First time question on this site, so please bear with me, thank you:
I have 6 coin-flip-type experiments for which I can calculate 6 binomial p-values. I would now like to calculate the significance of observing at least 4 p-values < 0.05 in six experiments total.
In one approach, I used Fisher's method (http://en.wikipedia.org/wiki/Fishers_method) to compound the p-values, but I wanted to add an additional test based on simulating the original coin-flip data.
To this end, I performed random coin-flips (P=0.5) for each of the 6 experiments; the total number of flips differs between these 6 experiments but is irrelevant. I then count how many times (out of 100 simulations) the binomial p-value < 0.05. Simulating the original data 100 times, I get the following number of significant binomial p-values ("false positive hits") from these 6 experiments:
12, 13, 9, 10, 7, 11
Or divided by 100 (= frequency of false positive hits in simulated experiments):
0.12, 0.13, 0.09, 0.1, 0.07, 0.11
How do I calculate the probability that 4 or more out of these 6 would be positive given these frequencies? I realize that for calculating the probability that 6/6 are positive, I would simply multiply 0.12 x 0.13 x 0.09 x 0.1 x 0.07 x 0.11. But for 1-5/6 it's more complicated. I'm leaning towards a hypergeometric test, since I have to draw 6 times and I think there's no replacement, but I want to double-check with you experts. Thank you!