# errEX: Calculates error, long term power and pass/fail criteria for... In proportion: Inference on Single Binomial Proportion and Bayesian Computations

## Description

Calculates error, long term power and pass/fail criteria for Exact method

## Usage

 `1` ```errEX(n, alp, phi, f, e) ```

## Arguments

 `n` - Number of trials `alp` - Alpha value (significance level required) `phi` - Null hypothesis value `f` - Failure criterion `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.

## Details

Evaluation of Confidence interval for `p` based on inverting equal-tailed binomial tests with null hypothesis H0: p = p0 using error due to the difference of achieved and nominal level of significance for the n + 1 intervals

## Value

A dataframe with

 `delalp` Delta-alpha is the increase of the nominal error with respect to real error `theta` Long term power of the test `Fail_Pass` Fail/pass based on the input f criterion

## References

[1] 2014 Martin Andres, A. and Alvarez Hernandez, M. Two-tailed asymptotic inferences for a proportion. Journal of Applied Statistics, 41, 7, 1516-1529

Other Error for base methods: `PloterrAS`, `PloterrAll`, `PloterrBA`, `PloterrEX`, `PloterrLR`, `PloterrLT`, `PloterrSC`, `PloterrTW`, `PloterrWD`, `errAS`, `errAll`, `errBA`, `errLR`, `errLT`, `errSC`, `errTW`, `errWD`
 ```1 2 3 4 5 6``` ```n=20; alp=0.05;phi=0.05; f=-2;e=0.5 # Mid-p errEX(n,alp,phi,f,e) n=20; alp=0.05;phi=0.05; f=-2;e=1 #Clopper-Pearson errEX(n,alp,phi,f,e) n=20; alp=0.05;phi=0.05; f=-2;e=c(0.1,0.5,0.95,1) #Range including Mid-p and Clopper-Pearson errEX(n,alp,phi,f,e) ```