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
str
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.
- count1
- Returns:
- results
results
instance
ortuple
If return_results is True, then a results instance with the information in attributes is returned. If return_results is False, then only
statistic
andpvalue
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
- results
Notes
- Status: experimental, API and defaults might still change.
More
methods
will be added.
The current default methods are
‘diff’: ‘agresti-caffo’,
‘ratio’: ‘log-adjusted’,
‘odds-ratio’: ‘logit-adjusted’