# BayesPropTest

simple Bayesian version of R's prop.test

## Bayesian Test of the Difference Between Proportions

### description

Provides a simple way to perform a Bayesian version of `prop.test`

using the beta distribution.

The default prior distributional parameters are *a* = 1 and *b* = 1.
The prior can be adjusted if you have reasonable information to work with.
If you set *a* < *b*, the density will be weighted toward the lower
half of the distribution, and setting *a* > *b* would weight it
toward the upper half. If *a* = 0.5, much more weight is given to values
near 0, while if *b* = 0.5, weight is stacked up near 1. Examples of
different shapes of the beta distribution based on different parameter values
can be seen at Rocscience.

A histogram is produced of the posterior distribution, with a red reference line marking "no difference."

### usage

`bayes.prop.test(n1, d1, n2, d2, a=1, b=1, rep=10000)`

### arguments

`n1`

The numerator of the first group. Required.

`d1`

The denominator of the first group. Required. The
proportion *n1/d1* should be greater than or equal to *n2/d2*.

`d2`

The denominator of the second group. Required. The
proportion *n2/d2* should be less than or equal to *n1/d1*.

`a`

Alpha prior parameter. Defaults to 1.

`b`

Beta prior parameter. Defaults to 1.

`rep`

Number of replications for the `rbeta`

function. Defaults to 10,000.

### examples

`bayes.prop.test(n1=50, d1=100, n2=20, d2=50)`

# difference | p-hat | 2.5% | 97.5% | prob.diff>0 |

# 0.10000000 | 0.09695006 | -0.07072376 | 0.25873452 | 0.87380000 |

### author

@Rmadillo