This is a question about, um, statistical forensics.
A colleague sent me some statistical results for validation. He claims that he used a "two sample t-test" to compare percentages of a phenomenon in two groups.
At first I thought that he meant a normal test for proportions (like prop.test in R), or a z-score test, however, I was unable to replicate his p-values.
Edit: yes, I am aware of replies like this one, stating that no, you actually can't use a t-test for proportions. So let me reformulate the question: do you know of any program that might claim to use a "two sample t-test for proportions"? Or, maybe, what other test could have been used to obtain the given p-values?
Consider the following (real) data. Below, I give the number of positives and group size.
Group k N
A 33 140
B 4 7
C 37 161
D 7 33
My colleague did pairwise comparisons and obtained the following p-values:
A vs B: p = 0.0374
C vs B: p = 0.041
D vs B: p = 0.606
My question: what test was used to obtained these p-values?
When I applied prop.test (z-test) from R (with Yates' correction for continuity), I got following p-values: 0.121, 0.107, 0.174. Without Yates' correction: 0.046, 0.039, 0.069 (close, but no banana).
(Of course, the simplest thing would be to ask my colleague what he did, but this is, for reasons beyond the scope of this discussion, not possible).
