statsmodels.stats.proportion.proportions_ztest¶
- statsmodels.stats.proportion.proportions_ztest(count, nobs, value=None, alternative='two-sided', prop_var=False)[source]¶
Test for proportions based on normal (z) test
- Parameters:
- count{
int
, array_like} the number of successes in nobs trials. If this is array_like, then the assumption is that this represents the number of successes for each independent sample
- nobs{
int
, array_like} the number of trials or observations, with the same length as count.
- value
float
, array_like orNone
,optional
This is the value of the null hypothesis equal to the proportion in the case of a one sample test. In the case of a two-sample test, the null hypothesis is that prop[0] - prop[1] = value, where prop is the proportion in the two samples. If not provided value = 0 and the null is prop[0] = prop[1]
- alternative
str
in
[‘two-sided’, ‘smaller’, ‘larger’] The alternative hypothesis can be either two-sided or one of the one- sided tests, smaller means that the alternative hypothesis is
prop < value
and larger meansprop > value
. In the two sample test, smaller means that the alternative hypothesis isp1 < p2
and larger meansp1 > p2
wherep1
is the proportion of the first sample andp2
of the second one.- prop_var
False
orfloat
in
(0, 1) If prop_var is false, then the variance of the proportion estimate is calculated based on the sample proportion. Alternatively, a proportion can be specified to calculate this variance. Common use case is to use the proportion under the Null hypothesis to specify the variance of the proportion estimate.
- count{
- Returns:
Notes
This uses a simple normal test for proportions. It should be the same as running the mean z-test on the data encoded 1 for event and 0 for no event so that the sum corresponds to the count.
In the one and two sample cases with two-sided alternative, this test produces the same p-value as
proportions_chisquare
, since the chisquare is the distribution of the square of a standard normal distribution.Examples
>>> count = 5 >>> nobs = 83 >>> value = .05 >>> stat, pval = proportions_ztest(count, nobs, value) >>> print('{0:0.3f}'.format(pval)) 0.695
>>> import numpy as np >>> from statsmodels.stats.proportion import proportions_ztest >>> count = np.array([5, 12]) >>> nobs = np.array([83, 99]) >>> stat, pval = proportions_ztest(count, nobs) >>> print('{0:0.3f}'.format(pval)) 0.159