KRUSKAL-WALLIS TEST

The Kruskal-Wallis test is similar to the Mann-Whitney U test. The Mann-Whitney U compared two groups, whereas the Kruskal-Wallis compares three or more groups. The experimenter wants to know if the difference among the groups is due to sampling error or is a real difference. The Kruskal-Wallis test determines whether a difference is present by finding out if the sums of the ranks for each of its groups differ significantly from each other. A significant value of H (based on the chi-square table or the Kruskal-Wallis table) implies that the medians of the distribution are not the same. When using the Kruskal-Wallis test, the experimenter does not have to be concerned about whether the test is one- or two-tailed. The only concern is whether a difference exists. The requirements for using this test are:

1. Ordinal level

2. Three or more groups

3. Independent groups

4. Simple random sample

The formula for the calculation is:

The symbols used in calculating the test are: N = total number of objects (n ₁ + n ₂ + n ₃ + ...), Df = k - 1 Degrees of freedom, equal to the number of groups minus one, n ₁ ,n ₂ ,n ₃ , ... = number of objects in group 1, group 2, group 3 and so on, ( & pound ; R ₁ ) ² , ( R ₂ ) ² , ( R ₃ ) ² , ... = sum of the ranks for group 1 squared, group 2 squared, group 3 squared, and so on.