Bootstrap Calculator

The Bootstrap Calculator performs bootstrap resampling to estimate confidence intervals and standard errors for your sample data. Enter your sample values, choose the number of bootstrap iterations, and select your desired confidence level — you get back the bootstrap mean, standard error, confidence interval bounds, and a distribution summary.

Enter your numeric sample values separated by commas.

Higher iterations give more stable estimates. 1000 is typically sufficient.

The probability that the true parameter falls within the computed interval.

Choose which statistic to estimate using bootstrap resampling.

Results

Bootstrap Estimate

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Bootstrap Standard Error

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CI Lower Bound

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CI Upper Bound

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Sample Size (n)

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Original Sample Statistic

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Bootstrap Distribution of Statistic

Results Table

Frequently Asked Questions

What is bootstrap resampling?

Bootstrap resampling is a statistical technique that repeatedly draws samples (with replacement) from your observed data to estimate the sampling distribution of a statistic. It allows you to compute confidence intervals and standard errors without assuming a specific distribution.

How many bootstrap iterations should I use?

A minimum of 1000 iterations is generally recommended for stable estimates. For more precise confidence intervals, especially at the 99% level, 5000–10000 iterations are preferable. More iterations increase accuracy but require more computation.

What is a bootstrap confidence interval?

A bootstrap confidence interval is a range of values within which the true population parameter is estimated to lie with a given probability (e.g., 95%). It is computed from the percentiles of the bootstrap distribution — for a 95% CI, the 2.5th and 97.5th percentiles are used.

What statistics can I estimate with bootstrapping?

Bootstrap resampling can estimate virtually any statistic — mean, median, standard deviation, correlation, regression coefficients, and more. This calculator supports mean, median, and standard deviation estimation.

What does bootstrap standard error mean?

The bootstrap standard error is the standard deviation of the bootstrap distribution of your chosen statistic. It estimates how much the statistic would vary across repeated samples from the same population.

Does bootstrap resampling require a large sample size?

Bootstrap methods work best with reasonably sized samples (typically n ≥ 20). With very small samples (n < 10), the bootstrap distribution may not accurately represent the true sampling distribution, leading to unreliable confidence intervals.

What is the difference between the original statistic and the bootstrap estimate?

The original statistic is calculated directly from your input data. The bootstrap estimate is the average of the statistic across all resampled datasets. They are usually very close, but slight differences reflect the variability captured by the resampling process.

Is bootstrap resampling the same as cross-validation?

No. Bootstrap resampling draws samples with replacement from your data to estimate a statistic's distribution, primarily for inference. Cross-validation splits data into training and test sets to evaluate model predictive performance. They serve different statistical purposes.

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