statsmodels.stats.rates.etest_poisson_2indep

statsmodels.stats.rates.etest_poisson_2indep(count1, exposure1, count2, exposure2, ratio_null=None, value=None, method='score', compare='ratio', alternative='two-sided', ygrid=None, y_grid=None)[source]

E-test for ratio of two sample Poisson rates.

Rates are defined as expected count divided by exposure.

The Null and alternative hypothesis for the rates, rate1 and rate2, of two independent Poisson samples are

for compare = ‘diff’

  • H0: rate1 - rate2 - value = 0

  • H1: rate1 - rate2 - value != 0 if alternative = ‘two-sided’

  • H1: rate1 - rate2 - value > 0 if alternative = ‘larger’

  • H1: rate1 - rate2 - value < 0 if alternative = ‘smaller’

for compare = ‘ratio’

  • H0: rate1 / rate2 - value = 0

  • H1: rate1 / rate2 - value != 0 if alternative = ‘two-sided’

  • H1: rate1 / rate2 - value > 0 if alternative = ‘larger’

  • H1: rate1 / rate2 - value < 0 if alternative = ‘smaller’

Parameters:
count1int

Number of events in first sample

exposure1float

Total exposure (time * subjects) in first sample

count2int

Number of events in first sample

exposure2float

Total exposure (time * subjects) in first sample

ratio_null: float

Ratio of the two Poisson rates under the Null hypothesis. Default is 1. Deprecated, use value instead.

valuefloat

Value of the ratio or diff of 2 independent rates under the null hypothesis. Default is equal rates, i.e. 1 for ratio and 0 for diff.

method{“score”, “wald”}

Method for the test statistic that defines the rejection region.

alternativestr

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

y_gridNone or 1-D ndarray

Grid values for counts of the Poisson distribution used for computing the pvalue. By default truncation is based on an upper tail Poisson quantiles.

ygridNone or 1-D ndarray

Same as y_grid. Deprecated. If both y_grid and ygrid are provided, ygrid will be ignored.

Returns:
stat_samplefloat

test statistic for the sample

pvaluefloat

References

Gu, Ng, Tang, Schucany 2008: Testing the Ratio of Two Poisson Rates, Biometrical Journal 50 (2008) 2, 2008 Ng, H. K. T., K. Gu, and M. L. Tang. 2007. “A Comparative Study of Tests for the Difference of Two Poisson Means.” Computational Statistics & Data Analysis 51 (6): 3085–99. https://doi.org/10.1016/j.csda.2006.02.004.