# ciTW: Wald-T method of CI estimation

### Description

Wald-T method of CI estimation

### Usage

 1 ciTW(n, alp) 

### Arguments

 n - Number of trials alp - Alpha value (significance level required)

### Details

An approximate method based on a t_approximation of the standardized point estimator for all x = 0, 1, 2 ..n; that is the point estimator divided by its estimated standard error. Essential boundary modification is when x = 0 or n,

\hat{p}=\frac{(x+2)}{(n+4)}

### Value

A dataframe with

 x  - Number of successes (positive samples) LTW  - Wald-T Lower limit UTW  - Wald-T Upper Limit LABB  - Wald-T Lower Abberation UABB  - Wald-T Upper Abberation ZWI  - Zero Width Interval

### 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

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 Basic methods of CI estimation: PlotciAS, PlotciAllg, PlotciAll, PlotciBA, PlotciEX, PlotciLR, PlotciLT, PlotciSC, PlotciTW, PlotciWD, ciAS, ciAll, ciBA, ciEX, ciLR, ciLT, ciSC, ciWD

### Examples

 1 2 n=5; alp=0.05 ciTW(n,alp) 

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