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Could we see some account of this concept of "correlation ratio"? All I can find is on Eric Weisstein's site, and it looks like what in conventional nomenclature is called an ''F''-statistic. [[User:Michael Hardy|Michael Hardy]] 21:02 Mar 19, 2003 (UTC)
{{WikiProject Statistics|importance = top}}
----
}}
it goes somewhat like:<br>
{{User:MiszaBot/config
correlation_ratio(Y|X) = 1 - E(var(Y|X))/var(Y) <br>
|maxarchivesize = 64K
I don't know the conventional nomenclature, but in the literature on similarity measures for image registration it is called just this...
|counter = 2
----
|algo = old(60d)
The relation between them is already there on the autocorrelation page. "...the autocorrelation is simply the correlation of the process against a time shifted version of itself." You can see this trivially by considering the equation for correlation if the series Y<sub>t</sub> = X<sub>t-k</sub>.
|archive = Talk:Correlation/Archive %(counter)d
--[[User:Rgclegg|Richard Clegg]] 20:43, 7 Feb 2005 (UTC)
}}
----
{{merged-from|Association (statistics)|12 June 2016}}
{{press | collapsed=yes
|org=''[[Football Paradise]]'' |date=March 18, 2018 |author=Heta, Marco |title=Neymar and the magical influence of an enigmatic amulet |quote=Wikipedia, the convenient data bank for journalists around the globe, defines correlation as follows: 'Correlation is any of a broad class of statistical relationships involving dependence, though in common usage it most often refers to how close two variables are to having a linear relationship with each other.' |accessdate=March 27, 2018
|url=https://www.footballparadise.com/neymar-magical-influence/
}}
{{Archives}}


This page currently tells only the mathematical aspects of correlation. While it is, obviously, a mathematical concept, it is used in many areas of research such as [[Psychology]] (my own field; sort of) in ways that would be better defined by ''purpose'' than mathematical properties. What I mean is, I'm not sure how to add information about ''what correlation is used for'' into this article - I wanted to put in the "vicars and tarts" demonstration of "correlation doesn't prove causality", for instance. But that would require a rather different definition of correlation, in terms of "the relationship between two variables" or something. Any ideas on how to rewrite would be welcome - if not, of course, I'll do it myself at some point...


== numerical instability ==
Oh, and I can't decide what to do about that ext. link - as is, it's rather useless, taking you to the homepage of a particular reference site (I suspect it of being "Wikispam"); but if you find the right page and break out of their frameset, there is actually some interesting info at [http://www.statsoft.com/textbook/stbasic.html#Correlations http://www.statsoft.com/textbook/stbasic.html#Correlations]. Ah well, maybe I'll come back to this after I've sorted out some of the [[memory]]-related pages... [[User:IMSoP|IMSoP]] 17:43, 20 May 2004 (UTC)


You need to be a little bit careful running around claiming algorithms are numerically unstable.
:I have now partially addressed the concerns above by putting in a link to [[spurious relationship]], which treats the "correlation does not imply causation" cliche. [[User:Michael Hardy|Michael Hardy]] 21:33, 20 May 2004 (UTC)
Instability depends on the range of numbers used. The one pass algorithm is stable if the full
calculation can be done using integer arithmetic without intermediate results overflowing. [[User:Charles Esson|Charles Esson]] ([[User talk:Charles Esson|talk]]) 08:11, 8 October 2009 (UTC)


:I am most used to numerical instability in the case where there is an exponentially growing term that should, ideally, be zero. This often happens in numerical integration. The term ill-conditioned is, for example, used in matrix operations where cancelation and round-off cause numerical problems. Seems to me that the latter is appropriate here. [[User:Gah4|Gah4]] ([[User talk:Gah4|talk]]) 23:20, 17 July 2018 (UTC)
I thought that the deleted stuff about the sample for correlation was useful. Not enough stats people pay attention to the difference between a statistic and an estimator for that statistic. The Pearson product-moment correlation coefficient page does cover this but it would be nice to see the treatment for the standard correlation too (IMHO at least).
--[[User:Rgclegg|Richard Clegg]] 20:21, 10 Feb 2005 (UTC)


