Talk:Kolmogorov–Smirnov test

message: This article seems overly complex. I have coded implimentations of a two sample KS test, I understand how the KS test works, but I can't understand anything past the first three introductory paragraphs. I would love it if someone could make this article a little more accessible. Bilz0r (talk) 09:59, 21 March 2009 (UTC)
replies: text: This looks like a matter of not understanding mathematical notation, rather than of complexity.  The empirical distribution function is just the function that jumps upward by 1/n at each of the n observed values.  The Kolmogorov–Smirnov test statistic is the maximum amount by which that differs from the hypothesized cumulative distribution function.  That's what the material just after the introductory section says. Michael Hardy (talk) 11:32, 21 March 2009 (UTC)
replies: text:  I see both points here - the explanation is actually quite concise and clear once the notation is understood. However, a person with limited statistical background would not be able to implement a K-S test solely from this article, and there are other websites I have come across that provide a clearer explanation of the procedure. I think this could be remedied with a simple example of a K-S test implementation on a simple distribution. In my opinion most mathematical articles on Wikipedia would be much more clear with a simple demonstration of how it could be used, but the large majority of them have none. Are such examples considered outside the bounds of Wikipedia? Otherwise I would be happy to throw an example or two on this page and others like it.  PowerWill500 (talk) 08:02, 9 June 2009 (UTC)
replies: text:  I agree with the topmost point; the introductory paragraphs say virtually nothing intelligible about what this test is useful for or how it actually works. I'm a software engineer and someone referred me to this page. Damned if I know what they thought I would learn from it. If I could ask the page a question, it would be "So what?" and the page would be mute in response. I'd propose improvements, but first I'll have to learn about the KS test.  — Preceding unsigned comment added by 76.123.2.3 (talk) 14:21, 24 November 2013 (UTC)
thread_title: Overly Complex

message: I'm thinking of adding a graphic to this page. something like a quantile quantile plot, because as a non-mathematician, this speaks to me 
in much clearer terms than sigma notation.
Tombadog (talk) 23:30, 31 December 2007 (UTC)
replies: text: Sure, that'd be useful. It's fairly common in the literature to accompany uses of the K-S test with some sort of graphical plot (e.g. a percentile plot) to make the point more clearly as well. --Delirium (talk) 10:34, 14 January 2008 (UTC)

text: Also appropriate may be to add a static graph of the Kolmogorov density function, a link to the interactive Kolmogorov-distribution applet or the corresponding examples of using the Kolmogorov-Smirnov test statistics to assess similarity of two distributions. Iwaterpolo (talk) 05:42, 3 February 2010 (UTC)
thread_title: Graphical representation

message: Michael Hardy has deleted the name "vodka test" from the Kolomogorov-Smirnov article.  But "vodka test" is a legitimate name that I've heard used. I think this name gets used because it's more memorable to english-speaking students than long Russian names.  That's why it should be mentioned on the Wiki K-S page too.
Googling around, I found that this name isn't as common as I supposed, but here are three references: a presentation mapping software documentation, and a professor's class handouts.  I could also site a stats book where the term is used (in a joking way).  Finally, from the google results I found, I suspect this term is used in the SPSS manual (though I haven't checked).
:I haven't heard this before, but I think probably if this is included in the article, it should say that it is a jocular mnemonic. Michael Hardy 01:54, 21 April 2006 (UTC)
thread_title:  Vodka Test 

message: Under "Miscellaneous", the Anderson-Darling test is recommended as it is just as sensitive at the tails of the distribution as the median. I think that it needs to be explicit here, as it is in the opening paragraphs of the article, that the Anderson-Darling test is only for testing normality. Buzwad 12:58, 18 May 2007 (UTC)
thread_title:  The Anderson-Darling test 

message: It would be nice to have an example section that gives some detail on how to use the 2-sample K-S test. Dsspiegel 23:36, 18 October 2007 (UTC)
replies: text: The SOCR resource provides several hands-on examples of how to use the Kolmogorov-Smirnov test including web-based java applets for computing the corresponding test-statistics. Iwaterpolo (talk) 05:38, 3 February 2010 (UTC)
thread_title:  Examples 

message: The author of the 1939 paper on the goodness of fit test was N. Smirnov, not V. I. Smirnov. GuidoGer (talk) 20:00, 21 March 2009 (UTC)
replies: text: Funny German and Russian versions of the article have the same mistake (Igny (talk) 17:37, 24 March 2009 (UTC)
thread_title:  False attribution 

message: All forumals have strange horizontal and vertical lines and commas.  —Preceding unsigned comment added by 141.3.74.90 (talk) 10:56, 24 August 2009 (UTC)
replies: text: Formulas look OK to me. Melcombe (talk) 11:13, 25 August 2009 (UTC)
thread_title:  Broken formulas 

