statsmodels.stats.rates.nonequivalence_poisson_2indep#

statsmodels.stats.rates.nonequivalence_poisson_2indep(count1, exposure1, count2, exposure2, low, upp, method='score', compare='ratio')[source]#

Test for non-equivalence, minimum effect for poisson

This reverses null and alternative hypothesis compared to equivalence testing. The null hypothesis is that the effect, ratio (or diff), is in an interval that specifies a range of irrelevant or unimportant differences between the two samples.

The Null and alternative hypothesis comparing the ratio of rates are

for compare = ‘ratio’:

  • H0: low < rate1 / rate2 < upp

  • H1: rate1 / rate2 <= low or upp <= rate1 / rate2

for compare = ‘diff’:

  • H0: rate1 - rate2 <= low or upp <= rate1 - rate2

  • H1: low < rate - rate < upp

Parameters:
count1int

Number of events in first sample.

exposure1float

Total exposure (time * subjects) in first sample.

count2int

Number of events in second sample.

exposure2float

Total exposure (time * subjects) in second sample.

low, uppfloat

Equivalence margin for the ratio or difference of Poisson rates.

methodstr

TOST uses test_poisson_2indep and has the same methods.

compare{‘diff’, ‘ratio’}

Default is “ratio”. If compare is ratio, then the test is for the rate ratio defined by ratio = rate1 / rate2. If compare is diff, then the test is for diff = rate1 - rate2.

Returns:
resultsinstance of HolderTuple class

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

Notes

This is implemented as two one-sided tests at the minimum effect boundaries (low, upp) with (nominal) size alpha / 2 each. The size of the test is the sum of the two one-tailed tests, which corresponds to an equal-tailed two-sided test. If low and upp are equal, then the result is the same as the standard two-sided test.

The p-value is computed as 2 * min(pvalue_low, pvalue_upp) in analogy to two-sided equal-tail tests.

In large samples the nominal size of the test will be below alpha.

References

[1]

Hodges, J. L., Jr., and E. L. Lehmann. 1954. Testing the Approximate Validity of Statistical Hypotheses. Journal of the Royal Statistical Society, Series B (Methodological) 16: 261-68.

[2]

Kim, Jae H., and Andrew P. Robinson. 2019. “Interval-Based Hypothesis Testing and Its Applications to Economics and Finance.” Econometrics 7 (2): 21. https://doi.org/10.3390/econometrics7020021.