I have two proportions (e.g., clickthrough rate (CTR) on a link in a control layout, and CTR on a link in an experimental layout), and I want to calculate a 95% confidence interval around the ratio of these proportions.
How do I do this? I know I can use the delta method to calculate the variance of this ratio, but I'm not sure what to do besides that. What should I use as the midpoint of the confidence interval (my observed ratio, or the expected ratio which is different), and how many standard deviations around this ratio should I take?
Should I be using the delta method variance at all? (I don't really care about the variance, just a confidence interval.) Should I use Fieller's Theorem, using Case 1 (since I'm doing proportions, I guess I satisfy the normal distribution requirement)? Should I just calculate a bootstrap sample?