Confidence intervals for multiple proportions

#1
Hi everyone,

I would like to know how to calculate confidence intervals for non-binomial proportion data of which I have multiple samples? I'll give an example to clarify:

Proportion1 Proportion2 Proportion3 Proportion4 Proportion5 Proportion6
Sample1 0.93926 0 0.00204 0.0585 0.0002 0
Sample2 0 0.95882 0.00088 0.03912 0.00118 0
Sample3 0 0.95718 0.00116 0.04054 0.00112 0
Sample4 0 0.96226 0.00098 0.03546 0.0013 0
Sample5 0.93972 0 0.00196 0.05812 0.0002 0

Mean 0.375796 0.575652 0.001404 0.046348 0.0008 0
Confidence ? ? ? ? ? ?

Note: I can take the mean here and avoid Simpson's paradox effects because all sample sizes are equal.

Additionally, if anyone can give me some tips on appropriate sample sizes for this type of data, that would be much appreciated.

Thanks in advance!

Michael
 
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#2
It seem like your data sums to one (1). Then maybe you can use the Dirichlet distribution. (The beta distribution is a special case of that.)

I did a quick search and found this one (that I have not read):
http://research.microsoft.com/en-us/um/people/minka/papers/dirichlet/minka-dirichlet.pdf

Maybe there is an error in the data:

Sample1 0.93926 0
Sample2 0 0.95882

About sample size I have not much comments. It depends on the variance and your precision demands (and significance level and power). Start with a normal approach could lead you in the right direction.