Bootstrap Calculator: Resampling-Based Statistical Inference
What is Bootstrap?
Bootstrap repeatedly resamples the original sample with replacement — drawing n observations B times — computes the target statistic (mean, median, standard deviation, Cpk, correlation, and so on) from each resample, and obtains its sampling distribution, giving standard errors and confidence intervals without normality assumptions or analytic formulas. It is especially suited to small samples, skewed distributions and complex statistics whose standard error has no closed form, and is a general tool of modern statistical inference.
When to Use It
Use it for small samples (n < 30), clearly skewed data, and statistics without an analytic standard error such as the median, quantiles, ratios or complex capability indices; also for comparing two groups with resampling tests and for regression coefficient inference. Bootstrap cannot fix data quality: it assumes the sample represents the population, so a biased sampling process gives biased resampling conclusions.
How to Use It (Step by Step)
Paste the sample data, choose the target statistic and the resampling count B (commonly 1,000–10,000), and the tool performs the resampling and outputs the estimate, standard error, 95% percentile and BCa confidence intervals, and a histogram of the bootstrap distribution. Set a random seed to make results reproducible; about 5,000 resamples is enough for routine analysis.
Key Formulas / Example
The percentile interval takes the 2.5th and 97.5th percentiles of the B bootstrap estimates. The bias-corrected and accelerated (BCa) interval further adjusts the endpoints for bias and skewness, giving closer-to-nominal coverage when the distribution is asymmetric; a markedly asymmetric bootstrap histogram is a sign to prefer BCa.