7.10.9.1. 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 or array number of successes nobs : int total number of trials alpha : float in (0, 1) significance level, default 0.05 method : string in [‘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 jeffrey : Jeffrey’s Bayesian Interval binom_test : experimental, inversion of binom_test

Returns:

ci_low, ci_upp : float lower and upper confidence level with coverage (approximately) 1-alpha. Note: Beta has coverage coverage is only 1-alpha on average for some other methods.)

Notes

Beta, the Clopper-Pearson 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.

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

http://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. TODO: Is this the correct one ?