I'm looking at multiple studies. I do not have the original data. One study I'm looking at provides means, standard deviations, and Mann-Whitney U values (with p). (How) can I convert from Mann-Whitney U to Z in R?

[Perhaps using a package such as MAd.]

This page provides some guidance. http://yatani.jp/HCIstats/MannWhitney#EffectSize I'm having the problem though that I am not generating the same U values as the original researchers did using the provided mean values.

From what I can tell - I've scoured pages and now talked to experts - this can't really happen. The closest I found was calculating:

 Z = {largest U value – [N1*N2]/2}/(N1)(N2)(N1+N2+1)]/12

but I don't have access to the original data - only a summary U, so I can't do this. The data was from a non-parametric (small n) sample - so I cannot meaningfully generate a corresponding data set. The purpose of this was conversion for a meta-analysis. I'll have to settle for p-value vote counting in my summary.

Though this is closing, I will note the U data I was hoping to convert- from: 1A. N. Antle, G. Corness, and M. Droumeva, “What the body knows: Exploring the benefits of embodied metaphors in hybrid physical digital environments,” Interact. Comput., vol. 21, no. 1–2, pp. 66–75, Jan. 2009.

One example would be, calculating the (z) effect size for "tempo". This wasn't done, because the data was non-parametric - owing to small sample size (most likely).

GroupA - M=123, sd= 108 GroupB - M = 71, sd = 59 Provided U - U=5.5, p<.0001

One can try to do such things as mes() from the compute.es package - but the results are beside the point as the data is non-parametric.

mes(123, 71, 108, 59, 10, 10, 95)

The aforementioned link provides a very nice way to calculate a more exact Mann-Witney U (Wilcoxon) - and the compute.es reference page is very helpful - but the missing, non-parametric data make the problem intractable (as far as I can tell). So, I'll be using p-values for a less informative "vote count" approach.