In sci.stat.edu Herman Rubin <[EMAIL PROTECTED]> wrote:
> In article <9deiug$l0h$[EMAIL PROTECTED]>,
> Ronald Bloom <[EMAIL PROTECTED]> wrote:
>>2.) The two row (col)marginals are treated as independent; and the
>>observed table under the null hypothesis is regarded as
>>being the result of two independent random samples from
>>identical binomial distributions. The significance test used
>>in this case is identical to the elementary test for the
>>difference between two sample proportions.
> This is a much more complicated testing situation than you
> seem to think. Because of the nuisance parameters, it is
> essentially impossible to come up with a "natural" test
> at the precise level, especially for small samples.
Some seem to feel that the "maximum likelihood" values
of the nuisance parameters when substituted for the parameter
give rise to the "best" test.
In this approach the "nuisance" parameters are simply
replaced with ML estimates based on the information at hand.
What do you think?
> But these parameters are unknown. Testing with nuisance
> parameters is very definitely not easy, and exact tests
What do you think of the test for 2x2 table effect whereby
one tests the "null" hypothesis of identical propensities
for "outcome" in the two rows, and uses a "pooled" estimate
for that probability; against the alternative in which one
uses separate estimates of separate outcome propensities
computed from the rows separately -- a likelihood ratio test.
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