Talk:Wilcoxon signed-rank test

message: Is the difference between these two tests that signed-rank test is paired and the ranked-sum test is unpaired? If so, perhaps this could be made more explicit? Such as:
"The Wilcoxon signed-rank test is not the same as the Wilcoxon rank-sum test. While both are nonparametric and involve summation of ranks, the Wilcoxon signed-rank test requires that the data is paired while the Wilcoxon rank-sum test is used for unpaired data."
--JonathanWilliford (talk) 20:38, 3 March 2015 (UTC)
thread_title: Difference between Wilcoxon signed-rank and ranked-sum test

message: It appears that some portion of this have been copied from a textbook: "The recommended cutoff varies from textbook to textbook — here we use 20 although some put it lower (10) or higher (25)." Is there a copyright violation happening here? 96.49.201.125 (talk) 04:39, 1 December 2009 (UTC)
thread_title:  Copyright violation? 

message: Im no expert, but pretty sure that this test can also deal with ORDINAL data
The test is in parts not well described, even I, as someone who teaches statistics, have difficulties to understand the test fully from the text. sigbert Mi Apr 11 08:09:57 CEST 2007
:NO! Since you are subtracting two values (e.g. pre vs. post) it has to be interval data, not just ordinal. --Statprof (talk) 17:18, 15 April 2008 (UTC)
replies: text: Wrong: As Statprof mentioned, subtracting values presupposes interval data: In your example it would presuppose that someone rated 10 is equally far away from someone rated 9 as someone rated, say 3 is from someone rated 2. 128.232.231.16 (talk)  —Preceding undated comment added 11:07, 2 March 2009 (UTC)

text: The above comment by 90.231.200.20 makes a lot of sense, but I couldn't find a source for that. --asqueella (talk) 12:30, 24 March 2011 (UTC)
replies: text: All known WP:Reliable sources say it works for ordinal data, so the article should reflect that, not ill-informed speculation and WP:original research. Subtracting values does not require interval data. Defining a measure of effect size might do so, but this is a hypothesis test, not a measure of effect size. Qwfp (talk) 19:21, 13 April 2011 (UTC)
thread_title:  Ordinal data 

message: Some statistics software (e.g. GraphPad Prism) claim to use the Wilcoxon Signed Rank test for non-parametric one sample testing. i.e. compares the median of a single group to a hypothetical median. Prism distinguishes from the more common two sample test by calling that the Wilcoxon matched pairs test. 
N.B. The one sample test on the difference between matched pairs in two groups seems to be equivalent to a Wilcoxon signed rank test on those two groups and comparing to the null hypothesis that the median difference is equal to zero. Although in the one sample test you can compare to any hypothetical median, not just one equal to zero.
If this is legitimate, a section on this should probably be included. I'm not completely sure so haven't just added it in. schroding79 (talk) 00:59, 2 September 2008 (UTC)
thread_title:  One sample testing against hypothesis 

message: The example describes the W+ statistic as a sum of the signed ranks.  This contradicts the "Test Procedure" section (and my understanding of the W+ statistic) that says W+ is the minimum of the sum of ranks for positive differences and the sum of ranks for negative differences.
:Yeah, I was trying to figure out how the test could be that the value is less than the critical value if it is this type of sum (i.e. if all were positive, then would not-reject always, but then it almost has to be a reject). Also, the previous section makes reference to the statistic converging (presumably in distribution) to the normal but then doesn't say what the mean and SD are. 018 (talk) 18:19, 3 February 2010 (UTC)
thread_title:  Example wrong? 

message: 65.78.66.242 commented on the article page: "The diecision rule state here is in error. According to Siegel & Castellan 1988 pp. 88-89, the stated decision rule is if the calculated value is less than or equal to the critical value then the null hypothesis is rejected (not retained as stated in the Wikipeda text)." MichaK (talk) 16:13, 25 October 2010 (UTC)
thread_title:  Conflict with Siegel & Castellan? 

message: According to , which is currently one of the external links at the end of this article, the test statistic W is computed as the sum of W+ and W-. This differs from this article, which uses the minimum of W+ and W-. Apparently this is an unresolved issue as some descriptions use only W+, others use the minimum of W+ and W-, and yet others use the sum of W+ and W-. I emailed the author of that page (Dr. Lowry) about this. He said that using the sum of W+ and W- will converge to approximate the Normal distribution with fewer comparisons, and that the method of using the minimum of W+ and W- date to the time when the properties of the relevant sampling distributions had to be worked out laboriously by hand, and are only useful for small-sample cases (where n is less than about 10). He referred me to Mosteller & Rourke, Sturdy Statistics: Nonparametrics and Order Statistics, Addison-Wesley, 1973. I believe his argument is sound, and I think that the method of using the minimum of W+ and W- will tend to lead to more false-positives simply because it relies on fewer observations. I propose that we change this article to describe the simpler and more robust method of computing W as the sum of W+ and W-.--Headlessplatter (talk) 18:25, 21 June 2011 (UTC)
thread_title:  The W statistic 

message: I have just added proper citation for the assumption of the wilcoxon signed rank test:
http://en.wikipedia.org/wiki/Wilcoxon_signed-rank_test#Assumptions
I am not sure this section is complete, since under the framework of randomization tests, the wilcox test has a different H0 (where it works on the effect of the treatment in changing the "distribution", and not necessarily a shift of location parameter).
Tal Galili (talk) 10:17, 8 December 2011 (UTC)
thread_title:  Assumptions for Wilcoxon-signed rank test - needs excpention 

