ciAll: CI estimation of 6 base methods (Wald, Wald-T, Likelihood,...
In proportion: Inference on Single Binomial Proportion and Bayesian Computations

Description Usage Arguments Details Value References See Also Examples

CI estimation of 6 base methods (Wald, Wald-T, Likelihood, Score, Logit-Wald, ArcSine)

1	ciAll(n, alp)

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

The Confidence Interval of 6 base methods (Wald, Wald-T, Likelihood, Score, Logit-Wald, ArcSine) for n given alp.

A dataframe with

`method`	- Name of the method
`x`	- Number of successes (positive samples)
`LLT`	- Lower limit
`ULT`	- Upper Limit
`LABB`	- Lower Abberation
`UABB`	- Upper Abberation
`ZWI`	- Zero Width Interval

[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, ciBA, ciEX, ciLR, ciLT, ciSC, ciTW, ciWD

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

       method x   LowerLimit UpperLimit LowerAbb UpperAbb ZWI
1        Wald 0 0.000000e+00  0.0000000       NO       NO YES
2        Wald 1 0.000000e+00  0.5506090      YES       NO  NO
3        Wald 2 0.000000e+00  0.8294066      YES       NO  NO
4        Wald 3 1.705934e-01  1.0000000       NO      YES  NO
5        Wald 4 4.493910e-01  1.0000000       NO      YES  NO
6        Wald 5 1.000000e+00  1.0000000       NO       NO YES
7     ArcSine 0 1.800863e-01  0.1800863       NO       NO YES
8     ArcSine 1 6.443278e-04  0.6154592       NO       NO  NO
9     ArcSine 2 5.952159e-02  0.8125129       NO       NO  NO
10    ArcSine 3 1.874871e-01  0.9404784       NO       NO  NO
11    ArcSine 4 3.845408e-01  0.9993557       NO       NO  NO
12    ArcSine 5 8.199137e-01  0.8199137       NO       NO  NO
13 Likelihood 0 2.525061e-05  0.3189979       NO       NO  NO
14 Likelihood 1 1.262562e-02  0.6282215       NO       NO  NO
15 Likelihood 2 8.073487e-02  0.8009072       NO       NO  NO
16 Likelihood 3 1.990928e-01  0.9192651       NO       NO  NO
17 Likelihood 4 3.717785e-01  0.9873744       NO       NO  NO
18 Likelihood 5 6.810021e-01  0.9999591       NO       NO  NO
19      Score 0 3.139253e-17  0.4344825       NO       NO  NO
20      Score 1 3.622411e-02  0.6244654       NO       NO  NO
21      Score 2 1.176208e-01  0.7692757       NO       NO  NO
22      Score 3 2.307243e-01  0.8823792       NO       NO  NO
23      Score 4 3.755346e-01  0.9637759       NO       NO  NO
24      Score 5 5.655175e-01  1.0000000       NO       NO  NO
25     Wald-T 0 0.000000e+00  0.6640117      YES       NO  NO
26     Wald-T 1 0.000000e+00  0.6437279      YES       NO  NO
27     Wald-T 2 0.000000e+00  0.8527525      YES       NO  NO
28     Wald-T 3 1.472475e-01  1.0000000       NO      YES  NO
29     Wald-T 4 3.562721e-01  1.0000000       NO      YES  NO
30     Wald-T 5 3.359883e-01  1.0000000       NO      YES  NO
31 Logit-Wald 0 0.000000e+00  0.5218238       NO       NO  NO
32 Logit-Wald 1 2.718309e-02  0.6910456       NO       NO  NO
33 Logit-Wald 2 1.002311e-01  0.7995892       NO       NO  NO
34 Logit-Wald 3 2.004108e-01  0.8997689       NO       NO  NO
35 Logit-Wald 4 3.089544e-01  0.9728169       NO       NO  NO
36 Logit-Wald 5 4.781762e-01  1.0000000       NO       NO  NO