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From |
"Nick Cox" <n.j.cox@durham.ac.uk> |

To |
<statalist@hsphsun2.harvard.edu> |

Subject |
st: RE: Spearman rank correlation |

Date |
Fri, 30 Aug 2002 14:50:28 +0100 |

Jens M. Lauritsen > Does anyone have good references for INTERPRETATION in > relation to size of > the spearman correlation coefficient. The nonparametric books I have looked at are disappointing in this respect. Once they have discussed the mechanics of calculation and the use of Spearman rank as a test statistic there is little or no attention to any use of Spearman rank as a measure. One answer is that as Spearman correlation is just Pearson correlation on the ranks, you interpret it just as you would Pearson correlation. However, it is then a good idea to see the data as Spearman sees them, i.e. look at scatter plots of ranked variables, which seems to be very rarely done. In Stata a -foreach- loop over variables producing a ranked version followed by -graph, matrix- makes this possible in a few lines. The best discussion I know is in Harold Jeffreys' "Theory of probability" (1939, 3rd edition 1961). This reference is given in [R] spearman. Broadly, Spearman rank can be thought of as a measure of monotonicity, just as Pearson correlation is a measure of linearity. However, the comparison is fraught with challenges to intuition, or what your intuition may be. Jeffreys shows that if -1 < x < 1 and y = x^3 then Pearson r = 0.917. This certainly holds if x is uniform on that interval. And you can readily verify this yourself by . set obs <whatever> . range x -1 1 . gen y = x^3 . corr x y This may be higher than many people using correlations would expect, if they argued that as this relationship is clearly and strongly nonlinear, then a measure of linearity would be way below 1. Or if their impression was that as the description "linear relationship" is qualitatively quite wrong for a cubic, then a quantitative measure would be very poor. However, Pearson correlation answers the question you ask, namely to give a measure of linearity, even when the question is ill-advised. I.J. Good in Biometrics December 1972 independently made a similar point, with more results. Of course, these examples are for exact relationships and real data show scatter as well. But even experienced analysts of data have found them striking. A quite different comment is that in some ways one or other version of Kendall's tau is easier to interpret, because it is a difference of probabilities, even though that's not your question. Roger Newson's expository article in Stata Journal 2(1), 2002 gives much more detail. My guess is that Roger will himself expand this point very fully. > > For a certain project we had to do many tables of these > estimates and I > produced a wrapper for the ci2 (by Poul Seek) and the > spearman commands > one can get this output, which is easy to convert to a > table in word by > copy and paste, plus select the output as a block and > "convert to text". > > If you dislike the ";" (e.g. because you are not a word > user) the just omit > that part. > > The same principle can be suded for any procedure where you > want only > estimates (here r(N) etc) and not the remaining texts of > that command. The > reason for "version 6" is that ci2 works only in version 6. [ ... ] The procedure -biv- published in the STB some years ago provides a wrapper for bivariate calculations such as these. It has been partly, but not completely, superseded by using -foreach- loops. It is not too difficult to initialise a matrix and then use two -foreach- loops over variables to fill that matrix with bivariate results. Then -matrix- can be used to tune the display. A code example is given in http://www.stata.com/support/meeting/8uk/fortitude.pdf Nick n.j.cox@durham.ac.uk * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**st: Spearman rank correlation***From:*"Jens M. Lauritsen" <JM.Lauritsen@dadlnet.dk>

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