https://peterstatistics.com/CrashCourse/2-SingleVar/Ordinal/Ordinal-3-Reporting.html

https://peterstatistics.com/CrashCourse/index.html

Hi. I hope the following link could help you:

http://www.sthda.com/english/wiki/unpaired-two-samples-wilcoxon-test-in-r

The wilcox.test function in R is a little peculiar with how it report results.

It actually calculates a z value, but doesn't report it.

One way to extract the z value is to use the wilcoxonZ function in the rcompanion package. (I wrote this function). It doesn't have as many input options as the original function, but otherwise uses the code from the original function.

A second way is to use the wilcox_test function in the coin package. Be sure to look up that package and function to understand it.

The reported W statistic is related to the U statistic. This post suggests they are actually the same ( https://stats.stackexchange.com/questions/79843/is-the-w-statistic-output-by-wilcox-test-in-r-the-same-as-the-u-statistic ).

U (and W) are somewhat difficult to interpret at a glance. They are related to the sample sizes. If I remember correctly, the maximum U is n1 * n2. But also, if I remember correctly, if you reversed the groups, U' = n1 * n2 - U. ***. Most readers would be familiar with z and p values.

Also, you might be interested in reporting an effect size statistic.

Cliff's delta and Vargha an Delaney's A are common. Also, the Glass rank biserial correlation, whose result is the same as Cliff's delta, though that could depend on what options are chosen in some cases. I added functions for these to code below, again with the caveat that I wrote these functions.

The Wilcoxon-Mann-Whitney test doesn't really test anything about means or medians per se, so it's difficult to know what descriptive statistics to report. I would probably report the median along with the min, max, 1st quartile, and 3rd quartile (Tukey's five number summary).

Since the test concerns comparing ranks of the data for the two groups, you could also include something like the mean rank for each group. In context of total N this should make sense. Or the proportion of where ranks in A > ranks in B and the proportion where ranks in B > ranks in A. Added some code below where this information can be reported by the cliffDelta or wilcoxonRG functions.

*** In the example below, there are 6 and 6 observations, for a n1*n2 of 36. As written, the wilcox.test function returns a W of 3, since of all possible comparisons between groups, some observation in A will be higher than some observation in B, 3 times [9 > 8, 11>8, and 11>10]. If you swap the data for A and B, the wilcox.test function returns a W of 33. 3 + 33 = 36. The p-value is the same either way. The z value is the same with a different sign. Cliff's delta and Glass RBC is the same with the opposite sign.

R CODE:

if(!require(rcompanion)){install.packages("rcompanion")}

if(!require(coin)){install.packages("coin")}

A = c(1, 3, 5, 7, 9, 11)

B = c(8, 10, 12, 14, 16, 18)

Y = c(A, B)

Group = factor(c(rep("A", length(A)), rep("B", length(B))))

Data = data.frame(Group, Y)

wilcox.test(Y ~ Group, data=Data, exact=FALSE, correct=FALSE)

library(rcompanion)

wilcoxonZ(A, B, digits=5)

library(coin)

wilcox_test(Y ~ Group, data=Data)

### Effect sizes

library(rcompanion)

cliffDelta(Y ~ Group, data=Data)

vda(Y ~ Group, data=Data)

wilcoxonRG(Y, Group)

### Summary statistics

summary(A)

summary(B)

wilcoxonRG(Y, Group, verbose=T)

cliffDelta(Y ~ Group, data=Data, verbose=TRUE)

Hi – don’t worry about being confused by what you have read and what people do in practice; from my experience people sometimes seem to ignore the usual conventions when running stats. For example, I would never run t-tests with ordinal data but find that some colleagues do. My advice is to stick to the “rules” and be able to explain why you did what you did. There are a couple of books you might find useful: Learning to use statistical tests in psychology by Greene and D’Oliveira (don’t be put off if you aren’t studying psychology the principles transfer to other disciplines) and Discovering statistics using R by Field, Mile and Field.

The Wilcoxon test should be used when the type of outcome variable is qualitative ordinal (freely distributable) and the type of samples are related, to demonstrate differences between two groups.

The Wilcoxon signed-rank test is the non-parametric version of the paired t-test. It is used to test whether there is a significant difference between two population means, i.e., two related samples.

Hi, Vladimir Vega Falcón . I hope these comments will be taken in the spirit they are offered. In certain parts of ResearchGate's Questions area, I've been doing my part to identify misinformation and unhelpful responses to benefit question posters and future readers.

So, I have to point out that your answer does not address the question at all, which asked about how to report the results of a test, specifically the W, U, z, and p statistics from a Wilcoxon test. Providing some very general information about the test certainly does not help the original poster, and also would not be useful for future readers.

I also need to point out that your post has incorrect information. The Wilcoxon signed-rank test is not a test about means.

_____________________________

Referenced post:

The Wilcoxon test should be used when the type of outcome variable is qualitative ordinal (freely distributable) and the type of samples are related, to demonstrate differences between two groups.

The Wilcoxon signed-rank test is the non-parametric version of the paired t-test. It is used to test whether there is a significant difference between two population means, i.e., two related samples.

Two other advantages to Sal Mangiafico Wilcoxon function to the base R function.

