Question

what values for h provide convincing evidence of a significant difference between treatments for the kruskal Wallis test

Answer 1

Kruskal-Wallis test by ranks is a non parametric method for testing whether two or more independent samples of equal or non equal size belongs to same distribution or not.

The null hypothesis assumed is samples(groups) are from identical population.

The alternative hypothesis assumed is at least one sample comes from different population than others.

The test statistic used is:

Where

N-total sample size, n_j- sample size of j^th group,R_j- sum of ranks in j^th group.

The distribution of Kruskal-Wallis test statistic approximates a chi-square distribution with k-1 degrees of freedom.

The critical value(table value) can be obtained from the table of critical values of chi-square distribution.

If the calculated critical value is less than the critical chi- square value(table value) the null hypothesis cannot be rejected.

If the calculated critical value is greater than the critical chi- square value(table value) the null hypothesis can be rejected and we can say that at least one sample comes from different population.

Thus the Kruskal-Wallis test provide evidence of significant difference between treatments if the calculated critical value(h) is greater than the table value.