# What is the value of an infinite odds ratios with non-signification p-value?

I have a contingency table as follows:

        Tumour
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
Inf


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

• 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. – whuber Jul 9 '20 at 13:49
• OK, so how shall I report it? OR=∞ (0.378-∞), p-val = 0.167? Thank you – Gigiux Jul 9 '20 at 16:41
• I would report it as "there aren't enough data either to estimate or detect a difference ($p=1/6$)." – whuber Jul 9 '20 at 16:54