Talk:Spearman's rank correlation coefficient

Move

This page was formerly at "Spearman's ρ" -- however, this breaks "move page" and is against the general naming principle that names should be the most common name, in English, where available. User:The Anome

Well, this may not be the most common name in English, but the change makes sense because it facilitates linking, especially now that the main alternative titles have redirect pages. I'll remember that next time. Thanks. User:Jfitzg

Would Spearman's rank correlation coefficient be nicer? -- Oliver P. 16:37 28 May 2003 (UTC)

That might definitely be better. Perhaps the main article should be there. John F.

So I moved it. Should have all the bases covered now. John F.

Clarifications

Schemilix (talk) 17:02, 12 October 2010 (UTC)Just a question on the graphic for the formula... I was under the impression it was n cubed, not n squared, that was part of the denominator for the equation. It's d^2 and n^3.

—Preceding unsigned comment added by Schemilix (talk • contribs) 17:01, 12 October 2010 (UTC)

From the article:

The value of ρ is equivalent to the Pearson product-moment correlation coefficient for the correlation between the ranked data.

Is this an identity or an approximation? If so, it it by definition, by co-incidence, or just for some particular family of distributions?

-- —Preceding unsigned comment added by 217.158.203.203 (talk • contribs)

Thanks. I'll clarify this. It's a special case of the Pearson. -- —Preceding unsigned comment added by Jfitzg (talk • contribs)

You say that "...Unlike the Pearson product-moment correlation coefficient, Spearman's rank correlation coefficient does not require the assumption that the relationship between the variables is linear, nor does it require the variables to be measured on interval scales; it can be used for variables measured at the ordinal level...." and "..However, Spearman's rho DOES ASSUME that subsequent ranks indicate equi-distant positions on the variable measured...". On the other hand, in the definition of interval scales scale they say: "..The numbers assigned to objects have all the features of ordinal measurements, and in addition equal differences between measurements represent equivalent intervals...". So, technically, Spearman's rank correlation DOES require the variables to be measured on interval scales?

The articles states that the values are converted to rankings. From the example given, this looks like fractional rankings. Is this correct? 130.88.90.73 (talk) 14:55, 8 October 2008 (UTC)

In the section on determining significance, the z-score is defined with reference to a function F(r) - what is this mystery function? Flies 1 (talk) 20:13, 30 June 2010 (UTC)

Questions

Does it anywhere in this article say that p is always a number between 1 and -1, and what high and low values mean? -- —Preceding unsigned comment added by Matt me (talk • contribs)

Request for help

its related to spearson`s rank correlation. the coffecient of correlation of two firms is -.10714 find the number of compnies if sum of square of diference is 62 -- —Preceding unsigned comment added by 61.2.189.36 (talk • contribs)

Suggestion

It may be helpful to explain how the data is ranked eg from highest to lowest... and apparently Spearman's does assume the direction of relationship is constant eg rising or falling. -- —Preceding unsigned comment added by 82.37.10.168 (talk • contribs)

• I agree, i think maybe having an example question would be very helpful and an explanation on the ranks as well. 82.198.250.66 08:20, 19 September 2006 (UTC)

One tailed, two tailed

The difference between a one talied and two talied test isn't mentioned, not that I know what it is, neither is the need for a null hypothesis. Sam Hayes 09:20, 17 April 2006 (UTC)

the working out of this correllation is wrong, the answer is actually -0.28. this page needs to be reviewed and its source's validility questioned. i am only 15 and have worked this out correctly. lauren campbell, mon 26th february. by the way im not meaning to brag or anything :)

help

it would be helpful if this was explained easier since i am only a gcse student. i do not understand what is going on. :( -- —Preceding unsigned comment added by 86.7.149.45 (talk • contribs)

Yeah, it would help if it were made intelligible for those who can't understand maths. I don't understand the page and I've been doing this in college and uni. :'( —Preceding unsigned comment added by 86.1.198.198 (talk • contribs)

the reason you don't understand this is because the working is all wrong, the data has to be ranked from highest to lowest, not lowest to highest as has been shown. lauren campbell mon 26th february 2007. its not actually that difficult.

