Different Outcomes of the Wilcoxon—Mann—Whitney Test from Different Statistics Packages

Abstract

The Wilcoxon—Mann—Whitney test enjoys great popularity among scientists comparing two groups of observations, especially when measurements made on a continuous scale are non-normally distributed. Triggered by different results for the procedure from two statistics programs, we compared the outcomes from 11 PC-based statistics packages. The findings were that the delivered p values ranged from significant to nonsignificant at the 5% level, depending on whether a large-sample approximation or an exact permutation form of the test was used and, in the former case, whether or not a correction for continuity was used and whether or not a correction for ties was made. Some packages also produced pseudo-exact p values, based on the null distribution under the assumption of no ties. A further crucial point is that the variant of the algorithm used for computation by the packages is rarely indicated in the output or documented in the Help facility and the manuals. We conclude that the only accurate form of the Wilcoxon—Mann—Whitney procedure is one in which the exact permutation null distribution is compiled for the actual data.