First, use the Critical Significance Level (α) chosen in Step 2 and degrees of freedom (df) calculated in Step 3 (df = one less than the number of samples) to find the Critical Value of Χ2 (Χ2critical) using a Critical Value Table such as the one below (e.g. if α = 0.05 and df = 2, then Χ2critical = 5.991).

Second, compare Χ2critical with the value for 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 ≥ X2critical (significant result).

Accept your Null Hypothesis if your calculated value is less than the Critical value; H < X2critical (non-significant result).

For example, if H = 9.260 and Χ2critical = 5.991 then reject the Null Hypothesis.

Table of Critical Values for Critical Significance Levels (α) of 0.9, 0.5, 0.1, 0.05 and 0.01 for the Chi-squared statistic where degrees of freedom (df) is one less than the number of samples for Kruskal-Wallis test.

 degrees of freedom α = 0.9 α = 0.5 α = 0.1 α = 0.05 α = 0.01 1 0.016 0.455 2.706 3.841 6.635 2 0.211 1.386 4.605 5.991 9.210 3 0.584 2.366 6.251 7.815 11.345 4 1.064 3.357 7.779 9.488 13.277 5 1.610 4.351 9.263 11.070 15.086 6 2.204 5.348 10.645 12.592 16.812 7 2.833 6.346 12.017 14.067 18.475 8 3.490 7.344 13.362 15.507 20.090

Critical values of the chi-square distribution generated using the CHINV() function in Microsoft Excel, which returns the inverse of the one-tailed probability of the chi-squared distribution. Table generated by Toby Carter.