# Mann-Whitney U & Wilcoxon W [duplicate]

I ran the Mann-Whitney in SPSS. In addition to the U, the output generated the Wilcoxon W and the Z score. Why would the W and Z be present in the output? I cannot explain them being present. Also, the U and W are very large and different. Why is that?

Edit: I understand now why the U and W are large. My sample is large. However, they are different!

• What does "U" mean? Have you consulted the software documentation?
– whuber
Oct 17 '19 at 13:39
• @Jayna The Mann-Whitney U test and the Wilcoxon rank sum test are equivalent, a fact noted by Mann and Whitney in their 1947 paper. They have the same p-value on the same data when testing the same pair of hypotheses. The correspondence is noted in answers to a number of questions already on site. The reason for the numbers being very large when sample sizes are large is also dealt with in a number of questions already on site. Oct 17 '19 at 13:45
• @Glen_b thank you. I’m new here and will look for questions and answers regarding the large U and W. I’m just learning SPSS and statistics in general. I understand that they are equivalent, but why would they they to not be identical? How would I explain why the Wilcoxon W is in the output? Oct 17 '19 at 14:43
• On equivalence and the large size, see 1. stats.stackexchange.com/questions/252976/… For more on equivalence see: 2. stats.stackexchange.com/questions/79843/… 3. stats.stackexchange.com/questions/30141/… Oct 17 '19 at 15:49
• The statistics are not identical because Mann&Whitney's definition of the statistic was different from Wilcoxon's. Both statistics will be given because a user looking for either test can get it with that one calculation (if you calculate U you can compute W from it trivially, and if you calculate W you can get U from it trivially) -- it's as easy to give both as it is to give one of the two statistics; you don't need a separate function for equivalent statistics. The Z score can give useful information that's not as readily apparent from either raw statistic, particularly with larger samples. Oct 17 '19 at 15:57