/Statsmodels

# 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_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 (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 `jeffreys` : Jeffreys Bayesian Interval `binom_test` : experimental, inversion of binom_test ci_low, ci_upp – lower and upper confidence level with coverage (approximately) 1-alpha. When a pandas object is returned, then the index is taken from the `count`. float, ndarray, or pandas Series or DataFrame

#### 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

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 ?

© 2009–2012 Statsmodels Developers
© 2006–2008 Scipy Developers
© 2006 Jonathan E. Taylor