exact-tests

This package implements the binomial, Hardy-Weinberg equilibrium, and Fisher's (2x2 and 2x3 so far) exact tests, along with corresponding discrete distributions (binomial, hypergeometric). scipy- and R-style interfaces are provided. cdf-like functions offer a fast 'approx' mode.

As of this writing, these functions (even in 'approx' mode) are more accurate, and often simultaneously more efficient, than their scipy counterparts: see the MPFR-comparison and benchmark scripts under utils/ . E.g.

$ utils/pbinom_accuracy.py
n in [2^5, 2^6): errRMS=0  approxErrRMS=7.31e-17  scipyErrRMS=0
n in [2^20, 2^21): errRMS=0  approxErrRMS=1.25e-15  scipyErrRMS=2.18e-15
n in [2^35, 2^36): errRMS=0  approxErrRMS=6.77e-15  scipyErrRMS=1.15e-14
$ utils/pbinom_accuracy.py -p 0.1  # scipy accuracy degrades more quickly with most values of p != 0.5, or k further from np
n in [2^5, 2^6): errRMS=0  approxErrRMS=1.06e-16  scipyErrRMS=4.22e-16
n in [2^20, 2^21): errRMS=0  approxErrRMS=1.62e-15  scipyErrRMS=1.23e-11
n in [2^35, 2^36): errRMS=0  approxErrRMS=5.48e-15  scipyErrRMS=3.47e-07
$ utils/pbinom_accuracy.py --z-score -2
n in [2^5, 2^6): errRMS=6.51e-17  approxErrRMS=2.48e-16  scipyErrRMS=1.96e-16
n in [2^20, 2^21): errRMS=0  approxErrRMS=5.08e-16  scipyErrRMS=1.01e-13
n in [2^35, 2^36): errRMS=0  approxErrRMS=6.87e-16  scipyErrRMS=1.66e-11
$ utils/pbinom_benchmark.py  # yes, default mode becomes slower than scipy for large n, that's why approx= exists
n=(2^5)-1: base=7.46e-07  approx=3e-07  scipy=3.03e-05 sec/iter
n=(2^20)-1: base=4.73e-05  approx=3.51e-06  scipy=2.93e-05 sec/iter
n=(2^35)-1: base=0.00114  approx=7.93e-05  scipy=9.52e-05 sec/iter

$ utils/binomtest_accuracy.py --z-score 1
n in [2^5, 2^6): errRMS=1.44e-16  scipyErrRMS=1.96e-16
n in [2^20, 2^21): errRMS=5.4e-16  scipyErrRMS=6e-14
n in [2^35, 2^36): errRMS=5.83e-16  scipyErrRMS=7.53e-12
$ utils/binomtest_benchmark.py --z-score 1  # ~100-200x speedup, better accuracy
n=(2^5)-1: base=1.18e-06  scipy=0.000235 sec/iter
n=(2^20)-1: base=4.13e-06  scipy=0.000546 sec/iter
n=(2^35)-1: base=5.93e-06  scipy=0.000887 sec/iter

$ utils/phyper_accuracy.py --z-score -0.5  # scipy accuracy degrades quickly
n in [2^5, 2^6): errRMS=0  approxErrRMS=1.72e-16  scipyErrRMS=2.84e-16
n in [2^20, 2^21): errRMS=0  approxErrRMS=3.01e-15  scipyErrRMS=1.73e-10
n in [2^35, 2^36): errRMS=0  approxErrRMS=3.93e-13  scipyErrRMS=1.05e-05
$ utils/phyper_benchmark.py --z-score -0.5  # scipy speed is ok, except...
n=(2^5)-1: base=8.83e-07  approx=2.83e-07  scipy=3.49e-05 sec/iter
n=(2^20)-1: base=6.96e-05  approx=5.37e-06  scipy=4.4e-05 sec/iter
n=(2^35)-1: base=0.00713  approx=0.000413  scipy=0.002 sec/iter
$ utils/phyper_benchmark.py --z-score 0.0001  # ...it blows up for large n when z approaches 0.
n=(2^5)-1: base=7.42e-07  approx=2.25e-07  scipy=3.52e-05 sec/iter
n=(2^20)-1: base=6.95e-05  approx=5.3e-06  scipy=0.000492 sec/iter
n=(2^35)-1: base=0.0146  approx=0.000851  scipy=2.7 sec/iter
$ utils/phyper_benchmark.py
n=(2^5)-1: base=7.5e-07  approx=2.04e-07  scipy=3.51e-05 sec/iter
n=(2^20)-1: base=6.88e-05  approx=5.32e-06  scipy=0.000492 sec/iter
n=(2^35)-1: base=0.0148  approx=0.000863  scipy=14.8 sec/iter

$ utils/fisher_exact_22_accuracy.py --z-score -1
n in [2^5, 2^6): errRMS=9.71e-17  scipyErrRMS=2.39e-16
n in [2^20, 2^21): errRMS=3.17e-15  scipyErrRMS=1.85e-10
n in [2^35, 2^36): errRMS=6.63e-13
$ utils/fisher_exact_22_benchmark.py --z-score -1  # ~75-250x speedup, better accuracy
n=(2^5)-1: base=1.07e-06  scipy=0.000258 sec/iter
n=(2^20)-1: base=8.34e-06  scipy=0.000667 sec/iter
n=(2^35)-1: base=0.000742 sec/iter

$ utils/odds_ratio_accuracy.py --z-score 1
n in [2^5, 2^6): estErrRMS=5.25e-16  ciLowErrRMS=7.12e-16  ciHighErrRMS=7.23e-16  scipyEstErrRMS=1.3e-15  scipyCiLowErrRMS=1.25e-14  scipyCiHighErrRMS=1.42e-15
n in [2^10, 2^11): estErrRMS=1.43e-16  ciLowErrRMS=2e-15  ciHighErrRMS=1.88e-15  scipyEstErrRMS=1.2e-14  scipyCiLowErrRMS=2.33e-14  scipyCiHighErrRMS=3.13e-14
n in [2^15, 2^16): estErrRMS=8.46e-17  ciLowErrRMS=7.79e-15  ciHighErrRMS=7.73e-15  scipyEstErrRMS=1.52e-12  scipyCiLowErrRMS=1.2e-11  scipyCiHighErrRMS=6.64e-13
n in [2^35, 2^36): estErrRMS=7.56e-17  ciLowErrRMS=8.35e-12  ciHighErrRMS=8.35e-12
$ utils/odds_ratio_benchmark.py --z-score 1  # 200x and larger speedups, better accuracy
n=(2^5)-1: est=8.75e-07  ci=8.21e-07  scipy_est=0.000456  scipy_ci=0.00254 sec/iter
n=(2^10)-1: est=7.71e-07  ci=1.62e-06  scipy_est=0.000512  scipy_ci=0.0273 sec/iter
n=(2^15)-1: est=3.03e-06  ci=6.29e-06  scipy_est=0.000702  scipy_ci=2.24 sec/iter
n=(2^35)-1: est=0.000943  ci=0.00172 sec/iter

$ utils/HWE_accuracy.py --maf 0.05 --z-score 1
n in [2^10, 2^11): errRMS=1.95e-16  snphweErrRMS=2.04e-16
n in [2^15, 2^16): errRMS=2.9e-16  snphweErrRMS=6.48e-16
n in [2^20, 2^21): errRMS=6.25e-16  snphweErrRMS=1.6e-15
$ utils/HWE_benchmark.py --maf 0.05 --z-score 1  # snphwe.snphwe() is accurate, but slow for biobank-scale cases (we're >200x as fast for n~=1m)
n=(2^10)-1: base=2.83e-07  snphwe=8.08e-07 sec/iter
n=(2^15)-1: base=4.5e-07  snphwe=1.24e-05 sec/iter
n=(2^20)-1: base=1.48e-06  snphwe=0.000388 sec/iter

The central building block is a high-precision log-factorial function utilizing the QD library (https://github.com/BL-highprecision/QD ).

Build instructions

PyPI:

python -m pip install 'pip>=20.3'
python -m pip install exact_tests

GitHub:

python -m pip install 'pip>=20.3'
python -m pip install -e 'git+https://github.com/chrchang/stats.git#egg=exact_tests&subdirectory=Python'

Or install from a cloned copy:

# clone repo
git clone https://github.com/chrchang/stats
# go to python folder
cd stats/Python
# install the package
python -m pip install -e .

You can test the package with pytest.

Example usage:
import exact_tests

exact_tests.binomtest(3, n=15, p=0.1, alternative="greater")
exact_tests.binomtest(2, 29, 0.1)
exact_tests.binomtest(2, 29, "0.1")
exact_tests.binomtest(2, 29, "0.1", midp=True)
exact_tests.binomtest(100, 10000, "0.000001", logp=True)
exact_tests.fisher_exact([[4, 0], [0, 4]], alternative="greater", midp=True)
exact_tests.fisher_exact([[10000, 20000], [30000, 40000], [50000, 60000]], logp=True)

Project links

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Key dates

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  • Released:
Newer release available (0.9.4)

1 maintainer

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Avatar for chrchang523 from gravatar.com chrchang523

Credits

Author: Christopher Chang

GitHub Statistics

Data verified by PyPI on Aug 2, 2026
The GitHub source repository was provided by the project maintainers and verified by PyPI at the time of upload. Stars, forks, and open issues/PRs are derived from that repository and have not been independently verified.

License expression

LGPL-3.0-only
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Requires

Python >=3.10

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0.9.4

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0.9.3

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0.9.1

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