== External links modified ==
:No -- you're wrong on two counts: There is no such thing as an estimator for a statistic; probably you mean as estimator of a population parameter; and statisticians pay a great deal of attention to such matters; it is non-statisticians who contribute to statistics articles on wikipedia and in journal article who loose sight of the distrinction. [[User:Michael Hardy|Michael Hardy]] 23:34, 10 Feb 2005 (UTC)


Hello fellow Wikipedians,
:... but I agree with you that the material on sample correlation should be here. [[User:Michael Hardy|Michael Hardy]] 23:34, 10 Feb 2005 (UTC)


I have just modified one external link on [[Correlation and dependence]]. Please take a moment to review [https://en.wikipedia.org/enwiki/w/index.php?diff=prev&oldid=795299390 my edit]. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit [[User:Cyberpower678/FaQs#InternetArchiveBot|this simple FaQ]] for additional information. I made the following changes:
:: Apologies, I was writing in haste. You are correct here that my comments refer to a population parameter rather than a "statistic" in the formal sense of a function on the data. My comments were intended to refer to contributors to wikipedia articles on staticss (in the wider sense). --[[User:Rgclegg|Richard Clegg]] 11:37, 11 Feb 2005 (UTC)
*Added archive https://web.archive.org/web/20150407112430/http://www.biostat.katerynakon.in.ua/en/association/correlation.html to http://biostat.katerynakon.in.ua/en/association/correlation.html


I think so too, but I was rushed. I will put the section back soon, but I will combine it with the Pearsons
When you have finished reviewing my changes, you may follow the instructions on the template below to fix any issues with the URLs.
section. [[User:PAR|Paul Reiser]] 21:09, 10 Feb 2005 (UTC)


{{sourcecheck|checked=false|needhelp=}}
: Thanks. I, for one, think it would help clarify this page.
--[[User:Rgclegg|Richard Clegg]] 22:45, 10 Feb 2005 (UTC)


Cheers.—[[User:InternetArchiveBot|'''<span style="color:darkgrey;font-family:monospace">InternetArchiveBot</span>''']] <span style="color:green;font-family:Rockwell">([[User talk:InternetArchiveBot|Report bug]])</span> 09:53, 13 August 2017 (UTC)


== Relationship between mean values? ==
== Cross-correlation in signal processing ==
what about the signal processing version of correlation? kind of the opposite of [[convolution]], with one function not reversed. also [[autocorrelation]]. does it have an article under a different name? if so, there should be a link. after reading this article over again, i believe the two are related. i will research some and see, (and add them to my to do list) but please add a bit if you know the connection... [[User:Omegatron|Omegatron]] 20:10, Feb 13, 2004 (UTC)


The third paragraph of the lead says
:This has been created under a separate article called [[cross-correlation]], although they are clearly related. Merge? Or link to each other? - [[User:Omegatron|Omegatron]] 04:37, Mar 20, 2005 (UTC)


:''when used in a technical sense, correlation refers to any of several specific types of relationship between mean values. ''
----
Correlation matrix search redirects to this page but I can't find here what a correlation matrix is. I have some idea from http://www.vias.org/tmdatanaleng/cc_covarmat.html , but don't feel confident enough to write an entry, and I am no sure where to add it.


I’m not sure what this means—e.g., in what sense does the Pearson correlation coefficient measure a relationship between mean values? Can we rewrite this more clearly? [[User:Loraof|Loraof]] ([[User talk:Loraof|talk]]) 19:29, 23 November 2017 (UTC)
[[Covariance_matrix]] exists.


:I attempted to improve the language there. Since it's referring to a technical sense I took the liberty of dealing with ambiguity by being slightly more technical. [[User:Glenbarnett|Glenbarnett]] ([[User talk:Glenbarnett|talk]]) 03:45, 19 April 2024 (UTC)
[[Scatter_matrix]] do not.


