In sci.stat.math Herman Rubin <[EMAIL PROTECTED]> wrote:
> In article <9dpcei$qcf$[EMAIL PROTECTED]>,
> Ronald Bloom <[EMAIL PROTECTED]> wrote:
>>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?
> They do not necessarily do so. The problem is more
> complicated than it looks.
please elaborate.
>>> 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.
> What is the distribution of the statistic? It very
other than "asymptotically" speaking, I don't think
*that* problem admits of any useful closed-form solution.
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