# Re: [R] Odds ratio in fisher.test()

From: Achim Zeileis (zeileis@ci.tuwien.ac.at)
Date: Wed 26 Feb 2003 - 18:42:25 EST

```Message-id: <200302260742.h1Q7gPOe021167@thorin.ci.tuwien.ac.at>

```

On Wednesday 26 February 2003 05:10, Andrew Criswell wrote:

> Hello:
>
> the difference between what I believe is the conventional definition
> of an odds ratio for a 2-by-2 table and the output produced by
> fisher.test()
>
> in R. Consider the following example:
> > Discrim <- matrix(c(1,10,24,17),
>
> + nr = 2,
> + dimnames = list(AGE = c('young', 'old'),
> + EMPLOY = c('fired', 'kept')))
>
> > Discrim
>
> EMPLOY
> AGE fired kept
> young 1 24
> old 10 17
>
> The conventional odds ratio is computed as
>
> > (1 * 17) / (24 * 10)
>
> [1] 0.07083333
>
> Why is it, when I use fisher.test(), I get an estimated odds ratio
> like that reported below? There, the difference seems slight, but
> with other cases it can be quite large.

>From help(fisher.test):

estimate: an estimate of the odds ratio. Note that the conditional
Maximum Likelihood Estimate (MLE) rather than the
unconditional MLE (the sample odds ratio) is used. Only
present in the 2 by 2 case.

Look at the code to see how it is computed.
Z

> > fisher.test(Discrim, alternative = 'two.sided')
>
> Fisher's Exact Test for Count Data
>
> data: Discrim
> p-value = 0.005242
> alternative hypothesis: true odds ratio is not equal to 1
> 95 percent confidence interval:
> 0.001573963 0.606416320
> sample estimates:
> odds ratio
> 0.07407528
>
>
> Thanks,
> ANDREW
>
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