two-sample-binomial 0.0.4

Several two-samples tests for count data

TwoSamplesBinomial: Two-sample testing for counts data

Usually in the context of a multiple testing approach to compare two or more frequency tables. Combine with multiple-hypothesis-testing to obtain a global test for the significance of the difference between the tables.

References:

• [1] D. L. Donoho and A. Kipnis. (2022) Higher criticism to compare two large frequency tables, with sensitivity to possible rare and weak differences. Annals of Statistics.
• [2] C. B. Dean. (1992) Testing for Overdispersion in Poisson and Binomial Regression Models. Journal of the American Statistical Association

Methods:

• bin_allocation_test (the test from [1])
• bin_variance_test (test from [2])
• bin_variance_test_df the same as bin_variance_test plus additional information

Additional auxiliary function of independent interest:

• poisson_test Vectorized one-sided Poisson test with an option to do a randomized test
• binom_test Vectorized one-sided binomial test with an option to do a randomized test
• binom_test_two_sided Vectorized Two-sided binomial test with an option to do a randomized test
• binom_test_two_sided_slow Vectorized two-sided binomial test using scipy.stats.binom_test

Example:

from twosample import bin_allocation_test, bin_variance_test
from multitest import MultiTest
import numpy as np

N = 100
n = 500
eps = 0.1
mu = 0.01

P = np.ones(N) / N
Q = P.copy()
Q[np.random.rand(N) < eps] += mu
Q = Q / Q.sum()

  
smp1 = np.random.multinomial(n, P)  # sample form P
smp2 = np.random.multinomial(n, Q)  # sample from Q

pvals_alloc = bin_allocation_test(smp1, smp2) # binomial P-values
pvals_var = bin_variance_test(smp1, smp2) # binomial P-values

mt_alloc = MultiTest(pvals_alloc)
mt_var = MultiTest(pvals_var)

print("HC(binomial_allocation) = ", mt_alloc.hc()[0])
print("HC(varaince) = ", mt_var.hc()[0])