message: The section on confidence intervals is complete garbage.  This article covers the paired-sample test, but it looks like someone copied some text that was intended for a single-sample non-paired test, and even did a poor job at that.  The notation doesn't make sense (e.g., D_i has a single subscript, but seems to define a 2-D matrix of differences), isn't consistent with the notation of the previous section, and the wording itself contains numerous typos, poor grammar, and awkward descriptions.
How to compute the confidence interval for the paired test is not at all obvious, and thus deserves coverage here.  As is, the section that is there is doing a disservice and would be better removed.  I would, however, like to have a reference for how it is done in the paired case. With the \min(W_-,W_+) in the test, I don't think it is as easy as using the Walsh averages of Zi.
-- Lonnie Chrisman 19:33, 8 December 2011 (UTC)
thread_title:  Confidence Interval section is not good 

message: Hello, I'm not an expert in this area and after a little reading from (http://www.cis.uoguelph.ca/~wineberg/publications/ECStat2004.pdf) I discovered how this test works. I think the average user looking this up would like to know how the tables for small sample sizes are generated.
(1) Essentially the ranks generated are uniformly distributed provided the source distributions are continuously distributed. Being continuously distributed means the probability of tie is zero (not impossible, just zero probability). Discrete distributions introduce the possibility of ties; each tie drives the distribution of ranks to be less uniform.
(2) A function of the sums (or differences) of uniform random variables (RV) is performed via convolution. This follows from the basics of the study of RVs.
(3) So in the limit the distribution approaches a normal distribution. Note this is not required to perform the test, but describes why once the sample size is sufficiently large (e.g., 30) then you can use the normal distribution. Otherwise the statistic is distributed according to the convolution of 'n uniform RVs.
Anyways, these are just my two cents.Mouse7mouse9 00:41, 9 August 2013 (UTC)
thread_title:  A new section discussing the theory behind it and why it works? 

message: In the history section it says that this test is also referred to as the "t-test for matched pairs" or the "t-test for dependent samples". Is this really true? Because those phrases should refer to the parametric paired-samples t-test, which of course is completely different than this, uses the mean, variance, correlation, assumes Gaussian distribution, etc. So if people do indeed refer to this test with those phrases, that would be either wrong or misleading, correct? Is this something that should be addressed in the article? Eflatmajor7th (talk) 22:32, 19 October 2013 (UTC)
replies: text: Hearing nothing, I'm going to delete the last sentence of the History section, to avoid confusion. Eflatmajor7th (talk) 08:41, 3 December 2013 (UTC)
thread_title:  "History" section 

message: What does it mean? "come from the same population"
It doesn't mean that $x_{i,1}$ has the same distribution as $x_{i,2}$, that would be strange.
Lockywolf (talk) 10:34, 28 May 2015 (UTC)
thread_title:  "come from the same population" 

message: This is impossible, since W is always positive.  — Preceding unsigned comment added by Lockywolf (talk • contribs) 11:07, 28 May 2015 (UTC)
thread_title:  As N r increases, the sampling distribution of W converges to a normal distribution.  

message: I highly doubt the correctness of the critical value W = 35 (two-paired, alpha=0.05, n=9). Have looked up multiple tables and it seems to be 5/5,4/6, depending on rounding in the table itself. The value of 35 indeed pops up in external link 1, but don't know why it says so.  — Preceding unsigned comment added by 89.146.22.128 (talk) 12:46, 9 December 2016 (UTC)
thread_title:  Critical value correct? 

message: I just ran some simulations on the distribution of the statistic as described here and the Variance formula seems to be off by a factor 4.
This might be a leftover from the earlier discussions on using only the positive or only the negative values. I'll fix this in the article, but I am not entirely sure about the references to older materials, which might report values for the test statistic using only the positiv or negative values. Xenonoxid (talk) 22:56, 17 June 2019 (UTC)
thread_title:  Variance off by factor 4 

message: Hello
When going to the Dutch wiki, I arrive at https://nl.wikipedia.org/wiki/Rangtekentoets. But it should go to https://nl.wikipedia.org/wiki/Wilcoxontoets The last one is about 2 samples. --Rcsmit (talk) 11:59, 2 November 2020 (UTC)
thread_title:  Link to the Dutch wikipedia 

message: I don't think a layperson would have a chance of understanding what Wilcoxon signed rank is from this article.
Perhaps adding a "Basic concept"/"Informal concept" section could solve that?
EditorPerson53 (talk) 00:01, 31 December 2021 (UTC)
replies: text: I hear that you would like additional explanation, but I'm not sure what you would like additional explanation of.  Could you be more specific about what you see as lacking?  Ozob (talk) 06:07, 31 December 2021 (UTC)
thread_title:  Clarity to a layperson 

message: In this article when the p-values were calculated keeping 0 and removing 0, where do 55 and 109 come from?
https://en.wikipedia.org/w/index.php?title=Wilcoxon_signed-rank_test
The W+ was 66. How was the p-value calculated. 
If the hypothesis test is an equivalency test such that H0 is µ≠0 and H1 is µ=0 or within a given boundary say -0.5 and 0.5 instead of testing for difference, how should one approach calculating the p-value ? Daannoo (talk) 23:10, 11 May 2023 (UTC)
thread_title:  Calculating the p-values