statsmodels.stats.rates.test_poisson_2indep(count1, exposure1, count2, exposure2, ratio_null=1, method='score', alternative='two-sided', etest_kwds=None)[source]

test for ratio of two sample Poisson intensities

If the two Poisson rates are g1 and g2, then the Null hypothesis is

  • H0: g1 / g2 = ratio_null

against one of the following alternatives

  • H1_2-sided: g1 / g2 != ratio_null

  • H1_larger: g1 / g2 > ratio_null

  • H1_smaller: g1 / g2 < ratio_null


Number of events in first sample.


Total exposure (time * subjects) in first sample.


Number of events in second sample.


Total exposure (time * subjects) in second sample.

ratio: float

ratio of the two Poisson rates under the Null hypothesis. Default is 1.


Method for the test statistic and the p-value. Defaults to ‘score’. Current Methods are based on Gu et. al 2008. Implemented are ‘wald’, ‘score’ and ‘sqrt’ based asymptotic normal distribution, and the exact conditional test ‘exact-cond’, and its mid-point version ‘cond-midp’. method=’etest’ and method=’etest-wald’ provide pvalues from etest_poisson_2indep using score or wald statistic respectively. see Notes.


The alternative hypothesis, H1, has to be one of the following

  • ‘two-sided’: H1: ratio of rates is not equal to ratio_null (default)

  • ‘larger’ : H1: ratio of rates is larger than ratio_null

  • ‘smaller’ : H1: ratio of rates is smaller than ratio_null

etest_kwds: dictionary

Additional parameters to be passed to the etest_poisson_2indep function, namely ygrid.

resultsinstance of HolderTuple class

The two main attributes are test statistic statistic and p-value pvalue.


  • ‘wald’: method W1A, wald test, variance based on separate estimates

  • ‘score’: method W2A, score test, variance based on estimate under Null

  • ‘wald-log’: W3A

  • ‘score-log’ W4A

  • ‘sqrt’: W5A, based on variance stabilizing square root transformation

  • ‘exact-cond’: exact conditional test based on binomial distribution

  • ‘cond-midp’: midpoint-pvalue of exact conditional test

  • ‘etest’: etest with score test statistic

  • ‘etest-wald’: etest with wald test statistic


Gu, Ng, Tang, Schucany 2008: Testing the Ratio of Two Poisson Rates, Biometrical Journal 50 (2008) 2, 2008