Analyze means, medians, and proportions through resampling controls. Inspect intervals, errors, and distributions with clarity. Export clean reports and plots for reproducible decisions today.
This section appears above the form after calculation.
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| # | Bootstrap Estimate |
|---|---|
| Run a calculation to see preview rows. | |
Use the responsive input grid below. Large screens show three columns, smaller screens show two, and mobile displays one column.
This sample illustrates a numeric dataset suitable for mean or median bootstrap intervals.
| Observation | Value |
|---|---|
| 1 | 12 |
| 2 | 15 |
| 3 | 14 |
| 4 | 18 |
| 5 | 16 |
| 6 | 19 |
| 7 | 21 |
| 8 | 17 |
| 9 | 20 |
| 10 | 22 |
| 11 | 24 |
| 12 | 18 |
| 13 | 16 |
| 14 | 23 |
| 15 | 25 |
Original sample statistic:
θ̂ = s(x₁, x₂, ..., xₙ)
Bootstrap resample:
Draw n observations with replacement from the original data to form each resample x*ᵇ.
Bootstrap statistic for each resample:
θ̂*ᵇ = s(x*ᵇ) for b = 1, 2, ..., B
Bootstrap standard error:
SEboot = √[ Σ(θ̂*ᵇ - mean(θ̂*))² / (B - 1) ]
Percentile interval:
[ Q(α/2), Q(1-α/2) ] from the sorted bootstrap estimates.
Basic interval:
[ 2θ̂ - Q(1-α/2), 2θ̂ - Q(α/2) ]
Normal interval:
[ θ̂ - z·SEboot, θ̂ + z·SEboot ]
Proportion mode: The calculator converts values meeting the success threshold into ones, and the rest into zeros. The bootstrap statistic then becomes the resampled mean of that binary series.
It estimates confidence intervals using bootstrap resampling. You can analyze a mean, median, or proportion and compare percentile, basic, and normal interval methods from the same dataset.
Use them when theoretical formulas are difficult, sample distributions are unclear, or you want a flexible interval from the observed data itself. They are especially useful for non-normal or small samples.
Percentile uses empirical bootstrap quantiles. Basic reflects the percentile bounds around the original estimate. Normal uses a z value and bootstrap standard error. Results can differ when distributions are skewed.
A few thousand resamples usually work well for routine analysis. Larger values can improve stability, but they also increase calculation time. Start with 2000 to 5000 and increase when needed.
Any numeric dataset can be used if you define a success threshold. Values at or above the threshold count as successes, while smaller values count as failures in each resample.
Bootstrap distributions can be skewed. Percentile and basic intervals often reflect that asymmetry, especially with small samples, outliers, or statistics like medians and proportions near boundaries.
Yes, but the statistic matters. Means remain sensitive to outliers, while medians are usually more robust. Always inspect the histogram to understand whether resampled estimates appear skewed or unstable.
They include the main summary metrics and a preview of bootstrap estimates. The CSV also saves the full distribution, which is useful for auditing, sharing, or later visualization.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.