Even if you were to discretize the levels of your ordinal variable into
say 1,5,8 etc. you have to assume that the underlying distribution
(i.e. the original distribution) is naturally an ordinal one (unless it
can be quantitatively measured). The natural way is to use a test that
assumes ordinal vs. dichotomous and compare the two. Perhaps, it is
wiser to use Mann-Whitney U test (a.k.a. Wilcoxon ranksum test) as you
mention. Note that STATA does not give an "exact" value for this test,
but uses a normal approximation (which kind of defeats the purpose of an
exact test...). For this test, the key assumption is that the underlying
distribution that you are comparing have to be the same (not necessarily
normal).
Alternatively, you can use a median test (which does have an exact
option). This is very close to a chi-squared or Fisher's exact test for
contingency tables.
You could also try to measure the strength of the relationship between
the two variables. This is usually not the ideal setting and may not be
appropriate in your setting, but may provide you with some clues as to
wheather or not there is some relationshop between the two variables.
For that you would need to use a "Rank Biserial Correlation" which, as
far as I know, is only implemented into a SAS macro.
Hope this helps.
--
Thomas Speidel
Statistical Associate
Department of Oncology
Tom Baker Cancer Centre
1331 - 29th Street N.W.
Calgary, AB, T2N 4N4
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