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Several two-samples tests for counts data

Project description

TwoSamplesBinomial: Two-sample testing for counts data

Usually in the context of a multiple testing approach to compare two or more frequency tables.


  • [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


  • 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


from scipy.stats import poisson

n = 100
k = 10

P = np.ones(n) / n
Q = P.copy()
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

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