether the rank sums differ significantly across the groups. If a significant difference is found, it suggests that at least one group has a different median than the others. Thus, this test is ideal for comparing multiple groups without assuming a specific distribution of the underlying data.

In contrast, other tests listed, such as the Mann-Whitney U Test, are designed for comparing two independent groups; the Wilcoxon signed-rank test is used for related samples, meaning pairs or repeated measures; and the Chi-square test assesses categorical data, rather than analyzing means or ranks directly. This makes the Kruskal-Wallis Test uniquely