I am having trouble presenting my results from statistical tests and see there are a few different ways of presenting them. I have given an example of how I have writien my result but just having trouble with the last sentence on whether it needs the W value and DF. Or do just include the P value and DF but write them in the sentence?
My Writing:
The data failed this normality test, so the non-parametric Mann-Whitney Test was suitable to compare the two groups. There was a significant difference of the annual total range distribution between 2015 and 2018 (Mann-Whitney Test, W = 115, P = 0.046, DF = 20)
I have attached an example found of how to present it and chose the 'Better' example to stick with but I am not sure if its any use including the W value.
There's nothing wrong with including the W statistic, but it probably isn't that useful for most readers. I take it you are using R software. (Does any other software package report W ?). If so, the p-value is actually determined from a z value for the unpaired case, unless the exact test is used. Your readers would probably be more familiar with the z value. With the caveat that I wrote it, there are methods to get the z value from R here: https://rcompanion.org/handbook/F_04.html , search for extracting the z value . ... I also recommend including an effect size statistic. The same webpage, with the same caveat, lists some appropriate ones. Glass rank biserial correlation coefficient, Vargha and Delaney's A, or Cliff's delta would probably be good.
Salvatore S. Mangiafico If there is nothing wrong I might include it. When I searched its meaning its the sum of the ranks of the first sample. I'm still a little confused by this.
I use minitab and I attached a screenshot of the data it presents
It's fine to include W.
EDIT: Yes, it's the sum of the ranks of the first sample. If you pool both groups, take the ranks in the pooled sample, and then get the sum of the ranks for those observation that were in the first group, that's what Minitab reports.
You can imagine that this isn't very useful for the reader. It's much more useful to report the probability of an observation in one group being larger than an observation in the other group.
One caution: the Minitab output suggests that the Mann-Whitney test is a test about the medians. This isn't necessarily true. I noticed in your write-up that you didn't mention a difference in medians to describe the test results. This is good. I mean, it's fine to report the medians also, but that's not what the M-W test is about
EDIT: In this response, I had originally included some instructions to calculate Cliff's delta or VDA from W, but it appears that Minitab and R report two different statistics for W. I think R reports Mann-Whitney U as W. (Oy!). .... The upshot is that I think it's a good idea to report these kinds of effect size statistics. For 8 and 13 observations, it's trivially easy to calculate these in R, even without installing the software (for example at, https://rdrr.io/snippets/ ).
You can run the following there. For these toy data, results should be somewhat similar to the results you report above. But you can simply swap-in your data.
x2015 = c(0.5, 1.5, 1.7, 2.5, 3.5, 4, 4.24, 4.6, 4.7, 4.8, 4.9, 5.5, 6.5)
x2018 = c(1, 3, 5, 6.9, 7.22, 11, 13, 15)
wilcox.test(x2015, x2018)
library(rcompanion)
vda(x = x2015, y = x2018)
cliffDelta(x = x2015, y = x2018)
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