Thanks a lot Erik, so said differently, it looks like I would (for instance) need at least 100 counts if I want to be at least 95% sure that a E / L ratio of 0.58 really indicates that E > L.
> sapply(1:10 * 10, function(n) binom.test(c(n/2, n/2), p=0.5, alternative = "l")$conf.int) %>% t %>% set_rownames(1:10 * 10)
[,1] [,2]
10 0 0.7775589
20 0 0.6980461
30 0 0.6611073
40 0 0.6389083
50 0 0.6237541
60 0 0.6125890
70 0 0.6039339
80 0 0.5969763
90 0 0.5912285
100 0 0.5863783
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Charles Plessy
Are you going to conduct RNA-seq on those two intervals? Or is it some targeted sequencing that you are looking for?
We are using CAGE (Cap Analysis Gene Expression) libraries of virus-infected cells, and the genomic intervals are viral promoters. (And yes, targeted enrichement is also planned, but that is a different story.)
Assuming the counts are Poisson-distributed with rate r, for r sufficiently large (> ~20, but the approximation is already quite good before this, it only improves as r increases), the Poisson distribution could be approximated by a Gaussian distribution with mean r and variance r. You could also view this as testing the ratio of the rates of two Poisson distributions, for this have a look at the R package rateratio.test.