StatReason

Bootstrap Calculator

Explore how much a statistic like the mean, median, or a correlation would plausibly vary if you could resample your data, using the bootstrap: repeatedly resampling your own data with replacement rather than assuming a textbook formula for its variability.

What this answers

This calculator answers "how much would this statistic plausibly vary if I could collect many more samples like mine?" for statistics that do not have a simple textbook formula for their uncertainty, or when you would rather not assume one.

How it is calculated

The bootstrap resamples your own data with replacement, the same size as your original sample, and recomputes the statistic on each resample, by default 9,999 times. The spread of those resampled statistics estimates how much the real statistic would vary across different samples from the same population. This calculator uses a seeded, fully reproducible pseudorandom generator; the same seed always produces the exact same resamples and the exact same result, displayed alongside the number of resamples used.

Worked example

For the values 1, 2, and 100, an extremely skewed tiny sample, the median is 2, but bootstrap resampling reveals just how uncertain that median actually is with only 3 values: the resample distribution and its percentile interval show a genuinely wide range of plausible medians, information a formula-based standard error would not convey nearly as directly.

Assumption audit

Calculated from your data: the observed statistic, the mean and standard deviation of the resampled statistics, and a percentile confidence interval, plus the exact seed and resample count used.
Evidence to review: your sample size; the bootstrap resamples only from the data you actually have, so a very small or unusual sample produces a bootstrap distribution that reflects that same smallness or peculiarity, not a magically larger effective sample.
You must verify: that your original sample was drawn in a way that makes it representative of the population you care about; a bootstrap cannot correct for a biased original sampling method, it can only describe the variability within the data you collected.

What this result does not mean

A bootstrap does not correct biased sampling and does not turn a small, unrepresentative sample into a reliable estimate of a larger population; it only describes how variable your chosen statistic is, given the sample you actually have.

Limitations

This calculator reports the percentile interval only; a bias-corrected and accelerated (BCa) interval, sometimes preferred for skewed statistics, is not implemented here, a documented simplification. The difference-of-means and correlation statistics require a second group or paired vector respectively.