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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!

Nick Cox
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Jayna
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    What does "U" mean? Have you consulted the software documentation? – whuber Oct 17 '19 at 13:39
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    @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. – Glen_b 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? – Jayna Oct 17 '19 at 14:43
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    On equivalence and the large size, see 1. https://stats.stackexchange.com/questions/252976/mann-whitney-u-statistic-seems-very-large-is-something-wrong/ For more on equivalence see: 2. https://stats.stackexchange.com/questions/79843/is-the-w-statistic-output-by-wilcox-test-in-r-the-same-as-the-u-statistic/
    1. https://stats.stackexchange.com/questions/30141/determine-if-a-heavy-tailed-distributed-process-has-improved-significantly/
     – Glen_b 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. – Glen_b Oct 17 '19 at 15:57
  • It's nice of SPSS to give you all three. In contrast, it's somewhat annoying that wilcox.test in R calculates the z value, but then doesn't pass it to the output anywhere. – Sal Mangiafico Oct 17 '19 at 16:10
  • @Glen_b I understand more now! Thank you! – Jayna Oct 17 '19 at 18:06
  • @SalMangiafico thank you! – Jayna Oct 17 '19 at 18:06

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