proportion (version 2.0.0)

lengthEX: Expected length and sum of length of Exact method

Description

Expected length and sum of length of Exact method

Usage

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"

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

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.

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

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

Examples

## 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)
## ---------------------------------------------