And the formula is (sometimes) incorrect. I know this and I'm only 14. Someone needs to do something about this, I would but I don't know how to do the symbols. George bennett 09:01, 9 July 2007 (UTC)

Hypothesis test with the student t-distribution

The authors don't mention the number of degrees of freedom for the aforementioned t-distribution which makes the information useless in practical terms :-|

89.164.3.138 07:55, 22 December 2006 (UTC)

I've just added an example

That walks through the process of doing spearman's rank by hand. I'm not sure if I got the right tone but hey. I just think this article was crying out for an example. The data is my own of course. --Grimboy 14:38, 10 February 2007 (UTC)

Thanks! The example was good but I've just changed it to remove all ties. It seems the formula cannot be used for ties. There is a tie-corrected formula and it seems the Japanese wikipedia page has it, but I cannot read it... --Rayjapan 05:53, 29 May 2007 (UTC)

The value of "d" in the example is lacking the correct sign. For clarity, it should be |d| or the minus sign should be added where appropriate. —Preceding unsigned comment added by 131.130.41.124 (talk) 13:39, 15 January 2008 (UTC)

Spearman's rho vs. Spearman's rank correlation

The article states that Spearman's rho is a case of Spearman's rank correlation. Really? I think, these are two names for the same thing, and the formula named here "Spearman's rho" is just one of estimators used to estimate Spearman's rank correlation/Spearman's rho in population. Olaf m (talk) 00:49, 16 May 2008 (UTC)

Fixed. Olaf m (talk) 19:11, 28 May 2008 (UTC)

If anyone has a spare moment…

Over on Judgment of Paris (wine) there's a statement "The original rankings appear to have been valid. The original and the Ashenfelter and Quandt re-calculations demonstrate a very high Spearman rank order correlation coefficient of .923." I have no idea whether this is 100% accurate or 100% BS. If anyone has a spare moment, could they have a look at this? Nunquam Dormio (talk) 15:46, 14 July 2008 (UTC)

Pearson correlation

Pearson product-moment correlation coefficient, a similar correlation method that instead relies on the data being linearly correlated.

In what sense does it "rely" on the data being linearly correlated? It's legitimate for any bivariate distribution. 72.75.93.12 (talk) 22:33, 9 April 2009 (UTC)

joint frequency distribution of the variables

I am concerned that the statement "without making any assumptions about the joint frequency distribution of the variables" may be somewhat misleading to readers. In particular that it would be read to imply that this is something special to Spearman's rank correlation coefficient; however other common measures of correlation, e.g. Kendall's tau and Pearson product-moment do not make any assumptions about the joint frequency distributions either; maybe rephrasing to something like "and whose properties are robust to assumptions about the joint frequency distribution of the variables"? Aetheogamous (talk) 16:31, 21 April 2009 (UTC)

The intent is to say that it does not prejudge the form of the relationship between variables in the sense that the Pearson coefficient "looks for" a linear relationship. It is this aspect of the joint distribution that is being targetted in what is written, not the marginal distributions and not the distribution of the residuals as might be implied by considerations of robustness. Of course, there may also be separate considerations of robustness, but I am not sure that you can do/say anything about aboutness unless you start making assumptions about the form of relationship. However, there may be something worth saying (if not already said) that the value of the coeeficient is invariant to montone transformations of either or both variables. Melcombe (talk) 16:57, 21 April 2009 (UTC)

Since there are several aspects of the joint distribution at play here and one in particular is being targeted, maybe the text could directly target the aspect that is intended. Something like "without making any assumptions about the nature of the monotonicity"? Aetheogamous (talk) 17:27, 21 April 2009 (UTC)

I have put in an attempt to do this, but the extra sentence added now needs further thought. Melcombe (talk) 08:59, 22 April 2009 (UTC)

MOSMATH

I just found the following in this article:

with degrees of freedom N-2.

I changed it to this:

with degrees of freedom N − 2.

Even today, some people don't know the norms of WP:MOSMATH. Michael Hardy (talk) 20:42, 10 June 2009 (UTC)

 Even today, some people don't know the difference between typesetting and knowledge.  —Preceding unsigned comment added by 24.62.203.42 (talk) 20:24, 28 July 2010 (UTC) 

Implementations of Spearman's rho

The MS Excel formulas

{=CORREL(RANK(x,x),RANK(y,y))}

or (for Excel 2010):

{=CORREL(RANK.EQ(x;x);RANK.EQ(y;y))}

work fine when data set has no ties.

When data set has ties use:

{=CORREL(RANK(x;x)+(COUNTIF(x;x)-1)/2;RANK(y;y)+(COUNTIF(y;y)-1)/2)}

or (for Excel 2010)

{=CORREL(RANK.AVE(x;x);RANK.AVE(y;y))}

Reference: Spearman's rank correlation coefficient in Microsoft Excel (German) — Preceding unsigned comment added by Christian.sch (talk • contribs) 11:57, 21 July 2011 (UTC)

And what is this doing in an encyclopaedic article? I strongly believe this should be removed. Tomcrocker (talk) 12:50, 10 October 2011 (UTC)