# Re: [R] strange fisher.test result

From: Ted Harding <ted.harding_at_nessie.mcc.ac.uk>
Date: Sat 31 Mar 2007 - 14:05:12 GMT

On 31-Mar-07 13:36:04, Williams Scott wrote:
> A simple question - using the following fishers test it appears that
> the P value is significant, but the CI includes 1. Is this result
> correct?
>

```>> data.50p10min <- matrix(c(16,15, 8, 24),nrow=2)
```

>
```>> fisher.test(data.50p10min)

>
>         Fisher's Exact Test for Count Data

```
> data: data.50p10min
>
> p-value = 0.03941
>
> alternative hypothesis: true odds ratio is not equal to 1
>
> 95 percent confidence interval:
> 0.9810441 10.7771597
>
> sample estimates:
> odds ratio
> 3.138456
>
> Scott

Remember that the distribution on which the Fisher Exact Test is based is a discrete distribution, so what you might expect based on experience with continuous distributions will not always be the case.

In the above case, I can see a possible explanation. The p-value is the probability of the set of data (more extreme to either side) such that the probability of (say) the element in row 1, col 1 of the 2x2 table exceeding an upper critical value is less than or equal to 0.25, and the same probabiltiy 0.025 for being less than a lower critical value.

On the other hand, the lower confidence bound for the OR is the smallest value of OR that would not be rejected by a 1-sided test at P-value 0.025, and the upper confidence bound for the OR is the largest value of OR that would not be rejected by a corresponding 1-sided test at P-value 0.025, on the given data.

There is no reason, with a discrete distribution, for the confidence interval results for OR to agree exactly with the significance test of "OR=1".

More than that I cannot say without further information.

If you would post the 2x2 table of your data, it would be possible to be more specific.

Best wishes,
Ted.

E-Mail: (Ted Harding) <ted.harding@nessie.mcc.ac.uk> Fax-to-email: +44 (0)870 094 0861
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