Litton Prosad Mowalie ,

You may find that you get different answers to your question, "What are the assumptions of the Wilcoxon signed-rank test." The assumptions may be expressed different ways, and some authors may add additional assumptions.

The role of symmetry in the assumptions of the test can be particularly confusing. See, for example, the discussion at the following link, but also my comment there about the confusion: https://stats.stackexchange.com/questions/348057/wilcoxon-signed-rank-symmetry-assumption .

To answer your question, I would have cited the assumptions listed in the Conover text. Those are already typed out in my comment at the previously mentioned link.

The signed-rank test cannot be used for nominal categorical data.

The signed-rank test is sometimes used for ordinal categorical data. However, because the test takes the difference in the paired values, it really treats the data as at interval data. * That is, it will treat your ordinal data as interval, whether you intend it or not.

The one-sample or two-sample sign test are potentially alternative tests, that can be used with strictly ordinal categorical data.

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* Technically, the test needs only data where the differences between values can be ranked. So, if your measured variable had three potential values: A, B, and C, and you know, for example, that (A - B) < (B - C), and then of course (A - C) is larger than either (A - B) or (B - C), you could order all the differences. But cases where this kind of situation occurs are probably rare.

@Litton Refer to the link below for assumptions of Wilcoxon Signed Rank Test.

https://www.statisticssolutions.com/free-resources/directory-of-statistical-analyses/assumptions-of-the-wilcox-sign-test/?__cf_chl_jschl_tk__=pmd_Ilq4fPxD3_Je.4_z5zqmLa5zx3nf8cjRWTZAdPxCOv4-1633796989-0-gqNtZGzNAnujcnBszQql

Imran Anwar ,

That page certainly doesn't make clear whether the test assumes continuous data or ordinal data. Oy.

In general, I wouldn't recommend that site. Looking around, I found lots of their explanations confusing at best.

See for example, the following page on the Wilcoxon signed-rank test. To me, it reads like an artificial intelligence wrote it, and I think I object to what's stated in every other sentence.

At least to me, even the example is incomprehensible.

https://www.statisticssolutions.com/free-resources/directory-of-statistical-analyses/wilcoxon-sign-test/

Wilcoxon signed rank test is a non parametric analogue of the Student's t test for paired data. It is used when we have a categorical independent variable with two dependent categories preferably time points, matched pairs etc. The outcome variable is assumed to be atleast measured on an ordinal scale. No distributional assumptions on the differences for each consecutive pairs are made. Here is a video ref : https://www.youtube.com/watch?v=TqCg2tb4wJ0

Anuraj Nayarisseri ,

A couple of objections:

• The video describes the WSR test as testing a hypothesis about median of the differences. This test is not a test about the median of the differences ---- unless there are additional assumptions about the data distribution. This is easy to show. I have an example below in R.

• I disagree that this test can be used with strictly ordinal data, as I noted above. Since the first step is taking the differences in the paired observations, the data need to be interval in nature, except the weird case I mentioned above in the footnote.

There's a lot of confusion and misinformation out there about this and other rank-based tests. I recommend consulting real textbooks ( e.g. Conover, Practical Nonparametric Statistics ), rather than websites and videos.

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Example in R. Note that the median in differences is exactly 0, but that the test reports a significant p value. ( There are many ties in the differences here, which could lead to somewhat different results depending on how the procedure handles these. But it would it would be easy to tweak the data to not have ties. It would just be more difficult to read.)

Before = c(1:20, 100, 101:120)

After = c(0:19, 100, 201:220)

Diff = Before - After

median(Diff)

wilcox.test(Before, After, paired=TRUE)

Diff

hist(Diff)

# Wilcoxon signed rank test with continuity correction

#

# V = 210, p-value = 0.005677

#

# In wilcox.test.default(Before, After, paired = TRUE) :

# cannot compute exact p-value with ties