# lengthEX: Expected length and sum of length of Exact method In proportion: Inference on Single Binomial Proportion and Bayesian Computations

## Description

Expected length and sum of length of Exact method

## Usage

 `1` ```lengthEX(n, alp, e, a, b) ```

## Arguments

 `n` - Number of trials `alp` - Alpha value (significance level required) `e` - Exact method indicator in [0, 1] 1: Clopper Pearson, 0.5: Mid P The input can also be a range of values between 0 and 1. `a` - Beta parameters for hypo "p" `b` - Beta parameters for hypo "p"

## Details

Evaluation of Confidence interval for `p` based on inverting equal-tailed binomial tests with null hypothesis H0: p = p0 using sum of length of the n + 1 intervals.

## Value

A dataframe with

 `sumLen` The sum of the expected length `explMean` The mean of the expected length `explSD` The Standard Deviation of the expected length `explMax` The max of the expected length `explLL` The Lower limit of the expected length calculated using mean - SD `explUL` The Upper limit of the expected length calculated using mean + SD

## 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

Other Expected length of base methods: `PlotexplAS`, `PlotexplAll`, `PlotexplBA`, `PlotexplEX`, `PlotexplLR`, `PlotexplLT`, `PlotexplSC`, `PlotexplTW`, `PlotexplWD`, `PlotlengthAS`, `PlotlengthAll`, `PlotlengthBA`, `PlotlengthEX`, `PlotlengthLR`, `PlotlengthLT`, `PlotlengthSC`, `PlotlengthTW`, `PlotlengthWD`, `lengthAS`, `lengthAll`, `lengthBA`, `lengthLR`, `lengthLT`, `lengthSC`, `lengthTW`, `lengthWD`
 ```1 2 3 4 5 6 7 8 9``` ```## Not run: n=5; alp=0.05;e=0.5;a=1;b=1 lengthEX(n,alp,e,a,b) n=5; alp=0.05;e=1;a=1;b=1 #Clopper-Pearson lengthEX(n,alp,e,a,b) n=5; alp=0.05;e=c(0.1,0.5,0.95,1);a=1;b=1 #Range including Mid-p and Clopper-Pearson lengthEX(n,alp,e,a,b) ## End(Not run) ```