# Bootstrap sampling for ratio of means with uneven sample sizes

I want to obtain a confidence interval for the ratio of means of two samples. The samples are of uneven size. They don't come from normal distributions. Is there anything methodologically wrong about using bootstrapping to estimate the confidence interval?

The algorithm would be similar to the approach in the first example here:

• Generate r resamples of sample A: A1, A2, ..., Ar
• Generate r resamples of sample B: B1, B2, ..., Br
• For i from 1 to r, calculate the ratio of means as ratio(i) = mean(Ai) / mean(Bi).
• Estimate the confidence interval using one of the methods for obtaining confidence intervals for bootstrapping, based on the ratio(i) values.
• I would say to maintain the uneven sample size when you do your bootstrap samples. The point of bootstrap is to mimic the original data collection by drawing from the next-best distribution if you don’t have the population: the empirical distribution.
– Dave
Commented Feb 16, 2020 at 3:55