message: I’ve checked the Peacock’s reference, and have to confess that I didn’t like it. The proposed multivariate extension is no-longer distribution-free, the author doesn’t even bother to derive its distribution, Monte-Carlo simulations in the article show that the distribution of the test statistic is 1.1 − 1.5 times greater than that of the K-S distribution for the case of selected 2-dimensional distributions. How does the statistic behave in more than 2 dimensions is not analyzed, but it is likely the discrepancies will become even larger. In short, this “multidimensional Kolmogorov−Smirnov statistic” cannot be reliably used for inference. I vote for undoing the recent addition  ... stpasha » talk » 22:59, 1 September 2009 (UTC)
replies: text: Maybe I'm missing something here, but wouldn't a multivariate KS test merely amount to testing whether the mahalanobis distances of the multivariate sample conform to a chi-square distribution with a given degrees of freedom? --Steerpike (talk) 00:07, 10 April 2010 (UTC)
thread_title:  The Kolmogorov-Smirnov statistic in more than one dimension 

message: It looks like the section "Kolmogorov-Smirnov test" is incorrect.  It says to calculate the D statistic and then calculate a p value based on the asymptotic Kolmogorov distribution K.  But that is only correct in the limit as the sample size goes to infinity.  In reality, it should compare to the Kolmogorov distribution for finite sample size.  The latter is much more difficult to calculate correctly in general.  There is a good discussion of the issues involved at http://www.iro.umontreal.ca/~lecuyer/myftp/papers/ksdist.pdf.  —Preceding unsigned comment added by 75.173.219.39 (talk) 18:22, 21 June 2010 (UTC)
thread_title:  Kolmogorov–Smirnov test - assuming infinite data 

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thread_title:  External links modified 

message: Hi SoylentPurple, 
sorry for the maybe trivial question, but in https://en.wikipedia.org/wiki/Kolmogorov–Smirnov_test#Two-sample_Kolmogorov–Smirnov_test you introduced the formula to directly translate the confidence level alpha into the constant c(alpha) you need in the Kolmogorov-Smirnov test. I would really appreciate if you could point me to a cite for this formula.  — Preceding unsigned comment added by 92.194.42.241 (talk) 21:15, 29 August 2018 (UTC)
thread_title:  Two-sample Kolmogorov–Smirnov test 

message: Has there been any work on the relationship of this to the said distance?  — Preceding unsigned comment added by Frederic Y Bois (talk • contribs) 14:58, 21 June 2019 (UTC)
thread_title:  Relationship to the [[Wasserstein metric]]? 

message: A Mikenaaman appears to have edited this page to include his own work in the references section.  The same letter (not a full journal article) (This is Mikenamman and the article was a full journal article)is now cited in four duplicate references (1, 2, 7, and 29).  Furthermore, he's managed to insert himself into the first paragraph.
 Mikenaaman, me, is the first person to ever describe the KS test in more than one dimension. KS only did the test for one dimension, but I generalized the result to all dimensions. I think that merits 
inclusion. In fact, I had to prove an impossible inequality to generalize the test. You should read the paper. It is pretty exciting stuff.
 This looks quite ham-handed, but I'm not a Wikipedian and I don't know how to purge it from the article.  — Preceding unsigned comment added by 160.72.85.212 (talk) 20:30, 30 April 2021 (UTC)
replies: text: Your paper might be a great break-though, but to make large changes to the Wikipedia article a secondary source (or better multiple secondary sources) that explain the importance of your findings are needed. To better understand the policy a good starting point is WP:PSTS. Nuretok (talk) 09:37, 5 September 2021 (UTC)
thread_title:  Self-Promotion 

message: The K-S test is currently summarised with the following sentence: "What is the probability that these two sets of samples were drawn from the same (but unknown) probability distribution?"
But this is an incorrect way to characterise the results of a hypothesis test. A more correct summary would be: "How unlikely would the data be if the two sets of samples were drawn from the same probability distribution?"
This might seem overly pedantic given that the quoted description is only claimed to describe the K-S test "in essence". But I do think the current wording is a problem, because it reinforces a common and very problematic misconception about hypothesis tests: that they give you the probability of a hypothesis being true or false.
See e.g.: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4877414/#:~:text=Common%20misinterpretations%20of%20single%20P,40%20%25%20chance%20of%20being%20true.
I would propose changing the current wording to something like my alternative suggestion. Tobycrisford (talk) 08:36, 9 January 2023 (UTC)
thread_title:  Misleading summary in article introduction? 

message: Biggerj1 (talk) 17:15, 26 July 2023 (UTC)
thread_title:  Outsource Kolomogorov distribution