Bootstrap Confidence Interval in Python

Estimates a confidence interval for a statistic (like the mean) using bootstrap resampling in pure Python.

Medium Python 3.9+ Aug 9, 2026 A/B testing & experimentation 15 views 0 copies

bootstrap confidence-interval statistics resampling numpy

Python code

23 lines

Python 3.9+

import random


def bootstrap_ci(data, statistic, n_bootstraps=1000, ci_level=0.95, seed=42):
    random.seed(seed)
    n = len(data)
    boot_stats = []

    for _ in range(n_bootstraps):
        sample = [random.choice(data) for _ in range(n)]
        boot_stats.append(statistic(sample))

    boot_stats.sort()
    lower_idx = int((1 - ci_level) / 2 * n_bootstraps)
    upper_idx = int((1 + ci_level) / 2 * n_bootstraps) - 1

    return boot_stats[lower_idx], boot_stats[upper_idx]


if __name__ == "__main__":
    data = [12, 15, 14, 10, 13, 11, 16, 14, 12, 13]
    ci_low, ci_high = bootstrap_ci(data, statistic=lambda x: sum(x) / len(x))
    print(f"95% Bootstrap CI for mean: [{ci_low:.2f}, {ci_high:.2f}]")

Output

stdout

95% Bootstrap CI for mean: [11.90, 14.20]

How it works

The bootstrap_ci function repeatedly resamples the original data with replacement, computes the statistic for each resample, and then uses the sorted list of bootstrap statistics to find the percentile-based confidence interval. Setting seed ensures reproducibility, which is important for debugging and sharing results. The function accepts any callable statistic, making it generic for means, medians, or custom metrics.

Common mistakes

Not setting a seed, which makes results non-reproducible
Using `random.sample` without replacement instead of `random.choice` with replacement
Forgetting that the statistic function must handle the resampled data correctly

Variations

Use `numpy.random.choice` for faster resampling on larger datasets
Employ the `bootstrap` function from `scipy.stats` for built-in CI computation

Real-world use cases

Calculating the confidence interval for an A/B test’s conversion rate difference without parametric assumptions.
Estimating the uncertainty of a median or other robust statistic in data analysis reports.
Validating the stability of a machine learning model’s performance metric on limited data.

Bootstrap Confidence Interval in Python

Python code

Output

How it works

Common mistakes

Variations

Real-world use cases

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Python code

Output

How it works

Common mistakes

Variations

Real-world use cases

More from A/B testing & experimentation

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