In popular texts on statistics, one often sees it claimed that use of a
rank test is consistent with testing hypotheses about population medians.
However 1) In many applications the null hypothesis is simply that the
distribution is the same in both groups which implies equality of mean,
medians and indeed all other measures of location (and dispersion etc)
between groups, so on that basis it is a test about population medians and
means 2) When inverting the hypothesis test to construct confidence
intervals, the relationship is actually between rank -tests and the
Hodges-Lehmann estimator, not the median, or differences between medians.
(Basically it turns out that the median of all pairwise differences is more
relevant than the difference of the medians.)
Is there something I have overlooked and is there any particular reason as
to why the medians (or rather, the difference between them) should be
associated with these tests (apart from the fact that the median is the
value that has middle rank)?
I am not so much interested in expert justification for the H-L estimator,
these are not in short supply, rather whether there is anything to be said
for the (difference in) median(s).
Stephen
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Stephen Senn
Professor of Statistics
Department of Statistics
15 University Gardens
<http://www.gla.ac.uk>University of Glasgow
G12 8QQ
Tel: +44 (0)141 330 5141
Fax: +44(0)141 330 4814
email [log in to unmask]
Private webpage: http://www.senns.demon.co.uk/home.html
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