I have count data from survey transects at several sites (typical n ~10). I am interested in whether the sample mean exceeds a threshold at [1-alpha]% confidence level (...knowing I have low power), and have used the typical formula for standard error of the mean: SD(x) / sqrt(n-1), which takes advantage of the property that the sampling distribution of the sample mean is approximately normal regardless of data's distribution.
Most the confidence intervals seem reasonable, but in some sites with odd distribution of data (e.g., lots of zeros, or many low values and a few very high), the CI will include negative values. I want to show the analysis to lay persons and would rather not have to explain why implausible population means of negative or zero values are in the confidence interval.
Can I ask for some input on whether there are other methods I might want to use for calculating SE of the mean and how I might implement and interpret/describe them?
Here are some of my data that produce negative lower 95% CI (R syntax):
A<- c(0, 0, 0, 9, 0, 0, 0, 0, 0, 4) B<- c(0, 0, 0, 1, 0, 0, 0, 0, 0) C<- c(10, 5, 8, 10, 4, 3, 4, 60, 1, 2)
Sorry I wasn't able to find an analogous example in the archives with a solution that seemed meaningful for my case (although this seemed relevant)