I'm trying to replicate a study. I have 165 observations of a proportion variable (the distribution is skewed to the right as many proportions are low). I need to report the CI. I've applied arcsin(sqrt), computed the mean and SE of the transformed proportions, got the CI, and transformed back to the original scale.
Now, the thing is, that the total proportion of the sample does not fall into that interval. (I feel it has to do with the lower bound of the binomial, that's why the study is stretching those values by arcsin(sqr)).
But how should I properly state this result?
The following article comments on this issue:
Comment: The logarithm is the only non-linear transformation that produces results that can be cleanly expressed in terms of the original data. Other transformations, such as the square root, are sometimes used, but it is difficult to restate their results in terms of the original data.
the raw data for one of the variables:
Eser 0 0 0 0 2 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 10 0 1 0 0 1 0 0 0 0 0 0 0 1 1 0 6 0 0 0 0 0 0 10 0 1 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 9 0 0 0 1 0 1 0 0 0 6 0 2 0 0 1 0 4 0 1 2 0 0 1 0 0 10 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 6 1 0 0 0 10 10 3 1 2 1 0 0 0 0 0 0 0 0 0 2 0 0 0 0 3 0
It's 165 proportions (between 0 and 1) computed as those counts out of n=20 for each case.
I want to compute CI for that proportion for whole sample.
I tried comparing sample variance, skewness and kurtosis to that of the theoretical binomial with the same p. My data seem to be somewhat underdispersed and the transformation did not normalize it anyway. So what would you suggest? I need to get some kind of confidence interval for the mean proportion.