1. Frank Wilcoxon's name is used rather than abbreviated prevent confusion with Rand Wilcox, and

2. information about the direction of the result is clear. Consider three groups, A, B, C

A A>B ... like Escher steps. This example is adapted from a forthcoming book by me. There are a lot of issues about why you would choose this procedure. If you really want to rank, you might look at the vanWaerdenTest function in PMCMRplus, which is more powerful.

Daniel Wright , This phenomenon interests me particularly from the point of view of post-hoc tests, and as an argument against pairwise tests that ignore the rest of the data. In this case, as you show, if you perform pairwise Mann-Whitney tests, you will get that each group is different from each other group, but then you will be unable to order the groups in any reasonable way. On the other hand, if you use Dunn's test (1964) to compare the three groups, it reports that no groups are different from any other groups, because it takes into account the ranks in all groups (p = 1). Likewise, a Kruskal-Wallis test reports no difference among groups (p = 1). R code for this follows.

A

Daniel Wright , just to be clear, all my wilcoxonZ() function does is extract the z statistic from the base wilcox.test() function. I didn't do anything smart. It is nice, though to have a signed statistic to indicate which group is bigger. That's why it's better to extract the original z statistic than to just back-calculate the z statistic from the p-value. ... The functions in the coin package also produce the z statistic, but if you are running them thousands of times for bootstrapping purposes, they can be slow.

Hi Sal Mangiafico , yea, my concern with the R function (other than the name but those goes back to S days) is the lack of output.

And the issue with intransitivity is that the ranks of the data are dependent on other data, so this is something that can happen with all rank tests. So if you believe the Wilcoxon is in some sense valid, all of those pairwise comparisons are different. Of course intransitivity is something we face in much real world decision making, but it is perhaps the different metrics are more obvious. I think examples like this making it clear the Wilcoxon isn't doing something like comparing medians (like Mood's test).

btw, if anyone is interested, here is the code I use for it (though as you can tell I don't usually recommend it) when I want more flexibility on what to output. This is a rather minimalist format, but you can alter to output whatever bits you want.

danW.test

Daniel Wright , I'm coming up with an error about the ties() function being missing.

I didn't copy the line above the function:

ties

Daniel Wright , when I use your example with the three groups, I'm getting a p-value of 2 in the output.

You mean

> A B C kruskal.test(c(A,B,C),rep(letters[1:3],each=600))

Kruskal-Wallis rank sum test

data: c(A, B, C) and rep(letters[1:3], each = 600)

Kruskal-Wallis chi-squared = 0, df = 2, p-value = 1

My function is just for two groups. I don't usually recommend it so haven't put in bells and whistles.

Daniel Wright , Okay. I think I just missed what the function does. ... As far as I can tell, it reports the W statistic from the Wilcoxon-Mann-Whitney test, and the W if the groups were reversed, and the reported p-value is the same (depending on the options). Is there something I missed ?

Yep, just replicates wilcox.test, but allows students to adapt if they want to adapt.

Okay. Got it.

I'm with Francesca and I'm not finding any of these comments helpful, but I do appreciate the attempts. I want to write my findings in an article and need to know what it would look like. Can someone talk down to me--kindly . . . if I have 10 responses pre and post evaluation in a Likert type scale 1-10, let's say the results are pre 3, 4, 5, 3, 2, 1, 4, 3, 4, 1 and post 3, 6, 5, 4, 7, 6, 9, 8, 7, 4. I'm using Excel and 1. found the difference between the two groups; 2. absolute differences; 3. rank the absolute differences; 4. There are only positive ranks; 5. and now I'm lost. I tried following the directions I found on a couple of sites, but they made my eyes cross. I see there is a "a" and "r" I have to report. After all that, I need to write it APA style. This may not be the place for a remedial stat class, and if so, just tell me and I'll keep beating up on it elsewhere. The class I took went over the paired T-test but didn't dig into the Wilcoxon.

Michael J Polacek ,

Hi, Michael.

a) To be clear, I think you are using the Wilcoxon signed rank test, for paired data. (There are similar tests, so it's important to be clear.)

b) I think you have something wrong in your procedure. Somewhere between 4) and 5), you would have to multiply the sign of the differences by the rank of the absolute value of the differences. If you work out some examples by hand, the logic of this should make sense.

c) There is free software to conduct these tests. It's just a suggestion, but something Jamovi, which is free, multi-platform, and GUI-based, is my recommendation.

c2) For your sample data, this is what I get. R code. You can run at https://rdrr.io/snippets/ without installing software.

Pre = c(3, 4, 5, 3, 2, 1, 4, 3, 4, 1)

Post = c(3, 6, 5, 4, 7, 6, 9, 8, 7, 4)

wilcox.test(Pre, Post, paired=TRUE, correct=FALSE)

And the results:

### Wilcoxon signed rank test

###

### V = 0, p-value = 0.01061

c3) There are variations of this, including how ties ( 0 differences) are handled. So the results might vary some.

d) I don't know about APA reporting for this test. But it should be something like how a (paired) t-test is reported. There will be no t statistic. But there will be some kind of test statistic, I think either W or z, depending on your software. And then of course you want to report the p value.

Thank you! I'll see if I can cipher this out.

It doesn't surprise me that I would have something wrong because I am like a chimp copying Shakespeare without understanding. Since I use pre and post-evaluations all the time, I want to become good at this process.

Would you mind reviewing my answer once I get it?

Michael J Polacek , sure. I wouldn't mind. If it's something not-to-shared-publicly, just send me a message on here, or I'm sure you can find my email.