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:¶

count1 : int¶

Count for first sample.

nobs1 : int¶

Sample size for first sample.

count2 : int¶

Count for the second sample.

nobs2 : int¶

Sample size for the second sample.

value : float¶

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.

method : string¶

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.

correction : bool¶

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_results : bool¶

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

Returns:¶

results – 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

Return type:¶

results instance or tuple