Date:         Tue, 24 Jul 2007 11:54:08 -0500
Reply-To:     Robin High <robinh@UNLSERVE.UNL.EDU>
Sender:       "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From:         Robin High <robinh@UNLSERVE.UNL.EDU>
Subject:      Re: Fisher's Exact Test vs Generalized Linear Models
Comments: To: Paige Miller <paige.miller@KODAK.COM>
In-Reply-To:  <1185210582.837579.182860@m3g2000hsh.googlegroups.com>
Content-Type: TEXT/PLAIN; charset=US-ASCII

> I have a binary response variable as the results of a simple designed
> experiment. The experiment could be either a one-factor experiment
> with k levels of the independent variable, or it might be a two-factor
> experiment with k1 and k2 levels of the independent variables.
>
> In either case, I can run Fisher's exact test or I can fit a
> generalized linear model. In SAS, you would use PROC FREQ for Fisher's
> exact test, or you can fit the generalized linear model with PROC
> GENMOD.

> Fisher's exact test and the generalized linear model test do not seem
> to give the same results when you test to see if the factor(s) have an
> effect.
>
> I am hoping someone can explains the pros and cons of each test, or
> point me to a reference.

Paige,

For a more elementary intro to each topic, the "Introduction to
Categorical Data Analysis" by Agresti contains helpful discussions.

Though, both are related to the same problem, the two techniques are
'miles' apart in what is under the hood. The mathematical derivation is
completely different. For starters, apply Fisher's test (based on the
hypergeometric distribution) if you have relatively 'small' counts in each
cell of an rxc table to check for independence of row and column effects.
If you have 'large' counts (that is, PROC FREQ doesn't give you a
warning), the Pearson or Likelihood ratio test are likely OK.

GENMOD is based on maximum likelihood theory (related to the Likelihood
ratio test above) which assumes you have relatively large sample sizes for
the asymptotics to work, as well as other assumptions depending on the
data and the model; not only a pvalue of no effect is given, but also
coefficients that help to interpret the differences.

Robin High