I have a data set with two groups. I have multiple trials with different N
s in each trial, and different numbers of trials for each group. In each trial, for each group, I am counting the number of successes.
How can I estimate the proportion of successes for each group under a binomial distribution (i.e. success or failure), with confidence intervals? How can I test whether the proportion of successes is the same between the two groups?
The standard Z-test for proportions is only described for one trial per group.
This question wasn't sufficient: Determining statistical significance of difference between two binomial distributions
Nor was this: Test if two binomial distributions are statistically different from each other
N
samples within a single trial are not perfectly independent, but it is fairly reasonable to assume independence. $\endgroup$N
individual samples in each trial (in each group), I know the outcome -- either success or failure. $\endgroup$