statsmodels.stats.proportion.test_proportions_2indep¶

statsmodels.stats.proportion.test_proportions_2indep(count1, nobs1, count2, nobs2, value=None, method=None, compare='diff', alternative='two-sided', correction=True, return_results=True)[source]¶

Hypothesis test for comparing two independent proportions

This assumes that we have two independent binomial samples.

The Null and alternative hypothesis are

for compare = ‘diff’

H0: prop1 - prop2 - value = 0
H1: prop1 - prop2 - value != 0 if alternative = ‘two-sided’
H1: prop1 - prop2 - value > 0 if alternative = ‘larger’
H1: prop1 - prop2 - value < 0 if alternative = ‘smaller’

for compare = ‘ratio’

H0: prop1 / prop2 - value = 0
H1: prop1 / prop2 - value != 0 if alternative = ‘two-sided’
H1: prop1 / prop2 - value > 0 if alternative = ‘larger’
H1: prop1 / prop2 - value < 0 if alternative = ‘smaller’

for compare = ‘odds-ratio’

H0: or - value = 0
H1: or - value != 0 if alternative = ‘two-sided’
H1: or - value > 0 if alternative = ‘larger’
H1: or - value < 0 if alternative = ‘smaller’

where odds-ratio or = prop1 / (1 - prop1) / (prop2 / (1 - prop2))

Parameters:¶

count1int

Count for first sample.

nobs1int

Sample size for first sample.

count2int

Count for the second sample.

nobs2int

Sample size for the second sample.

valuefloat

Value of the difference, risk ratio or odds ratio of 2 independent proportions under the null hypothesis. Default is equal proportions, 0 for diff and 1 for risk-ratio and for odds-ratio.

methodstr

Method for computing the hypothesis test. If method is None, then a default method is used. The default might change as more methods are added.

diff:

‘wald’,
‘agresti-caffo’
‘score’ if correction is True, then this uses the degrees of freedom
correction nobs / (nobs - 1) as in Miettinen Nurminen 1985

ratio:

‘log’: wald test using log transformation
‘log-adjusted’: wald test using log transformation,
adds 0.5 to counts
‘score’: if correction is True, then this uses the degrees of freedom
correction nobs / (nobs - 1) as in Miettinen Nurminen 1985

odds-ratio:

‘logit’: wald test using logit transformation
‘logit-adjusted’: wald test using logit transformation,
adds 0.5 to counts
‘logit-smoothed’: wald test using logit transformation, biases
cell counts towards independence by adding two observations in total.
‘score’ if correction is True, then this uses the degrees of freedom
correction nobs / (nobs - 1) as in Miettinen Nurminen 1985

compare{‘diff’, ‘ratio’ ‘odds-ratio’}

If compare is diff, then the hypothesis test is for the risk difference diff = p1 - p2. If compare is ratio, then the hypothesis test is for the risk ratio defined by ratio = p1 / p2. If compare is odds-ratio, then the hypothesis test is for the odds-ratio defined by or = p1 / (1 - p1) / (p2 / (1 - p2)

alternative{‘two-sided’, ‘smaller’, ‘larger’}

alternative hypothesis, which can be two-sided or either one of the one-sided tests.

correctionbool

If correction is True (default), then the Miettinen and Nurminen small sample correction to the variance nobs / (nobs - 1) is used. Applies only if method=’score’.

return_resultsbool

If true, then a results instance with extra information is returned, otherwise a tuple with statistic and pvalue is returned.

Returns:¶

resultsresults instance or tuple

If return_results is True, then a results instance with the information in attributes is returned. If return_results is False, then only statistic and pvalue are returned.

statisticfloat: test statistic asymptotically normal distributed N(0, 1)
pvaluefloat: p-value based on normal distribution
other attributes :: additional information about the hypothesis test