difficulty 3/5
Bootstrap
Resample your own data with replacement, recompute the statistic, and read the spread. It gives you an interval for statistics that have no formula — and quietly fails for some that do.
Intuition
A confidence interval answers "if I ran this experiment again, how much would the estimate move?" — and the honest way to answer it would be to run the experiment again, a thousand times. You cannot. You have one sample.
The bootstrap's move is to pretend you can. Treat the sample as if it were the population and draw from it. Think Stats states it in one line — "I treat the observed pregnancies as if they were the entire population and draw samples, with replacement, from the observed sample" [1, §10.4].
This sounds like cheating. The reason it is not is that the sampling distribution depends on the shape of the population, and the sample is the best estimate of that shape you have. The reason it sometimes is cheating — and the reason this page has a coverage table — is that the sample is a bad estimate of the parts of the shape it never saw.
Formal definition
How it works
Where it's used
Why & when
Worked example
Pitfalls
Check yourself
3 questions
The questions on this page come with access. They are graded on the server, so the answers stay there until you have given yours.
On the cheat sheet: Statistical testing →
Sources
- Think Stats, 2nd ed.book · retrieved 2026-09-12https://greenteapress.com/thinkstats2/html/index.html
- NIST/SEMATECH e-Handbook of Statistical Methodsstandard · retrieved 2026-09-12https://www.itl.nist.gov/div898/handbook/eda/section3/eda334.htm
- SciPy reference — scipy.stats.bootstrapdocs · retrieved 2026-09-12https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.bootstrap.html