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Conclusion
When to use the Kruskal-Wallis H test
The Kruskal-Wallis H test is direct extension of the Mann-Whitney U test for more than two independent samples.
The test can only be used if all the samples can be ranked in numerical size and all samples are in the same units; thus the data must be at least ordinal.
What we need to know
The data in the samples must be at least ordinal so that each item in the combined sample can be ranked in order of size (remembering to retain the identity of each item).
Sampling distribution
The sample distribution is denoted as H and the distribution of H approximates the chi-square (χ2) distribution for j-1 degrees of freedom (where j is the number of samples).
Critical values
The critical value of the testing statistic can be found from tables critical χ2 values for the relevant significance level and degrees of freedom (i.e. j-1, where j is the number of samples).
An on-line version of the chi-square critical values table can be found, for example, at the Engineering Statistics Handbook:
Worked example A group of 25 people in the UK were given a political spectrum test (0 extreme left wing through to 20 extreme right wing). The group consisted of three samples based on their views about the monarchy: 'in favour of dissolution', 'indifferent', 'retain monarchy'. Is there any evidence to suggest right wingers are more in favour of retaining the monarchy?
Decision: Cannot reject the null hypotheses (H0) as calculated chi-square (0.43) is less than the critical value of 5.99; there is no signifcant difference between samples.
1. The following scores on a scale of conservativism (0 to 100, with 100 being ultraconservative) were achived by three seminar groups who together constituted a first-year politics degree course. Is there any significant difference in the results of the three groups. What does the result suggest?
Seminar 1: 76, 14, 23, 29, 41, 56, 83 42
Seminar 2: 76, 63, 24, 88, 37, 69, 49, 48
Seminar 3: 60, 67, 63, 29, 28, 51, 35, 80, 40
2. A survey of parents to see how important it was for them that their senior-school children achieved sufficient grades to apply for university. A score of 1 in the table below suggests an indifference to going to university while a score of 9 indicates it is seen as essential by parents. Is there any significant difference between the three occupation groups?
