In sci.stat.consult Juha Puranen <[EMAIL PROTECTED]> wrote:
:>
:> Please clarify what is meant by "the distribution does not
:> involve [the fixed marginals]". I am not clear on this:
:> the Fisher test statistic (hypergeometric upper tail probability)
:> certainly *does* depend on the fixed marginals in this
:> case -- they appear in every term in that tail sum.
sorry; didn't say it right
: Usual the assumptions for Fishers exact test are not true.
: What you can fix are the row margins, or column margins or grand total
These aren't assumptions any more than specific fixed x values are
assumptions in linear regression
Kendall and Stuart say (under exact test of independence 2x2 table)
We may now demonstrate the remarkable result, first given by Tocher
(1950) that the exact test based on the Case I probabilities actually
gives UMPU tests for Cases II and III
The probability statements for case I (fixed marginals) are valid
conditional on the marginals for every set of marginals and do not
involve the nuisance parameters for Cases II and III and thus are valid
unconditionally for all three cases.
This is exactly analagous to the regression model
y = bx + e
where you derive the t test for b conditional on the specific x values you
observe, treating them as fixed. The statistic (a function of the
x's) has the same t distribution regardless of what x values you observe,
even if they happen to be sampled from ANY probability distribution
Thus the regression test for fixed x values is valid for random x values
=================================================================
Instructions for joining and leaving this list and remarks about
the problem of INAPPROPRIATE MESSAGES are available at
http://jse.stat.ncsu.edu/
=================================================================
