Not sure if you can help me but here's the problem.
I have two binomial proportions A and B (95% CI) -
$A = 2\% \pm 0.2\%,\quad B = 3\% \pm 0.2\%.$
In other words, B's proportion is 50% higher than A's.
Business people tend to prefer speaking about this difference in terms of a percentage increase. In other words, B's proportion is 50% higher than A's. How do I go about calculating a Confidence Interval for the 50% increase of B's proportion over A.
I've done some research into Fieller’s formula which is said to provide exact percent effect. However, besides not understanding Fieller's theorem, I don't know how I would go about calculating this in R.
Can anyone help?
Edit: E.g., if the CI for those intervals is 95%, the CI for the 50% increase = 98.52%.