Statistical test recommendation for efficacy of three different drugs with categorical responses I have a really small study sample of 70, in which they are being medicated with 3 different drugs (A,B,C). The study aimed to determine the efficacy of each drug in treating the disease and the outcome of treatment is either success or failure. I have tried analysing the data using the chi-square test and fisher's exact test, however, my supervisor advised me on using the logistic regression test. Would that be possible to carry that out with a small study sample, with which all variables are categorical?




Treatment
A
B
C




Success
23
11
12


Failure
12
5
7




(Very new to stats)
Update :
Hypothesis - Drug A is more effective than Drug B or Drug C in treating the condition

To test pairwise drug A vs drug B and drug A vs drug C for superiority of drug A, you may want to conduct one-tail Fisher's exact tests between those pairs. In R, it will be:
data <- matrix(c(23, 11, 12, 12, 5, 7), nrow=3, byrow=FALSE)
fisher.test(data[1:2,], alternative = "greater")
fisher.test(data[c(1,3),], alternative = "greater")

P.S. There is absolutely no statistical significance in these tests (the superiority of drug A vs either drug B or C is not supported).
