Optimized confidence intervals for binomial proportions

Last update (strlen doesn't work any more on images): January 15, 2012.

The program display the optimized values of binomial distribution 95% confidence intervals for proportion from n = 2 to n = 1000 computed using a completely new and original algorithm. Usage:

For (n = 20, X = 5):
http://l.academicdirect.ro/Statistics/binomial_distribution/?n=20

For (n = 20):
http://l.academicdirect.ro/Statistics/binomial_distribution/?n=20&X=5

Sorana D. BOLBOACA, Lorentz JÄNTSCHI, Optimized Confidence Intervals for Binomial Distributed Samples, International Journal of Pure and Applied Mathematics, Academic Publications, ISSN 1311-8080, Sofia, Bulgaria, 47(1), p. 1-8, Zbl pre05492615, 2008.
References for behaviour of other CI calculation methods:

Binomial Distribution Sample Confidence Intervals Estimation 1. Sampling and Medical Key Parameters Calculation, Tudor DRUGAN, Sorana BOLBOACĂ, Lorentz JÄNTSCHI, Andrei ACHIMAS CADARIU, http://lejpt.academicdirect.org/A03.

Binomial Distribution Sample Confidence Intervals Estimation 2. Proportion-like Medical Key Parameters, Sorana BOLBOACĂ, Andrei ACHIMAS CADARIU, http://lejpt.academicdirect.org/A03.

Results for (n = 20):

	ci			er
0.0							0%
0.5							5%
1.0							10%
	0.0	0.5	1.0	0	10	20

n	X	_95%ci_L%	_95%ci_U%	_95%ci_L	_95%ci_U	er	X_L	X_U
20	0	0	14.75	0.0000	0.1475	0.000	0	3
20	1	0.25	24.75	0.0025	0.2475	7.548	0	5
20	2	0.25	29.75	0.0025	0.2975	4.317	0	6
20	3	5.25	39.75	0.0525	0.3975	6.069	1	8
20	4	5.25	44.75	0.0525	0.4475	4.367	1	9
20	5	10.25	49.75	0.1025	0.4975	6.524	2	10
20	6	10.25	54.75	0.1025	0.5475	5.263	2	11
20	7	15.25	59.75	0.1525	0.5975	3.170	3	12
20	8	20.25	64.75	0.2025	0.6475	3.699	4	13
20	9	25.25	69.75	0.2525	0.6975	4.028	5	14
20	10	25.25	74.75	0.2525	0.7475	4.139	5	15
20	11	30.25	74.75	0.3025	0.7475	4.028	6	15
20	12	35.25	79.75	0.3525	0.7975	3.699	7	16
20	13	40.25	84.75	0.4025	0.8475	3.170	8	17
20	14	45.25	89.75	0.4525	0.8975	5.263	9	18
20	15	50.25	89.75	0.5025	0.8975	6.524	10	18
20	16	55.25	94.75	0.5525	0.9475	4.367	11	19
20	17	60.25	94.75	0.6025	0.9475	6.069	12	19
20	18	70.25	99.75	0.7025	0.9975	4.317	14	20
20	19	75.25	99.75	0.7525	0.9975	7.548	15	20
20	20	85.25	100	0.8525	1.0000	0.000	17	20