I'm doing a Mann-Whitney U test to compare two very large samples (sample size 1 = 13250; samlple size 2 = 38871) originating from a raster image. I know t-tests are not recommended to compare rasters, because since rasters have so many values, they will almost surely detect a significant difference, no matter how small that difference might be (see this post in gis.stackexchange.com and point 3 of the first answer to this post).
My question is whether the same problem applies to Mann-Whitney or not. I ran the test on SPSS and got the following results:
- Test Statistics
- selection frequency
- Mann-Whitney U 4094520,000
- Wilcoxon W 759591276,000
- Z -210,227
- Asymp. Sig. (2-tailed) ,000
While I did expect to find a difference between the groups, I don't know what to make of such large values.
There is a paper which did the same thing I did. See the last sentence of the Material and Methods section. However, they obtained much smaller values http://icesjms.oxfordjournals.org/content/69/1/75/T5.expansion.html (they don't make clear if these are Mann-Whitney Us or z-scores). Granted they used a smaller sample (combined sample size = 5629), but the difference in the magnitude of the values still seem strange to me.
So, are my results simply the result of a very large sample, but still valid? Or should I use another test?