I have a contingency table as follows:

Healthy Pos Neg
    Pos   4   0
    Neg   2   3

I ran Fisher's exact test to get the odds ratio (using R) and I got:

    Fisher's Exact Test for Count Data

data:  meld
p-value = 0.1667
alternative hypothesis: true odds ratio is not equal to 1
95 percent confidence interval:
 0.3779205       Inf
sample estimates:
odds ratio 

How shall I interpret the result? An infinite OR sounds already bad to me, but coupled with a non-significant p-value (inclusion of 1 in the CI), I'd say there is no difference between the classes. Am I right?

Thank you

  • $\begingroup$ The Inf does not designate an infinite odds ratio--it's simply a way of stating there is no upper confidence limit. In other words, there is 95% confidence that the odds ratio exceeds 0.3779. No special reinterpretation is required. $\endgroup$ – whuber Jul 9 '20 at 13:49
  • $\begingroup$ OK, so how shall I report it? OR=∞ (0.378-∞), p-val = 0.167? Thank you $\endgroup$ – Gigiux Jul 9 '20 at 16:41
  • 2
    $\begingroup$ I would report it as "there aren't enough data either to estimate or detect a difference ($p=1/6$)." $\endgroup$ – whuber Jul 9 '20 at 16:54

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