Binoculars: Binomial Confidence Intervals

This is a small package that provides functions to compute the confidence interval for a binomial proportion. I made it because I spend altogether too much time staring at the Binomial proportion confidence interval wiki page.

Presently, the package implements:

• The Normal Approximation
• The Wilson Interval (no continuity correction)
• Jeffrey's interval (via scipy.stats.beta)
• Clopper-Pearson interval (also via scipy.stats.beta)

If you haven't spent a lot of time thinking about which interval you should use (and why would you want to?), I suggest using the Wilson interval or Jeffrey's interval. Jeffrey's interval is returned by default by the binomial_confidence function in this package.

You oughtn't use the normal approximation if you don't have to. It produces patently inaccurate values with low/high probabilities at low Ns. The plot at the top of this readme shows the normal approximation producing lower lower bounds of less than 0 in these cases.

Install

pip install binoculars

Usage

from binoculars import binomial_confidence

N, p = 100, 0.2

binomial_confidence(p, N)  # default to jeffrey's interval
# (0.1307892803998113, 0.28628125447599173)

binomial_confidence(p, N, tail='lower') # grab one tail
# 0.1307892803998113

# set Z value
binomial_confidence(p, N, tail='lower', z=2.58)
# 0.11212431621448567

# choose your method

binomial_confidence(p, N, method='normal')
# (0.12160000000000001, 0.2784)

binomial_confidence(p, N, method='wilson')
# (0.1333659225590988, 0.28883096192650237)

Development

I honestly do not imagine touching this a lot. But maybe you want to add one of the other interval methods?

1. Make a python 3.6+ venv
2. pip install -e .[test]
3. black lib --check
4. pytest

Later (?)

• Add confidence intervals for odds ratios, differences
• Add the unimplemented intervals
• Add plots comparing the intervals to readme.