== External video ==
--[[User:Dax5|Dax5]] 19:16, 7 May 2005 (UTC)


I find the external video "floating link", Lecture 21: Covariance and Correlation, Statistics 110, Harvard University, 49:25, April 29, 2013 slightly unwikipedian. I somewhat dislike external links within a wikipedia article in general (I think they should be relegated to the bottom of the page) but I feel this one crosses some line.
== Random Variables ==
[[Special:Contributions/129.240.43.144|129.240.43.144]] ([[User talk:129.240.43.144|talk]]) 11:31, 28 September 2018 (UTC)
:Agree. Removed per [[Template:External media#When to use]] - readers will ''not'' expect this type of media in the article. (I watched the beginning and it's not like it was compelling viewing.) Thanks for posting this. [[User:Qwfp|Qwfp]] ([[User talk:Qwfp|talk]]) 19:34, 28 September 2018 (UTC)


== Main photo incorrect? ==
I was the one that put the disclaimer on "random" variables. If anybody would like to discuss, I'm all ears, so to speak. <small>&mdash;''The preceding [[Wikipedia:Sign your posts on talk pages|unsigned]] comment was added by'' [[User:Phili|Phili]] ([[User talk:Phili|talk]]&nbsp;&bull;&nbsp;[[Special:Contributions/Phili|contribs]]) {{{2|}}}.</small><!--Inserted with Template:Unsigned-->


Image here: https://en.wikipedia.org/wiki/Correlation_and_dependence#/media/File:Correlation_examples2.svg
: I reverted that note. You wrote:


The figure second from the left on the bottom row says correlation 0. For all the other figures in that row it makes sense to me, because they are symmetrical and that symmetry is either flat or vertical. However in that example, which is a square tilted upward at an angle, the data are correlated linearly are they not? <!-- Template:Unsigned IP --><small class="autosigned">—&nbsp;Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/192.195.81.229|192.195.81.229]] ([[User talk:192.195.81.229#top|talk]]) 21:11, 19 March 2019 (UTC)</small> <!--Autosigned by SineBot-->
::Several places in this article refer to "random" variables. By definition a random variable has no correlation with anything else (if it does have a correlation the variable is either 1) not random, or 2) the correlation is a coincidence likely due to a small sample size). It is more accurate to think of these not as random variables, but simply as variables that have an undetermined relationship.


: By definition, a [[random variable]] is just a [[measurable function]] one some probability space. And yes, two random variables can be very much correlated. :) [[User:Oleg Alexandrov|Oleg Alexandrov]] ([[User talk:Oleg Alexandrov|talk]]) 01:56, 30 November 2005 (UTC)
:I believe the intent is that the square is rotated about its center. The correlation should be zero for any rotation angle. [[User:Glenbarnett|Glenbarnett]] ([[User talk:Glenbarnett|talk]]) 03:25, 19 April 2024 (UTC)
::The image is slightly flattened (squished vertically relative to its width) which may be distorting the visual impression a bit (without actually changing the correlation). Note the "ring" looks elliptical when it was intended to be circular [[User:Glenbarnett|Glenbarnett]] ([[User talk:Glenbarnett|talk]]) 03:27, 19 April 2024 (UTC)
:::I would add that this article at one point in the past used to say something along the lines that the third row of plots in that image showed dependence with zero correlation. While it doesn't actually say that now, people will continue to gain that impression (because all but one of those plots does that). However the last plot (the four 'circular' point clouds arranged in a square) looks to actually be showing a pair of independent bimodal variables. More specifically I think that in that example each margin is a 50-50 mixture of two Gaussians with different mean but the same standard deviation (albeit the issue is much more general). If within each of the point four clouds the variables were independent, the plot as a whole is. The algebra is easy enough but if algebraic arguments are unconvincing, I was able to replicate the impression of the image by recentering four bivariate standard normals at the corners of a square in the x-y plane and sampling from each with equal probability. For such an example, the empirical bivariate copula is uniform over the unit square. [[User:Glenbarnett|Glenbarnett]] ([[User talk:Glenbarnett|talk]]) 03:58, 19 April 2024 (UTC)


==Article title: discrepancy with the content==
The "unsigned" person wrote utter nonsense. This is a crackpot. [[User:Michael Hardy|Michael Hardy]] 02:38, 30 November 2005 (UTC)
Hello. I wonder why the article is titled 'Correlation and dependence', but the definition states 'correlation or dependence is any statistical relationship ...'. How can this be correctly resolved? --[[User:TadejM|TadejM]] <sup>[[User talk:TadejM|my talk]]</sup> 10:56, 20 July 2021 (UTC)
:That might be a bit harsh. [[User:Phli]] has exactly three edits so far. Let's assume he just isn't familiar with the technical notion of a random variable, until proved otherwise. --[[User:Trovatore|Trovatore]] 21:13, 5 December 2005 (UTC)


