NUMBAT OER - Open Educational Resources

First, use the Critical Significance Level (α) chosen in Step 2 and sample sizes (e.g. n1, n2 and n3) calculated in Step 3 to find the Critical Value of H (Hcritical) using a Critical Value Table such as the one below
e.g. if α=0.05, n1 = 5, n2 = 5 and n3 = 5 then Hcritical = 5.780.

Second, compare Hcritical with the value of the H statistic calculated in Step 3.

Reject your Null Hypothesis if your calculated value is greater than or equal to the Critical value; H ≥ Hcritical (significant result).

Accept your Null Hypothesis if your calculated value is less than the Critical value; H < Hcritical (non-significant result).

For example, if H = 13.382 and Hcritical = 5.780 then reject the Null Hypothesis.

Table of Critical Values for a Critical Significance Level (α) of 0.05 and three samples for the H statistic where n1 is the size of the first sample, n2 is the size of the second sample and n3 the size of the third sample.

n1 n2 n3 H
2 2 2 -
3 2 1 -
3 2 2 4.714
3 3 1 5.143
3 3 2 5.361
3 3 3 5.600
4 2 1 -
4 2 2 5.333
4 3 1 5.208
4 3 2 5.444
4 3 3 5.791
4 4 1 4.967
4 4 2 5.455
4 4 3 5.598
4 4 4 5.692
5 2 1 5.000
5 2 2 5.160
5 3 1 4.960
5 3 2 5.251
5 3 3 5.648
5 4 1 4.985
5 4 2 5.273
5 4 3 5.656
5 4 4 5.657
5 5 1 5.127
5 5 2 5.338
5 5 3 5.705
5 5 4 5.666
5 5 5 5.780

Critical values of the Kruskal-Wallis H distribution based on Zar (1999) and sources therein.
Zar, JH (1999) Biostatistical Analysis 4th edition. Prentice-Hall, New Jersey.