Question

I am trying to estimate the median of a population. I create many bootstrapped samples from my original sample, and I calculate the median of each. Which percentiles of my bootstrapped medians should I use to form a two-sided 80% confidence interval for the population median?

Answer 1

Answer 2

To form a two-sided 80% confidence interval for the population median using bootstrapped samples, you can use the percentiles of the bootstrapped medians. Since it is a two-sided interval, you will need to consider both the lower and upper percentiles.

Here's how you can proceed:

1. Generate a large number of bootstrapped samples from your original sample (e.g., by randomly sampling with replacement).

2. Calculate the median for each bootstrapped sample.

3. Sort the bootstrapped medians in ascending order.

4. Determine the percentiles for the confidence interval. In this case, since you want an 80% confidence interval, you need to find the percentiles that cover 10% on each tail of the distribution. This means you need to find the lower 10th percentile and the upper 90th percentile of the bootstrapped medians.

For example, if you have 1000 bootstrapped medians, the lower 10th percentile would correspond to the median at the 100th position (10% * 1000 = 100), and the upper 90th percentile would correspond to the median at the 900th position (90% * 1000 = 900).

These percentiles will give you the range within which the population median is estimated to fall with 80% confidence.