Kruskal-Wallis Test

The non-parametric analogue for a one-way ANOVA test is the Kruskal-Wallis test.

The non-parametric analogue for a one-way ANOVA test is the Kruskal-Wallis test.

Remember that a non-parametric test is used when the distribution is either highly skewed or we are comparing ordinal or rank ordered data.

Example of a skewed distribution

1 2 3 4 5 6

Example of rank ordered data

Football Players Basketball Players1st 2nd

3rd

4th 5th 6th

7th

8th 9th

10th

Rank ordered-comparison of

amount of pizza slices eaten in one

sitting

Similar to the Mann-Whitney U test, the Kruskal-Wallis test evaluates the differences among groups by estimating differences in ranks among them.

Similar to the Mann-Whitney U test, the Kruskal-Wallis test evaluates the differences among groups by estimating differences in ranks among them.

For example, four groups of students, freshman, sophomores, juniors, and seniors might be tested for their preference to watch rugby.

The measurement of their preference might be conducted on an ordinal scale with five points on the scale; strong dislike, dislike, neutral, like, and strong like. Such a Like-it scale renders ordinal preference and should be treated with a non-parametric test.

The measurement of their preference might be conducted on an ordinal scale with five points on the scale; strong dislike, dislike, neutral, like, and strong like. Such a Like-it scale renders ordinal preference and should be treated with a non-parametric test.

Freshmen Sophomores Juniors Seniorsstrong dislike dislike like strong like

dislike Neutral Neutral likestrong dislike like like strong like

Neutral like strong like Neutralstrong dislike Neutral dislike likestrong dislike strong dislike like strong like

Here is the data rank ordered using the “like it” scale

Freshmen Sophomores Juniors Seniors5th 4th 2nd 1st4th 3rd 3rd 2nd

5th 2nd 2nd 1st3rd 2nd 1st 3rd

5th 3rd 4th 2nd

5th 5th 2nd 1st

As with ANOVA, here we are determining how more than two levels (Freshmen, Sophomores, Juniors, and Seniors) of the independent variable (year in school) compare in terms of the dependent variable (their preference for rugby).

preference for

Freshman

Sophomore

Junior

Senior

Similar to one-way ANOVA, a significant Kruskal-Wallis result should be followed up with post-hoc tests (also non-parametric) to determine where the differences between groups are occurring.

preference for

Freshman

Sophomore

Junior

Senior