Bootstrap Confidence Interval Calculator: Resampling Simulator
Paste one or two samples, build a bootstrap distribution, and compare percentile, basic, t with bootstrap SE, and BCa intervals.
At a glance
- Computes
- Percentile, basic, t with bootstrap SE, and BCa confidence intervals
- You supply
- One sample, two samples, or paired x and y values
- Use when
- You have a real sample and want an interval without assuming a distribution
- Not for
- Sampling from a known population Central Limit Theorem Simulator
Runs in your browser. Your data is never uploaded and never put in the link.
Paste one sample and this page resamples it: percentile, basic, t with a bootstrap standard error and BCa intervals, ten thousand resamples on the primary draw, with a coverage mode that checks whether the interval you chose actually covers at the rate it claims. The distribution it plots is centered on your estimate, because the only population this page can draw from is your data. For parametric intervals with a distributional assumption behind them, confidence intervals computes Wilson, Clopper-Pearson, Wald and one-sample t. For the picture centered on a parameter rather than an estimate, the central limit theorem instrument draws from populations whose parameters are known exactly.
Original sample
1, 2, 2, 3, 3, 3, 4, 5, 8, 19
One bootstrap resample
5, 1, 3, 2, 5, 5, 3, 1, 3, 3
| Value | Times drawn |
|---|---|
| 1 | 2 |
| 2 | 1 |
| 3 | 4 |
| 4 | 0 |
| 5 | 3 |
| 8 | 0 |
| 19 | 0 |
Density by bootstrap mean; 28 bins of width 0.346 (fd rule)
95% percentile interval
2.597500 to 8.402500
Point estimate 5; 2,000 resamples; seed eigenstate-bootstrap-seed
| Method | Lower | Upper | Width |
|---|---|---|---|
| Percentile | 2.597500 | 8.402500 | 5.805000 |
| Basic | 1.597500 | 7.402500 | 5.805000 |
| t with bootstrap SE | 1.433681 | 8.566319 | 7.132638 |
| BCa | 3.000000 | 10.49433 | 7.494331 |
| Detail | Value |
|---|---|
| Bootstrap standard error | 1.576513 |
| Skewness g1 | 0.6004 |
| Excess kurtosis g2 | 0.1524 |
| Undefined resamples | 0 |
| Quantile convention | R type 7 |
| BCa bias correction | SciPy mid-rank ties |
Shown without JavaScript: 2,000 resamples of the 10-value skewed example, seed "eigenstate-bootstrap-seed". Enable JavaScript to paste your own data and run 10,000.
What resampling with replacement actually does
Draw one value from your sample, write it down, put it back, and repeat until the resample is the same size as the original. Duplicates and omissions are expected.
The four interval methods, and when each is right
The percentile interval reads quantiles directly. The basic interval reflects them around the point estimate. The t with bootstrap SE interval uses the resample standard error with a t multiplier. BCa adjusts for bias and acceleration.
Does the interval actually cover 95 percent of the time
Coverage mode draws fresh samples from a known population, builds an interval for each, and counts whether the interval contains the truth. Misses below and above the truth are reported separately.
Where the bootstrap fails
The bootstrap does not rescue a statistic that is undefined on the original sample. It is unreliable for a sample maximum, tiny samples, constant data, and resampling designs whose dependence structure is ignored.
Which quantile convention this page uses
Intervals use R type 7 linear interpolation, matching NumPy and SciPy. R boot uses a different rank convention, and BCa in R also uses a strict bias count while this page follows SciPy's mid-rank treatment of ties.
The bootstrap distribution and the sampling distribution are centered on different things
This plot is centered on your sample statistic because your sample is the only population it can draw from. A sampling distribution is centered on a population parameter. To watch that picture, use the central limit theorem instrument.
theta-star = T(resample(x)); interval = method(theta-star)
How?
How this is calculated
All four methods are computed from one shared replicate vector. The standard error uses the number of usable replicates minus one. BCa uses a scaled jackknife acceleration and SciPy's mid-rank bias convention.
Formula: theta-star = T(resample(x)); interval = method(theta-star)
Assumptions, limits, and privacy
Paste up to 5,000 values per column. Resamples run in this browser, data stays in memory, and links contain settings only. Replicate export is capped at the latest 100,000 values.
Sources
- What Teachers Should Know About the Bootstrap. The American Statistician preprint. Retrieved .
- scipy.stats.bootstrap. SciPy. Retrieved .
- boot: Bootstrap Functions. CRAN. Retrieved .