I'm analysing 2 groups of patients with 2 different DISEASE_STAGES: MILD disease and MODERATE disease, as defined by a complex clinical diagnosis. The sample size is relatively small: a total of 80 patients characterised by SMOKING_STATUS with 3 levels: active smoker, ex-smoker and never smoked.
I've performed a Fisher exact test because one cell has a frequency of 1
fisher.test(matrix(c(1, 5, 14, 3, 33, 22), nrow=2, ncol=3, byrow=TRUE)) Fisher's Exact Test for Count Data p-value = 0.03039 alternative hypothesis: two.sided
I reject the null hypothesis that the disease is not affected by smoking status.
My question: Is it possible and how can I perform a post-hoc analysis with pairwise comparisons of the proportions for a Fisher exact test? How should I correct p-values to account for the multiple testing (what kind of statistical significance should I accept for these subgroup comparisons)?