From: Petr Savicky <savicky_at_cs.cas.cz>

Date: Thu, 12 Feb 2009 13:33:33 +0100

R-devel_at_r-project.org mailing list

https://stat.ethz.ch/mailman/listinfo/r-devel Received on Thu 12 Feb 2009 - 11:49:48 GMT

Date: Thu, 12 Feb 2009 13:33:33 +0100

Hi All:

help(cor.test) claims

For Spearman's test, p-values are computed using algorithm AS 89.

Algorithm AS 89 was introduced by the paper D. J. Best & D. E. Roberts (1975), Algorithm AS 89: The Upper Tail Probabilities of Spearman's rho. Applied Statistics, Vol. 24, No. 3, 377-379. Table 1(a) in this paper presents maximum absolute error |\Delta_m|, of the approximation for all possible values of the statistic S for samples sizes n = 7, 9, 11, 13. The presented errors are

n |\Delta_m|

7 0.0046 9 0.0011 11 0.0006 13 0.0005

Due to the problem explained in detail including a patch at https://stat.ethz.ch/pipermail/r-devel/2009-January/051936.html the error of R implementation of Spearman's rank correlation test is larger than the above bounds for the sample size n = 11 and some of the values of S, which correspond to positive correlation.

For example, for n = 11 and S = 90, we have
x <- 1:11

y <- c(6:1, 7, 11:8)

out <- cor.test(x, y, method="spearman", alternative="greater")
out$statistic # 90

out$p.value # 0.02921104

while the correct p-value is 0.03044548, so the absolute difference
is 0.00123444. This is larger than the absolute error 0.0006 guaranteed
for AS 89. In my opinion, this means that the claim from help(cor.test)
cited above is not correct.

To see the error of AS 89 in the example above, one can use cor.test(x, -y, method="spearman", alternative="less")$p.value # 0.03036413 since on the side of negative correlation, R calls AS 89 correctly. So, for the x, y above, correctly called AS 89 has absolute error 0.00008135.

There is a package pspearman currently included to CRAN, which provides a correction of the problem without the need to modify R base.

Petr.

R-devel_at_r-project.org mailing list

https://stat.ethz.ch/mailman/listinfo/r-devel Received on Thu 12 Feb 2009 - 11:49:48 GMT

Archive maintained by Robert King, hosted by
the discipline of
statistics at the
University of Newcastle,
Australia.

Archive generated by hypermail 2.2.0, at Thu 12 Feb 2009 - 12:30:22 GMT.

*
Mailing list information is available at https://stat.ethz.ch/mailman/listinfo/r-devel.
Please read the posting
guide before posting to the list.
*