From: WLTPIRIE@VTVM1.BITNET (Walt Pirie)
Newsgroups: bit.listserv.edstat-l
Subject: Fisher's r to z
Date: 12 Nov 92 20:39:15 GMT
Reply-To: Walt Pirie <WLTPIRIE@VTVM1.BITNET>
Comments: Gated by NETNEWS@AUVM.AMERICAN.EDU

Someone else may recall a little more detail, but here's some.
Kendall's methods test and provide an unbiased estimate of a
function of probability of concordance P[(Y2-Y1)(X2-X1)>0].
That's fairly easy to show, and something Kendall knew.
Spearman's methods can be characterised as a test of something
similar, grade correlation, or a function of P[(Y2-Y1)(X3-X1)>0].
It also provides an estimate, but is only asymptotically unbiased.
It's not likely Spearman knew of that relationship. But anyway,
they really are quite similar. More so than most people are aware of.
All comparative work I've seen, both theoretical for ARE, and
simulations, indicate that for all alternatives studied , the tests
have almost identical performance, as Andy indicates below.
I also agree that confidence intervals are of questionable utility
here. There is an approximate confidence interval procedure for
Kendall, of questionable accuracy, but none I know of for Spearman.
From papers I've seen, the distribution of Spearman's when rho is
not zero is much more difficult, and useful results have not been
obtained.
Walt


I agree with the comments of Dave Krantz, Walt Pirie and Paul Jackson
that correlation, and especially the "nonparametric" correlations may
be meaningful or useful without bivariate normality. (I also do agree
with Larry Ries that users of correlation coefficients often are
unaware of these issues and thereby misused any and all of the
"correlations."

My question concerns the meaning and performance of Spearman's. I was
taught (by Doug Wolfe) that while Kendall's estimates a well-defined
parameter describing monotonic association, Spearman's estimates
nothing in particular, and therefore the meaning of any inferences
(especially CI's, if anyone ever gives them) from Spearman's is
unclear. Subsequently I've read that simulation studies show the
behavior of Spearman's and Kendall's to be similar but with Spearman's
having slightly greater power. Unfortunately I've lost the reference,
and can't figure out what these assertions would mean without knowing
what models were assumed and what hypotheses/parameters were being
addressed. So can anyone help by either giving references to these
studies or explaining what they were about?

Thanks.

- Andy Taylor
  Department of Zoology            ataylor@lala.zoo.hawaii.edu
  University of Hawaii at Manoa    taylor@uhunix.bitnet

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