Statistica Sinica

Ying Kuen Cheung and Jerome H. Klotz

Abstract:We give an improved algorithm for calculating the exact null distribution of th e two sample Mann Whitney Wilcoxon rank sum statistic. The algorithm modifies the update method of Smid using a minimal linked list wh ich directs calculation of only those intermediate probabilities required for the final value. Using an efficient shortened representation of the list of required intermediat e values, exact probabilities for sample sizes of the order of 100 for each of th e two samples can be computed on a personal computer for cases covering the range from many ties with few different values to few ties with many different values.

Key words and phrases:Distribution two sample rank sum test, exact P-value, linked list, ties, update algorithm.