I don't think there is an agreement in the statistical community. In the
clinical trials circles conditional tests are highly regarded and the
most convincing evidence I have seen so far is Yates (1984, J. of Royal
Stat Soc, A147:426-463).
Mithat
In article <8kjlju$ni8$[EMAIL PROTECTED]>,
Ron Bloom <[EMAIL PROTECTED]> wrote:
> Regarding significance tests for 2x2 tables.
> I do not know what to make of all the debating this
> way and that way in the literature.
>
> Q: Under what circumstance does one use the "exact test"
> conditional on the "marginals being what they are" ?
>
> I have seen the distinction made (supposedly helpful)
> between -- e.g. -- case/control studies, where the
> marginal totals are chosen by the experimentor, and
> are therefore NOT random variables; and retrospective
> analysis of risk-factor and disease incidence data,
> where the marginal totals are NOT chosen by the
> experimentor, and are (therefore) regarded as random
> binomial variates.
>
> Supposedly, then, one ought use the "conditional" exact
> test (i.e. Fisher's) in the former case, whereas one
> ought use an "unconditional" exact test in the latter case.
>
> But it seems that the marginals in either case can be
> thought of as either "random" or "determined", depending
> on how one "thinks of the problem". In other words,
> in the retrospective incidence/risk-factor data, the
> marginals look like "random" quantities if you think
> of the researcher having simply "gathered up" whatever
> washed up at his doorstep; but they look like "fixed"
> quantities if you think of the researcher having
> been somewhat partial to a particular ratio of cases
> to controls. Neither instance seems utterly clear-cut,
> and moreover, why should I, when confronted with a
> single 2x2 table have to worry about what the researchers
> state of mind was when he either "gathered" or "selected"
> the observations?
>
> To put it another way, when I want to compute a "p-value"
> which somehow expresses the "extremity" of the single
> observed 2x2 table, I need to consider the universe
> from which that table was drawn. There are different
> ways of construing the universe ... corresponding to
> "conditional" or "unconditional" tests. But the universe
> is a fiction, for all I have on hand is a *single*
> 2x2 table. Now the researcher's methodology (if I
> knew of it) would tend to cause me to favor one universe
> over the other. (Is this an observation drawn from
> a family having fixed marginals or not? )
>
> But this strikes me as an unstable basis for choice of
> a statistical test. As I said above, a single table
> with preselected marginals can be treated as an instance
> of a selection with *random* marginals, that just happens
> to be the same! So the choice of the appropriate
> statistical test seems to rest upon an optical illusion
> of the sort where two images are combined in such a
> way that the visible one depends on the angle of viewing.
>
> How does one correctly view the choice of test?
>
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