:I've moved the article to 'Correlation' in accordance with the principle of using one article for one concept. In addition, the article defines both terms as synonyms. --[[User:TadejM|TadejM]] <sup>[[User talk:TadejM|my talk]]</sup> 14:24, 20 July 2021 (UTC)
== Disambiguation : geometry ==

Isn't correlation also a term in projective geometry? When PG(V) and
PG(W) are projective spaces, a correlation <math>\alpha</math> is a bijection from the subspaces of V to the subspaces of W, such that
<math>V\subset W</math> is equivalent with <math>W^{\alpha}\subset V^{\alpha}</math>

==Diagram==
Perhaps I'm being thick, but after a minute or two of scrutinising it I couldn't work out how to read the diagram on this article. Which scatter plot corresponds to which coefficient, and why are they arranged in that way? It is not clear. [[User:Bfinn|Ben Finn]] 22:12, 18 January 2006 (UTC)
:You're right -- I'd never looked for that. I'll leave a note to the author of the illustration. [[User:Michael Hardy|Michael Hardy]] 00:33, 19 January 2006 (UTC)
::Wait -- it's stated in the caption. You have to read it carefully. [[User:Michael Hardy|Michael Hardy]] 00:36, 19 January 2006 (UTC)

:The figure is not very intuitive... --[[User:128.135.82.179|128.135.82.179]] 06:13, 6 February 2006 (UTC)

I actually thought the figure is awesome, but now that I consider it, I wonder if it is intuitive and informative only for those who understand correlation well enough not to really need the figure. Also, I think it would be instructive to show a high-correlation scatterplot where the variances of the two underlying series are in a ratio of, say, 1:6 rather than 1:1 in the plots shown. --[[User:Brianboonstra|Brianboonstra]] 15:53, 3 March 2006 (UTC)

I have no clue how that figure works, and I'm in a PhD program. --[http://cns.bu.edu/~storer Alex Storer] 22:50, 17 April 2006 (UTC)

----

I have added this sentence to the caption to try to clarify it, in case anyone is still confused:

::Each square in the upper right corresponds to its mirror-image square in the lower left, the "mirror" being the diagonal of the whole array.

[[User:Michael Hardy|Michael Hardy]] 22:14, 22 April 2006 (UTC)

----

I understand the figure, but I think it's WAY too complicated, especially for someone who doesn't already know what it is. Its slightly neat to see that you have four different data sets generated, and you're looking at all pairs... but I think for most people it would be MUCH MUCH clearer if you just showed four examples in a row, with labels directly above: R2 in {0, .5, .75, 1 } or something. [[User:24.7.106.155|24.7.106.155]] 09:27, 7 May 2006 (UTC)

== Intercorrelation ==

Sometimes one sees the term "intercorrelation". What does this exactly signifies? I associate "intercorrelation" as the correlation between two different variables - but that is what standard "correlation" is. It seems to me that "inter" is redundant... And the opposite of [[autocorrelation]] is not intercorrelation but [[cross-correlation]]... -[[User:Fnielsen|fnielsen]] 15:43, 10 February 2006 (UTC)
: I guess "intercorrelation" has some utility in multivariate analysis(?), see, e.g., [[supermatrix]]. - [[User:Fnielsen|fnielsen]] 15:49, 10 February 2006 (UTC)

== Algorithms ==

I just yesterday inserted a disclaimer about using the formula supplied as the basis for a one-pass algorithm, and included pseudocode for a stable single-pass algorithm in a separate section. For standard deviation, there is a separate page instead, at [[Algorithms_for_calculating_variance]], but it seems to me that an analogous separate page should contain this algorithm only if a similar explication of the problems of numerical instability is included.--[[User:Brianboonstra|Brianboonstra]] 16:00, 3 March 2006 (UTC)

The last_x and last_y variables are unused in the pseudocode. They should probably be removed, no ? -- 29 March 2006

