I frequently see in the outputs quoted from biomedical,
epidemiological statistical software, in analysis
of the usual 2x2 tables e.g.
Disease Well
Risk Factor a b
No Risk c d
frequently *both* chi-squared test and test on log(odds)
are quoted.
Now both of these tests rest upon the same asymptotic
substitutions of certain continuous distributions
for the exact (discrete) sampling distributino of
2x2 table under such and such hypotheses.
Moreoever, it would appear that the same table that
gives a "significantly large" chi-square would
give a significantly large log(odds). Of course
one checks the tail-probability of the former in
the "chi-squared 1-df" distribution, and of the
latter in a gaussian with approximate variance
1/a+1/b+1/c+|1/d. But don't the results of
the two tests more or less support the same
decision? Why do canned software packages
quote so many different statistics whose
intrinsic tendencies towards "significance"
or non-significance are obviously correlated
with each other. Is it because folklore
somehow plays a large part in what the
"right test is" ?
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