Re: st: Re: Fischer's exact when the expected counts are known

[Mike Lacy <Michael.Lacy@colostate.edu>]

>From: Ricardo Ovaldia <ovaldia@yahoo.com>
>Subject: st: Fischer's exact when the expected counts are known
>
>Dear all,
>
>Is there a command or a way to trick -tabulate- to perform a Fisher's
>exact test when the expected counts are known.
>
>For example the observe counts are:
>30 20 15 35
>
>Under the null the expected counts are
>20 30 30 20
>
>I want to test this using a fisher exact test.
>

-------
>
>Date: Mon, 9 Feb 2009 14:55:21 -0500
>From: Steven Samuels <sjhsamuels@earthlink.net>
>Subject: Re: st: Re: Fischer's exact when the expected counts are known
>
>Richard has multinomial data: four categories with expected counts.
>There is no such thing as a Fisher Exact Test for multinomial data;
>Fisher's test is for two-way tables, and tests the hypothesis of
>independence. Richard wants to test the fit of the observed data to
>the expected.  He needs Ben Jann's -mgof- (from SSC) or the packages
>listed at the bottom of its help page.  -mgof- uses simulation to
>approximate the exact distributions of  the Pearson Chi Square and
>likelihood-ratio goodness-of-fit tests.
>

I can think of another way to interpret the intent that might make 
this do-able. Suppose we presume that the goal is to test the 
observed table's evidence of association (i.e., odds ratio) against 
the odds ratio implied by the expected frequencies that were given, 
as opposed to the full multinomial approach.

 I don't know that there is any stock way to do this in Stata, but 
one *can* calculate  the noncentral probability of obtaining a table 
with at least as large an odds ratio  as that observed, given a 
"true" odds ratio that is not null, and given fixed  marginals per 
the observed table. This would involve a noncentral hypergeometric
 distrbution as opposed to the central hypergeometric used in the 
special case of  Fisher's test when the null odds ratio is assumed to 
be 1.0.  I don't have the formula for the non-null case right to 
hand, but IIRC it is quite similar to the regular hypergeometric 
probability with the assumed odds ratio as a multiplier.   Perhaps
 someone has already implemented this.  SAS offers the point 
probability for this as the function PROBHYPER.

Regards,
=-=-=-=-=-=-=-=-=-=-=-=-=
Mike Lacy
Fort Collins CO USA
(970) 491-6721 office


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