It probably should be good enough but one thing you could do is some bootstrapping to see if the distribution is good enough.

It sounds like your situation is a little more complex since you have different groups but you should be able to use a similar idea to approximate the sampling distribution for whatever statistic you're looking at.Code:`# Making some fake data a <- rpois(50, 6) a[a>=10] <- 10 # Takes a random sample the same size as 'a' from 'a' # with replacement, then calculates the mean. # Does this 10000 times samp <- replicate(10000, mean(sample(a, replace = TRUE))) # Examine the distribution. 'samp' should approximate # the true sampling distribution so we can use this # to assess whether the distribution is close to normal. hist(samp)`