Calculator Inputs
Enter values separated by commas, spaces, semicolons, or new lines. The page uses one stacked layout, while the input controls switch to 3, 2, and 1 columns responsively.
Example Data Table
This sample dataset is included so you can test the calculator instantly and compare methods on the same observations.
| Observation | Value | Observation | Value |
|---|---|---|---|
| 1 | 12.4 | 7 | 11.9 |
| 2 | 11.8 | 8 | 12.2 |
| 3 | 13.1 | 9 | 13.8 |
| 4 | 14.0 | 10 | 12.9 |
| 5 | 12.7 | 11 | 13.3 |
| 6 | 13.5 | 12 | 12.6 |
Formula Used
The calculator applies bootstrap resampling with replacement. It repeatedly rebuilds samples of the same size as the original dataset and recomputes your chosen statistic.
Draw n observations with replacement from the original sample x = {x1, x2, ..., xn}.
For each bootstrap sample b, compute T*b = statistic(sample b).
Percentile interval = [Q(α/2), Q(1 - α/2)]
Basic interval = [2T0 - Q(1 - α/2), 2T0 - Q(α/2)]
Normal interval = T0 ± z × SEboot
T0 = statistic from the original sample
Bias = mean(T*b) - T0
SEboot = standard deviation of the bootstrap statistics
How to Use This Calculator
- Paste numeric values into the dataset box using commas, spaces, or line breaks.
- Select the statistic you want to estimate, such as mean, median, variance, or a threshold proportion.
- Choose a confidence interval method and set the confidence level.
- Enter the number of bootstrap samples, decimal precision, and histogram bins.
- Click Calculate Interval to show the result above the form.
- Review the method comparison table, distribution graph, and summary metrics.
- Use the CSV or PDF buttons to export your result for reports or team review.
Frequently Asked Questions
1. What is a bootstrap confidence interval?
It is an interval estimated by repeatedly resampling your observed data with replacement. The resulting distribution of the statistic helps approximate uncertainty without relying only on strict analytical formulas.
2. Which method should I choose first?
Percentile intervals are a practical default for many tasks. Basic intervals can adjust around the original estimate, while normal intervals are useful when the bootstrap distribution is fairly symmetric.
3. How many bootstrap samples are enough?
Around 1000 to 5000 resamples work well for many analyses. Use more when you need greater stability, higher confidence levels, or when the statistic has a skewed distribution.
4. Does the data need to be normally distributed?
No. Bootstrap methods are popular because they can work well even when the raw data is not normal. Still, very small samples or extreme outliers can affect interval reliability.
5. What statistics can this page estimate?
You can estimate confidence intervals for the mean, median, sum, sample standard deviation, sample variance, and a proportion defined by a success threshold.
6. How does proportion mode work?
In proportion mode, any value greater than or equal to the threshold is treated as a success. The calculator then bootstraps the share of successes across repeated resamples.
7. Why do my results change slightly between runs?
Bootstrap sampling uses randomness. If you want repeatable results, enter a fixed random seed. Increasing the number of resamples can also reduce small run-to-run differences.
8. What does the export include?
The CSV export includes summary values and the full bootstrap distribution. The PDF export creates a clean report snapshot with the key interval metrics and the chart.