proportion (version 2.0.0)

ciEXx: Exact method of CI estimation

Description

Exact method of CI estimation

Usage

ciEXx(x, n, alp, e)

Arguments

x

- Number of sucess

n

- Number of trials

alp

- Alpha value (significance level required)

e

- Exact method indicator in [0, 1] 1: Clopper Pearson, 0.5: Mid P

Value

A dataframe with

x

- Number of successes (positive samples)

LEXx

- Exact Lower limit

UEXx

- Exact Upper Limit

Details

Confidence interval for p (for the given x and n), based on inverting equal-tailed binomial tests with null hypothesis \(H0: p = p0 \) and calculated from the cumulative binomial distribution. Exact two sided P-value is usually calculated as $$P= 2[e*Pr(X = x) + min({Pr(X < x), Pr(X > x)})]$$ where probabilities are found at null value of p and \(0 <= e <= 1.\)

References

[1] 1993 Vollset SE. Confidence intervals for a binomial proportion. Statistics in Medicine: 12; 809 - 824.

[2] 1998 Agresti A and Coull BA. Approximate is better than "Exact" for interval estimation of binomial proportions. The American Statistician: 52; 119 - 126.

[3] 1998 Newcombe RG. Two-sided confidence intervals for the single proportion: Comparison of seven methods. Statistics in Medicine: 17; 857 - 872.

[4] 2001 Brown LD, Cai TT and DasGupta A. Interval estimation for a binomial proportion. Statistical Science: 16; 101 - 133.

[5] 2002 Pan W. Approximate confidence intervals for one proportion and difference of two proportions Computational Statistics and Data Analysis 40, 128, 143-157.

[6] 2008 Pires, A.M., Amado, C. Interval Estimators for a Binomial Proportion: Comparison of Twenty Methods. REVSTAT - Statistical Journal, 6, 165-197.

[7] 2014 Martin Andres, A. and Alvarez Hernandez, M. Two-tailed asymptotic inferences for a proportion. Journal of Applied Statistics, 41, 7, 1516-1529

See Also

prop.test and binom.test for equivalent base Stats R functionality, binom.confint provides similar functionality for 11 methods, wald2ci which provides multiple functions for CI calculation , binom.blaker.limits which calculates Blaker CI which is not covered here and propCI which provides similar functionality.

Other Base methods of CI estimation given x & n: PlotciAllxg, PlotciAllx, PlotciEXx, ciASx, ciAllx, ciBAx, ciLRx, ciLTx, ciSCx, ciTWx, ciWDx

Examples

x=5; n=5; alp=0.05;e=0.5
ciEXx(x,n,alp,e) #Mid-p
x=5; n=5; alp=0.05;e=1 #Clopper Pearson
ciEXx(x,n,alp,e)
x=5; n=5; alp=0.05;e=c(0.1,0.5,0.95,1) #Range including Mid-p and Clopper-Pearson
ciEXx(x,n,alp,e)