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I've performed a two-sided Fisher's exact test on the following data, and the results include Infinity for the upper confidence interval and odds ratio. Are these results erroneous, and if not how do I interpret them? I've done a bunch of searching and reading, but have a hard time wrapping my head around why the infinite results occur. When I add 0.5 to each cell I still obtain infinity.

Data:

enter image description here

    Fisher's Exact Test for Count Data

p-value = 0.002719
alternative hypothesis: true odds ratio is not equal to 1
95 percent confidence interval:
 2.196186      Inf
sample estimates:
odds ratio 
       Inf

Any insight is greatly appreciated

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Knowing the formula to calculate the odds ratio will tell you why you get an 'Inf' value. Basically, you're dividing by 0. There's a lot of documentation available on the net (here you can find an example).

As to adding 0.5 to all values, the R implementation of the Fisher's Test only works with nonnegative integers. Even if you add 0.5, the values will be rounded to integers (so 0.5 will become 0).

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    $\begingroup$ There is no need to add 0.5. An infinite upper limit is the correct answer; there is nothing wrong with it. But for reasons discussed at length on this site, Fisher's so-called "exact" test is not very accurate. $\endgroup$ – Frank Harrell Jul 2 '19 at 10:58
  • $\begingroup$ Thanks Daniel, you're of course right; I understand the number side and should have clarified my question. It's the interpretation I struggle with - the p-value is significant but how do I report or understand the interpretation of infinite odds ratios? Are the results even valuable despite the infinite OR? And Frank thanks too, I've read over the Fisher's, especially that it's conservative. I might go with other tests but would still like to understand this $\endgroup$ – Emily Jul 5 '19 at 3:13
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The issue is not the results of Fisher's test - as Frank Harrell pointed out, you are dividing by 0.

The results are fine, I think it's the question that needs work. That is, rather than ask about the odds ratio, you might want to ask about something else, like a test of proportions. This topic has an extensive literature.

Are the results variable? Well, not from this sample, but you might, of course, get different values in a different sample. You might get a 1 instead of a 0 for the upper right cell.

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