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Nov. 16, 2017
Jan. 18, 2017

bootstrapped - confidence intervals made easy

bootstrapped is a Python library that allows you to build confidence intervals from data. This is useful in a variety of contexts - including during ad-hoc a/b test analysis.

Motivating Example - A/B Test

Imagine we own a website and think changing the color of a 'subscribe' button will improve signups. One method to measure the improvement is to conduct an A/B test where we show 50% of people the old version and 50% of the people the new version. We can use the bootstrap to understand how much the button color improves responses and give us the error bars associated with the test - this will give us lower and upper bounds on how good we should expect the change to be!

The Gist - Mean of a Sample

Given a sample of data - we can generate a bunch of new samples by 're-sampling' from what we have gathered. We calculate the mean for each generated sample. We can use the means from the generated samples to understand the variation in the larger population and can construct error bars for the true mean.

bootstrapped - Benefits

  • Efficient computation of confidence intervals
  • Functions to handle single populations and a/b tests
  • Functions to understand statistical power
  • Multithreaded support to speed-up bootstrap computations
  • Dense and sparse array support

Example Usage

import numpy as np
import bootstrapped.bootstrap as bs
import bootstrapped.stats_functions as bs_stats

mean = 100
stdev = 10

population = np.random.normal(loc=mean, scale=stdev, size=50000)

# take 1k 'samples' from the larger population
samples = population[:1000]

print(bs.bootstrap(samples, stat_func=bs_stats.mean))
>> 100.08  (99.46, 100.69)

print(bs.bootstrap(samples, stat_func=bs_stats.std))
>> 9.49  (9.92, 10.36)

Extended Examples


bootstrapped requires numpy. The power analysis functions require matplotlib and pandas.


pip install bootstrapped

How bootstrapped works

bootstrapped provides pivotal (aka empirical) based confidence intervals based on bootstrap re-sampling with replacement. The percentile method is also available.

For more information please see:

  1. Bootstrap confidence intervals (good intro)
  2. An introduction to Bootstrap Methods
  3. The Bootstrap, Advanced Data Analysis
  4. When the bootstrap dosen't work
  5. (book) An Introduction to the Bootstrap
  6. (book) Bootstrap Methods and their Application

See the CONTRIBUTING file for how to help out.


Spencer Beecher, Don van der Drift, David Martin, Lindsay Vass, Sergey Goder, Benedict Lim, and Matt Langner.

Special thanks to Eytan Bakshy.


bootstrapped is BSD-licensed. We also provide an additional patent grant.

Latest Releases
 May. 29 2017
 May. 29 2017