# Ratio Confidence Interval for Proportions

Wondering if Fieller's theorem is used for the 'ratio' value in the compare argument in statsmodels.stats.proportion.confint_proportions_2indep method from the statsmodel module. If not, what is it? I'm trying to display the confidence interval of the % difference between p1-p2

Also, how can I interpret the numbers. I got the following 95% conf intervals with ratio: (1.05, 1.31).

EDIT: When computing for the risk ratio, the 95%CI is :(1.05, 1.31) What does it mean? Is that that the click through rate for the control group (metric being analyzed) is between 5% and 31% more likely to be clicked than the treatment group ?

Data: P1 = 30.97% n=50000, P2 = 26.34%, n=50050 Delta = -14.9% How can i get the CI for the Delta?

• You appear to be asking two different questions. Do you need a confidence interval for the difference or for their ratio? Concerning your bold question, that's a matter of what a confidence interval means: you can find good information at stats.stackexchange.com/questions/26450.
– whuber
May 23, 2022 at 19:02
• Re the edit and recent comments: In AB testing usually the datasets are so large you can use Normal-theory approximations. See stats.stackexchange.com/questions/388294 for instance.
– whuber
May 23, 2022 at 21:00
• For such large datasets--as I wrote--Normal approximations will be fine. One source of software for these calculations is cran.r-project.org/web/packages/PropCIs/index.html.
– whuber
May 24, 2022 at 13:41
• I still don't know for sure what you mean by "% difference," but for examples see stats.stackexchange.com/….
– whuber
May 24, 2022 at 19:51
• Okay, so at a minimum please stop calling that ratio a "difference:" you're going to confuse most readers. Call it a ratio. The Normal approximations still work. Research delta method for details.
– whuber
May 24, 2022 at 22:16