Agreed, and done. [[User:Brianboonstra|Brianboonstra]] 18:31, 11 April 2006 (UTC)

== Table ==

The table at the beginning of the article is flawed in almost every regard. First, it is poorly designed. Suppose a reader wants to know what a low correlation is. He or she looks at the row, sees "low," and sees that the cell below it says "> -0.9." At first glance, this makes it sound as though ANY correlation that is greater than -0.9 is low, including 0, 0.9, etc. Then the next column says "low: < -0.4." It takes a moment to figure out that the author was actually intending to convey "low: -0.9 < r < -0.4." Something like this would be better:

{| border="1" cellpadding="5" cellspacing="0" align="center"
|+'''Correlation coefficient'''
|-
| High correlation || Low correlation || No correlation (random) || Low correlation || High correlation
|-
| &minus;1 < r < &minus;0.9 || &minus;0.9 < r < &minus;0.4 || &minus;0.4 < r < +0.4 || +0.4 < r < +0.9 || +0.9 < r < +1
|-
|}

though some letter other than r might be better, and less-than-or-equal-to signs belong in there somewhere. That brings up the second problem, though: Where on earth did these numbers come from? Cohen, for example, defines a "small" correlation as 0.10 <= |r| < 0.3, a "medium" correlation as 0.3 <= |r| < 0.5, and a "large" correlation as 0.5 <= |r| <=1. I know of no one who thinks that a correlation between -0.4 and 0.4 signifies no correlation.

Then there's the argument--made by Cohen himself, among others--that any such distinctions are potentially flawed and misleading, and that the "importance" of correlations depends on the context. No such disclaimer appears in the article, and the reader might take these values as dogma.

I suggest that the table be removed entirely. Failing that, it should at the very least be revised for clarity as described above, and a disclaimer should be added. The values in the table should be changed to Cohen's values, or else the source of these values should be mentioned somewhere.

I'd be happy to make all of the changes that I can, but as I'm new to Wikipedia I thought I'd defer to more experienced authors.

--[[User:Trilateral chairman|Trilateral chairman]] 22:51, 22 March 2006 (UTC)

:I agree with everything you say. My preference would be to have a statement to the effect that various descriptions of ranges of correlations have been offered. One such description could perhaps be included with a reference. The point ''should'' be made that whether or not a correlation is of consequence or sufficient depends on the context and purposes at hand. If you're confirming a physical law with pretty good equipment, 0.9 might be a poor correlation. If you're ascertaining whether a selection measurement correlates with later performance measurements, 0.9 would be excellent (you'd be lucky to do better!). The table with scatterplots corresponding with each (linear) correlation coefficient is excellent. The table to which you refer is not referenced and it is hardly a commonly agreed classificatioin. On this basis alone it should not appear in the article. [[Be bold]]! [[User:Holon|Holon]] 01:15, 23 March 2006 (UTC)

Okay. I've removed the old table, added Cohen's table with a citation, and added the disclaimer with the explanation you suggested. Here is the old table if anyone wants it:

{| border="1" cellpadding="5" cellspacing="0" align="center"
|+'''Correlation coefficient'''
|-
| High correlation || High || Low || Low || No || No correlation (random) || No || Low || Low || High || High correlation
|-
| &minus;1 || < &minus;0.9 || > &minus;0.9 || < &minus;0.4 || > &minus;0.4 || 0 || < +0.4 || > +0.4 || < +0.9 || > +0.9 || +1
|-
|}

--[[User:Trilateral chairman|Trilateral chairman]] 01:18, 24 March 2006 (UTC)

== Formulas: What is E? ==

What is the E in the first equations? Why isn't the E replaced by capital sigma indicating the sum of?

I have seen E before in statistics texts. If it is some standard notation, it should be explained.

[[User:Gary Cziko|Gary]] 16:24, 28 March 2006 (UTC)


I think it is the [[expected value]].

