# hypotestBAF4x: Bayesain Hypothesis testing given x: Hypothesis 4: Theta <=... In proportion: Inference on Single Binomial Proportion and Bayesian Computations

## Description

Bayesain Hypothesis testing given x: Hypothesis 4: Theta <= Theta0 Vs Theta > Theta0

## Usage

 `1` ```hypotestBAF4x(x, n, th0, a0, b0, a1, b1) ```

## Arguments

 `x` - Number of success `n` - Number of trials from data `th0` - Hypothetical parameter for H0 `a0` - Priors for hypothesis H0 `b0` - Priors for hypothesis H0 `a1` - Priors for hypothesis H1 `b1` - Priors for hypothesis H1

## Details

Computes Bayes factor under Beta-Binomial model for the model: p <= p0 Vs p > p0 from the given number of trials `n` and for given number of successes x = 0, 1, 2......n We use the following guideline for reporting the results:

• 1/3 <= BaFa01 < 1: Evidence against H0 is not worth more than a bare mention.

• 1/20 <= BaFa01 < 1/3: Evidence against H0 is positive.

• 1/150 <= BaFa01 < 1/20: Evidence against H0 is strong.

• BaFa10 < 1/150: Evidence against H0 is very strong.

• 1 <= BaFa01 < 3: Evidence against H1 is not worth more than a bare mention.

• 3 <= BaFa01 < 20: Evidence against H1 is positive.

• 20 <= BaFa01 < 150: Evidence against H1 is strong.

• 150 <= BaFa01: Evidence against H1 is very strong.

## Value

A dataframe with

 `x` Number of successes `BaFa01` Bayesian Factor

## References

[1] 2006 Ghosh M, Delampady M and Samanta T. An introduction to Bayesian analysis: Theory and Methods. Springer, New York

[2] 2014 Sakthivel S, Subbiah M and Ramakrishnan R Default prior approach for Bayesian testing of hypotheses involving single binomial proportion International Journal of Statistics and Analysis, 4 (2), 139 - 153

Other Hypothesis testing: `hypotestBAF1x`, `hypotestBAF1`, `hypotestBAF2x`, `hypotestBAF2`, `hypotestBAF3x`, `hypotestBAF3`, `hypotestBAF4`, `hypotestBAF5x`, `hypotestBAF5`, `hypotestBAF6x`, `hypotestBAF6`
 ```1 2``` ```x=682; n=925; th0=0.75;a0=0.5; b0=0.5; a1=3; b1=3 hypotestBAF4x(x,n,th0,a0,b0,a1,b1) ```