Kruskal-Wallis Exact Probability Tables

J. Patrick Meyer, University of Virginia
Michael A. Seaman, University of South Carolina

Website updated: February 4, 2015


Using a recursive algorithm, we computed the exact probability distribution for the Kruskal-Wallis H statistic for total sample sizes up to 105 for three groups and up to 40 for four groups. The complete distribution files require 1 terabyte of storage. For brevity, we have created these critical value tables for significance levels of 0.1, 0.05, and 0.01. We list the critical value for which the p-value is less than or equal to the nominal significance level. The following tables contain these conservative critical values followed by the corresponding exact p-value.

Details of the algorithm and a comparison to asymptotic approximations are described in this paper and also discussed in Meyer and Seaman (2014). Please contact Patrick Meyer or Michael Seaman if you have any questions.

Please use the following references when citing these tables.

Meyer, J. P., & Seaman, M. A. (2014). A comparison of the exact Kruskal-Wallis distribution to asymptotic approximations for all sample sizes up to 105. Journal of Experimental Education, 81(2), 139-156.

Meyer, J. P., & Seaman, M. A. (2008). Expanded table of the Kruskal-Wallis statistic. Retrieved from

Critical Value Tables

Three group critical value tables. This pdf file is 196 pages long (338KB).

Four group critical value tables. This pdf file is 19 pages long (80KB).