::The article says explicitly that it is [[expected value]], and gives a link to that article. [[User:Michael Hardy|Michael Hardy]] 00:12, 30 March 2006 (UTC)

Latest revision as of 03:58, 19 April 2024


numerical instability

[edit]

You need to be a little bit careful running around claiming algorithms are numerically unstable. Instability depends on the range of numbers used. The one pass algorithm is stable if the full calculation can be done using integer arithmetic without intermediate results overflowing. Charles Esson (talk) 08:11, 8 October 2009 (UTC)[reply]

I am most used to numerical instability in the case where there is an exponentially growing term that should, ideally, be zero. This often happens in numerical integration. The term ill-conditioned is, for example, used in matrix operations where cancelation and round-off cause numerical problems. Seems to me that the latter is appropriate here. Gah4 (talk) 23:20, 17 July 2018 (UTC)[reply]
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Relationship between mean values?

[edit]

The third paragraph of the lead says

when used in a technical sense, correlation refers to any of several specific types of relationship between mean values.

I’m not sure what this means—e.g., in what sense does the Pearson correlation coefficient measure a relationship between mean values? Can we rewrite this more clearly? Loraof (talk) 19:29, 23 November 2017 (UTC)[reply]

I attempted to improve the language there. Since it's referring to a technical sense I took the liberty of dealing with ambiguity by being slightly more technical. Glenbarnett (talk) 03:45, 19 April 2024 (UTC)[reply]

External video

[edit]

I find the external video "floating link", Lecture 21: Covariance and Correlation, Statistics 110, Harvard University, 49:25, April 29, 2013 slightly unwikipedian. I somewhat dislike external links within a wikipedia article in general (I think they should be relegated to the bottom of the page) but I feel this one crosses some line. 129.240.43.144 (talk) 11:31, 28 September 2018 (UTC)[reply]

Agree. Removed per Template:External media#When to use - readers will not expect this type of media in the article. (I watched the beginning and it's not like it was compelling viewing.) Thanks for posting this. Qwfp (talk) 19:34, 28 September 2018 (UTC)[reply]

Main photo incorrect?

[edit]

Image here: https://en.wikipedia.org/wiki/Correlation_and_dependence#/media/File:Correlation_examples2.svg

The figure second from the left on the bottom row says correlation 0. For all the other figures in that row it makes sense to me, because they are symmetrical and that symmetry is either flat or vertical. However in that example, which is a square tilted upward at an angle, the data are correlated linearly are they not? — Preceding unsigned comment added by 192.195.81.229 (talk) 21:11, 19 March 2019 (UTC)[reply]

I believe the intent is that the square is rotated about its center. The correlation should be zero for any rotation angle. Glenbarnett (talk) 03:25, 19 April 2024 (UTC)[reply]
The image is slightly flattened (squished vertically relative to its width) which may be distorting the visual impression a bit (without actually changing the correlation). Note the "ring" looks elliptical when it was intended to be circular Glenbarnett (talk) 03:27, 19 April 2024 (UTC)[reply]
I would add that this article at one point in the past used to say something along the lines that the third row of plots in that image showed dependence with zero correlation. While it doesn't actually say that now, people will continue to gain that impression (because all but one of those plots does that). However the last plot (the four 'circular' point clouds arranged in a square) looks to actually be showing a pair of independent bimodal variables. More specifically I think that in that example each margin is a 50-50 mixture of two Gaussians with different mean but the same standard deviation (albeit the issue is much more general). If within each of the point four clouds the variables were independent, the plot as a whole is. The algebra is easy enough but if algebraic arguments are unconvincing, I was able to replicate the impression of the image by recentering four bivariate standard normals at the corners of a square in the x-y plane and sampling from each with equal probability. For such an example, the empirical bivariate copula is uniform over the unit square. Glenbarnett (talk) 03:58, 19 April 2024 (UTC)[reply]

Article title: discrepancy with the content

[edit]

Hello. I wonder why the article is titled 'Correlation and dependence', but the definition states 'correlation or dependence is any statistical relationship ...'. How can this be correctly resolved? --TadejM my talk 10:56, 20 July 2021 (UTC)[reply]

I've moved the article to 'Correlation' in accordance with the principle of using one article for one concept. In addition, the article defines both terms as synonyms. --TadejM my talk 14:24, 20 July 2021 (UTC)[reply]
Retrieved from "https://en.wikipedia.org/enwiki/w/index.php?title=Talk:Correlation&oldid=1219668338"