Let's assume a cell based assay, in which some cells have an irregular shape. We can calculate the proportion of irregularly shaped cells as
2 experimental treatments are assayed independently with 3 replicates each. Each replicate is an independently cultured petry-dish, in which cells are counted as described after some time.
Because of the binary outcome per cell, it seems reasonable to assume a bernoulli-distributed random process.
How would I compare such proportion data? A 2-sample binomial test comes to mind, but it's unclear how to include the replicated measurements.
And related to the comparison, I'd like to plot the mean of my proportions and a confidence interval. How would I calculate the CI?
There's a related question for count data in How to calculate confidence interval for count data in R? but I suspect that proportions should be dealt with differently.