statsmodels.stats.proportion.proportion_confint¶
- statsmodels.stats.proportion.proportion_confint(count, nobs, alpha=0.05, method='normal')[source]¶
confidence interval for a binomial proportion
- Parameters:
- count
int
orarray_array_like
number of successes, can be pandas Series or DataFrame
- nobs
int
total number of trials
- alpha
float
in
(0, 1) significance level, default 0.05
- method{‘normal’, ‘agresti_coull’, ‘beta’, ‘wilson’, ‘binom_test’}
default: ‘normal’ method to use for confidence interval, currently available methods :
normal : asymptotic normal approximation
agresti_coull : Agresti-Coull interval
beta : Clopper-Pearson interval based on Beta distribution
wilson : Wilson Score interval
jeffreys : Jeffreys Bayesian Interval
binom_test : experimental, inversion of binom_test
- count
- Returns:
Notes
Beta, the Clopper-Pearson exact interval has coverage at least 1-alpha, but is in general conservative. Most of the other methods have average coverage equal to 1-alpha, but will have smaller coverage in some cases.
The ‘beta’ and ‘jeffreys’ interval are central, they use alpha/2 in each tail, and alpha is not adjusted at the boundaries. In the extreme case when count is zero or equal to nobs, then the coverage will be only 1 - alpha/2 in the case of ‘beta’.
The confidence intervals are clipped to be in the [0, 1] interval in the case of ‘normal’ and ‘agresti_coull’.
Method “binom_test” directly inverts the binomial test in scipy.stats. which has discrete steps.
- TODO: binom_test intervals raise an exception in small samples if one
interval bound is close to zero or one.
References
https://en.wikipedia.org/wiki/Binomial_proportion_confidence_interval
- Brown, Lawrence D.; Cai, T. Tony; DasGupta, Anirban (2001). “Interval
Estimation for a Binomial Proportion”, Statistical Science 16 (2): 101–133. doi:10.1214/ss/1009213286.