# 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])
```
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"description": "# TwoSamplesBinomial: Two-sample testing for counts data\nUsually in the context of a multiple testing approach to compare two or more frequency tables. Combine with ``multiple-hypothesis-testing`` to\nobtain a global test for the significance of the difference between the \ntables.\n\nReferences:\n- [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. \n- [2] C. B. Dean. (1992) Testing for Overdispersion in Poisson and Binomial Regression Models. Journal of the American Statistical Association\n\n\n## Methods:\n- ``bin_allocation_test`` (the test from [1])\n- ``bin_variance_test`` (test from [2])\n- ``bin_variance_test_df`` the same as ``bin_variance_test`` plus additional information\n\n\n### Additional auxiliary function of independent interest:\n - ``poisson_test`` Vectorized one-sided Poisson test with an option to do a randomized test\n - ``binom_test`` Vectorized one-sided binomial test with an option to do a randomized test\n - ``binom_test_two_sided`` Vectorized Two-sided binomial test with an option to do a randomized test\n - ``binom_test_two_sided_slow`` Vectorized two-sided binomial test using scipy.stats.binom_test\n\n## Example:\n```\nfrom twosample import bin_allocation_test, bin_variance_test\nfrom multitest import MultiTest\nimport numpy as np\n\nN = 100\nn = 500\neps = 0.1\nmu = 0.01\n\nP = np.ones(N) / N\nQ = P.copy()\nQ[np.random.rand(N) < eps] += mu\nQ = Q / Q.sum()\n\n \nsmp1 = np.random.multinomial(n, P) # sample form P\nsmp2 = np.random.multinomial(n, Q) # sample from Q\n\npvals_alloc = bin_allocation_test(smp1, smp2) # binomial P-values\npvals_var = bin_variance_test(smp1, smp2) # binomial P-values\n\nmt_alloc = MultiTest(pvals_alloc)\nmt_var = MultiTest(pvals_var)\n\nprint(\"HC(binomial_allocation) = \", mt_alloc.hc()[0])\nprint(\"HC(varaince) = \", mt_var.hc()[0])\n```\n",
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