statsmodels.stats.rates.power_poisson_ratio_2indep

statsmodels.stats.rates.power_poisson_ratio_2indep(rate1, rate2, nobs1, nobs_ratio=1, exposure=1, value=0, alpha=0.05, dispersion=1, alternative='smaller', method_var='alt', return_results=True)[source]

Power of test of ratio of 2 independent poisson rates.

This is based on Zhu and Zhu and Lakkis. It does not directly correspond to test_poisson_2indep.

Parameters:

  • rate1 (float) – Poisson rate for the first sample, treatment group, under the alternative hypothesis.

  • rate2 (float) – Poisson rate for the second sample, reference group, under the alternative hypothesis.

  • nobs1 (float or int) – Number of observations in sample 1.

  • nobs_ratio (float) – Sample size ratio, nobs2 = nobs_ratio * nobs1.

  • exposure (float) – Exposure for each observation. Total exposure is nobs1 * exposure and nobs2 * exposure.

  • alpha (float 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.

  • value (float) – Rate ratio, rate1 / rate2, under the null hypothesis.

  • dispersion (float) – Dispersion coefficient for quasi-Poisson. Dispersion different from one can capture over or under dispersion relative to Poisson distribution.

  • method_var ({"score", "alt"}) – The variance of the test statistic for the null hypothesis given the rates under 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".

  • alternative (string, '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’.

  • return_results (bool) – If true, then a results instance with extra information is returned, otherwise only the computed power is returned.

Returns:

results – 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.

powerfloat

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 :

std_null

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

std_alt

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

Return type:

results instance or float

References