statsmodels.stats.rates.power_negbin_ratio_2indep¶

statsmodels.stats.rates.power_negbin_ratio_2indep(rate1, rate2, nobs1, nobs_ratio=1, exposure=1, value=1, alpha=0.05, dispersion=0.01, alternative='two-sided', method_var='alt', return_results=True)[source]¶

Power of test of ratio of 2 independent negative binomial rates.

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.

low : float

Lower equivalence margin for the rate ratio, rate1 / rate2.

upp : float

Upper equivalence margin for the rate ratio, rate1 / rate2.

nobs_ratio : float¶

Sample size ratio, nobs2 = nobs_ratio * nobs1.

exposure : float¶

Exposure for each observation. Total exposure is nobs1 * exposure and nobs2 * exposure.

value : float¶

Rate ratio, rate1 / rate2, under the null hypothesis.

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.

dispersion : float >= 0.¶

Dispersion parameter for Negative Binomial distribution. The Poisson limiting case corresponds to dispersion=0.

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", or based on a moment constrained estimate, method_var="ftotal". see references.

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