Bootstrap estimation

Make the uncertainty in a small sample visible by resampling the observations themselves.

Interactive laboratory 10 · Resampling

What does your sample say about uncertainty?

We have 12 synthetic observations of waiting time (minutes), with an unusually long wait in the tail. Draw new samples of 12 values with replacement from these observations. Every bar in the histogram describes a bootstrap sample mean, not an individual waiting time.

Original sample mean—
Bootstrap standard deviation—
Percentile interval—
Exact synthetic source data and numerical histogram bins

Waiting times: .

Bootstrap mean intervalNumber of replicates

This is the simplest percentile bootstrap, conditional on a small empirical sample. The displayed endpoints vary across runs; nominal coverage is not guaranteed, especially for small, skewed datasets. Repeatedly sampling the same nonrepresentative observations also does not correct selection bias.

Read the accompanying lesson →