After reading several posts on this site, I am still not sure on how to proceed. I have a set of genes, and have the proportion of mutated sites in each of them. This is an example in R:
myStats<- data.frame(
SampleName = paste(
'GeneName', 1:9, sep = ''),
PropOfMutations = c(
0.12210201, 0.13885505, 0.12861272,
0.12845850, 0.14886364, 0.10860927,
0.12933458, 0.08028169, 0.08295195))
I am using proportions as each gene has different length, and each of its nucleotides has a chance to mutate.
I want to test if any of the genes has a proportion of mutations higher than expected, as compared to the whole dataset. Would it be correct in this case to use the z-test:
z <- (p-p0)/sqrt(p0(1-p0)/n)
where n is the total no. of genes I have, and p0 the mean of all values? Please let me know if I need to add any additional details.
I have also checked the distribution of my data:

