permutations-stats

Python-only permutation-based statistical tests, accelerated with numba.

Status

Statistical tests

Brunner Munzel [1], Mann Whitney Wilcoxon [2, 3], Wilcoxon signed rank test [3], and Friedman [4] tests are implemented.

Exact tests (all combinations) and approximate method (simulation) are available.

Functions for bootstrapping-based confidence intervals calculations for mean, median and standard deviation are also implemented (not documented yet).

Why this package ?

This work aims to provide fast permutation-based statistical tests in Python. Some tests are not available publicly in an exact mode (computing all possible permutations) or with simulations. If certain assumptions cannot be made about the data (such as normality) or if the sample is not large enough, the existing implementations should not be used.
For example, the Brunner Munzel [1] test is implemented in scipy but not with an exact calculation. The statistic can be used with the public API but it can take some time if ran several thousands of times (e.g. the p-value is also calculated for each iteration).

This packages reimplements the looping of permutations and statistical tests with numba. A few seconds are required to compile on the fly for the first function call. Then, acceleration is critical as shown in this output from tests comparing the Brunner Munzel statistic calculation with scipy:

tests/stat_tests.py
200 tests with 5 and 4 data points - Permutations-stats: 2.375s, Scipy: 0.076s, diff: -2.299s
.
200 tests with 3 and 3 data points - Permutations-stats: 0.002s, Scipy: 0.077s, diff: 0.075s
.
200 tests with 10 and 12 data points - Permutations-stats: 0.004s, Scipy: 0.079s, diff: 0.075s
.
10000 tests with 18 and 10 data points - Permutations-stats: 0.220s, Scipy: 3.806s, diff: 3.586s
.
20000 tests with 18 and 15 data points - Permutations-stats: 0.477s, Scipy: 7.645s, diff: 7.168s
.
30000 tests with 18 and 19 data points - Permutations-stats: 0.769s, Scipy: 11.468s, diff: 10.699s

Dependencies

• numpy
• numba

And for development testing only

• scipy ≥1.5
• pytest

Usage

Basic usage:

import numpy as np
from permutations_stats.permutations import permutation_test

# Sample data
x = np.arange(9)
y = (np.arange(9) -0.2) * 1.1

permutation_test(x, y, test="brunner_munzel")
# PermutationsResults(statistic=0.2776044311308564, pvalue=0.7475935828877005, permutations=24310, test='brunner_munzel', alternative='TWO_SIDED', method='exact')

More examples on usage.ipynb and a detailed demonstration on doc/demo.ipynb.

Perspective

• If sample sizes and/or the number of iterations are small, acceleration is not expected with numba, and using numpy alone should be the fastest option.
  Thresholds for numba use will be better determined to decide the function to call (without user intervention).

License

GNU General Public License v3.0 only.

Cite

If you find this software useful for your academic work, please cite ... TBD.

Acknowledgements

We would like to thank Marianne Paesmans, Lieveke Ameye and Luigi Moretti at Institut Jules Bordet for their support during the development of this package.

References

[1] Brunner, E. and Munzel, U. (2000), The Nonparametric Behrens‐Fisher Problem: Asymptotic Theory and a Small‐Sample Approximation. Biom. J., 42: 17-25. doi:10.1002/(SICI)1521-4036(200001)42:1<17::AID-BIMJ17>3.0.CO;2-U

[2] Mann, H. B. and D. R. Whitney (1947). "On a Test of Whether one of Two Random Variables is Stochastically Larger than the Other." Ann. Math. Statist. 18(1): 50-60.

[3] Wilcoxon, F. (1945). "Individual Comparisons by Ranking Methods." Biometrics Bulletin 1(6): 80-83.

[4] Friedman, M. (1937). "The Use of Ranks to Avoid the Assumption of Normality Implicit in the Analysis of Variance." Journal of the American Statistical Association 32(200): 675-701.