# Non-parametric bootstrap for 95%CI calculation in stratified sample in R

I am estimating the population mean of the 2023 value of cars from a stratified sample. The value of the cars is right skewed on visual inspection, and some basic diagnostics indicate normality assumptions are violated. I need to calculate the 95%CI of the calculated population mean. My first thought was to use accelerated bootstrap, however, after a bit of research, I can’t seem to find a package in R that calculates this for stratified samples. Before I go trying to code this from scratch, is there an alternative non-parametric approach in R to calculating confidence intervals in skewed stratified samples?

You don’t need normality or symmetry to estimate a population mean’s sampling variance, though those things are helpful.

There are several bootstrap methods that have been developed for complex samples (i.e., samples selected with stratified sampling, cluster sampling, unequal selection probabilities, etc.)

The R packages ‘svrep’ and ‘survey’ implement several of them. The ‘svrep’ documentation describes how to implement a number of bootstrap methods for complex surveys and explains how to pick one that’s appropriate for your sample.

https://cran.r-project.org/web/packages/svrep/vignettes/bootstrap-replicates.html

The following paper offers an excellent overview of the many bootstrap methods developed for complex samples.

https://projecteuclid.org/journals/statistics-surveys/volume-10/issue-none/A-survey-of-bootstrap-methods-in-finite-population-sampling/10.1214/16-SS113.full

• Thanks! I had a read of these earlier in the week. Helpful resources. I imagine that if sample is skewed, but the bootstrap distribution is approx normal, obtaining the confidence intervals is fine, but if the bootstrap distribution is skewed then non-parametric methods must be used? Apr 10 at 8:48