I asked the question of whether a chi-squ approximation
was always less conservative than a fishers exact in
contingency tables and reported last week that the answer
is no by counter-example and that Paul Swank very kindly
did a run of 1M simulations. I have been asked by another
Allstat member for a summary of these 1 M simulations and
present it as follows:
f Frequency Percent
-----------------------------------------
------------
999343 0 999343 99.93
99.93
1 657 0.07
1000000
100.00
657 times out of 1 million the exact test was less
conservative. This is
based on a 2 by 2 with an average cell size of 20 with a
standard deviation
of 5.
Obviously this doesn't mean that generally we should
expect 657 times out of a million the exact test to be less
conservative than the approximation since it will depend on
the assumptions (mean cell size of 20 , sd = 5) that go into
the simulation. However it does first of all provide us with
counter examples and secondly maybe it suggests that the
exact test is more likely to be conservative in real world
situations?
hope this helps,
yours,
Roger Humphry
Roger Humphry
Epidemiology Unit,
SAC, VSD,
Stratherrick Rd,
Drummondhill,
Inverness,
IV2 4JZ
UK
Tel: 01463 243 030
Fax: 01463 711 103
http://www.sac.ac.uk/vet/external/epiunithome.htm
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