[Rd] wilcox.test point estimates perverse (PR#1150)

[charlie@muskrat.stat.umn.edu]

The point estimates produced by wilcox.test are perverse (not wrong, just
brain damaged).  The Hodges-Lehmann estimator that goes with the signed
rank test is the median of the Walsh averages.  The Hodges-Lehmann estimator
that goes with the rank sum test is the median of the pairwise differences.

wilcox.test agrees except that it uses the following very peculiar definition
of "sample median": if the number of items is even, the average of the two
middle items (agrees with the usual definition), and if the number of items
is odd, the average of the two on either side of the middle item in sorted
order (huh???  why???).  I know this is asymptotically equivalent to the
usual definition, but

  * Why get answers that disagree with every nonparametrics textbook?

  * If wilcox.test is right then median is wrong and should be fixed
    (just kidding, don't mess with median!)

Thus the complicated code in lines 87--89 of wilcox.test.default
should be replaced by the simple

  ESTIMATE <- median(diffs)

and the complicated code in lines 214-216 of wilcox.test.default should
be again be replaced replaced by the simple

  ESTIMATE <- median(diffs)

Moreover, there is NO "correction for ties" in the Hodges-Lehmann estimator.
Thus the code in lines 147-148 and 272-273 is silly.  The code for the point
estimate should be done by exactly the same code when there are ties or zeroes
(or both) and when there are not.  Reference: Sections 3.2 and 4.2 of
Hollander and Wolfe.

I understand that one doesn't want to produce the vector diffs (which is
order n^2 when n is large), but one doesn't have to to calculate the median
if this is taken to C.

Moreover that uniroot stuff sometimes crashes (sorry, I didn't save the
examples, but take my word for it, it's not bulletproof).

Note that the confidence intervals are also bizarre in the case of ties, but
that's another bug report.
-- 
Charles Geyer
Professor, School of Statistics
University of Minnesota
charlie@stat.umn.edu

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