statsmodels.stats.rates.power_poisson_diff_2indep(rate1, rate2, nobs1, nobs_ratio=1, alpha=0.05, value=0, method_var='score', alternative='two-sided', return_results=True)[source]

Power of ztest for the difference between two independent poisson rates.


Poisson rate for the first sample, treatment group, under the alternative hypothesis.


Poisson rate for the second sample, reference group, under the alternative hypothesis.

nobs1float or int

Number of observations in sample 1.


Sample size ratio, nobs2 = nobs_ratio * nobs1.

alphafloat in interval (0,1)

Significance level, e.g. 0.05, is the probability of a type I error, that is wrong rejections if the Null Hypothesis is true.


Difference between rates 1 and 2 under the null hypothesis.

method_var{“score”, “alt”}

The variance of the test statistic for the null hypothesis given the rates uder the alternative, can be either equal to the rates under the alternative method_var="alt", or estimated under the constrained of the null hypothesis, method_var="score".

alternativestr, ‘two-sided’ (default), ‘larger’, ‘smaller’

Alternative hypothesis whether the power is calculated for a two-sided (default) or one sided test. The one-sided test can be either ‘larger’, ‘smaller’.


If true, then a results instance with extra information is returned, otherwise only the computed power is returned.

resultsresults instance or float

If return_results is False, then only the power is returned. If return_results is True, then a results instance with the information in attributes is returned.


Power of the test, e.g. 0.8, is one minus the probability of a type II error. Power is the probability that the test correctly rejects the Null Hypothesis if the Alternative Hypothesis is true.

Other attributes in results instance include :


standard error of difference under the null hypothesis (without sqrt(nobs1))


standard error of difference under the alternative hypothesis (without sqrt(nobs1))



Stucke, Kathrin, and Meinhard Kieser. 2013. “Sample Size Calculations for Noninferiority Trials with Poisson Distributed Count Data.” Biometrical Journal 55 (2): 203–16.


PASS manual chapter 436

Last update: Jun 14, 2024