Bootstrap Resampling, explained.
The nonparametric bootstrap approximates sampling variability by repeatedly resampling observations with replacement from the empirical sample.
Why it happens
Two hundred size-six resamples are drawn from 1, 2, 2, 4, 7, 9. Their means form a histogram and percentile range. Omitting 9 changes the empirical distribution rather than supplying missing population data.
The nonparametric bootstrap approximates sampling variability by repeatedly resampling observations with replacement from the empirical sample.
Read the result
The histogram describes means of resamples from the observed empirical distribution, not new observations from the unknown population.
A worked example
A six-value sample and its resampled means
Inspect the observed values one, two, two, four, seven and nine before generating resamples.
Open an individual size-six resample to see repeated observations and its calculated mean.
Omit nine and compare the changed range, recognising this as sensitivity analysis rather than correction of an outlier.
OPTIONAL DEEPER DETAILGo deeper: inside the model
Inside this model
Two hundred size-six resamples are drawn from 1, 2, 2, 4, 7, 9. Their means form a histogram and percentile range. Omitting 9 changes the empirical distribution rather than supplying missing population data.
Where this idea is useful
A practical use
Use resampling to explore an estimator’s sensitivity while checking whether the sample represents the process you care about.
A common misconception
“Resampling creates information about outcomes the sample never captured.”
The empirical bootstrap can reuse observed values in new combinations, but it cannot discover an absent tail or undo biased sampling.
What this explanation leaves out
- Six observations are a very small empirical sample. Resampling cannot reconstruct missing tails or repair selection bias; the displayed percentile range is not guaranteed coverage.
Are the percentile endpoints guaranteed to cover the population mean?
No. Small samples, skew and estimator behaviour affect coverage; the displayed fifth and 195th ordered means are a teaching percentile range.
Which important population behaviour might be absent from the sample you are resampling?
Associated thinkers
Associations marked provisional are awaiting source review.
Further reading
Explore the original research or the teaching reference behind this experiment.