# errBA: 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 Bayesian method

## Usage

 `1` ```errBA(n, alp, phi, f, a, b) ```

## Arguments

 `n` - Number of trials `alp` - Alpha value (significance level required) `phi` - Null hypothesis value `f` - Failure criterion `a` - Beta parameters for hypo "p" `b` - Beta parameters for hypo "p"

## Details

Evaluation of Bayesian Highest Probability Density (HPD) and two tailed intervals using error due to the difference of achieved and nominal level of significance for the n + 1 intervals for the Beta - Binomial conjugate prior model for the probability of success `p`

## 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 `method` Name of method - Quantile or HPD

## 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`, `errEX`, `errLR`, `errLT`, `errSC`, `errTW`, `errWD`
 ```1 2``` ```n=20; alp=0.05; phi=0.05; f=-2;a=0.5;b=0.5 errBA(n,alp,phi,f,a,b) ```