# bayes.binom.test: Bayesian First Aid Alternative to the Binomial Test In rasmusab/bayesian_first_aid: Bayesian replacements for the most commonly used statistical tests in R.

## Description

`bayes.binom.test` estimates the relative frequency of success using Bayesian estimation and is intended as a replacement for `binom.test`.

## Usage

 ```1 2``` ```bayes.binom.test(x, n, comp.theta = 0.5, alternative = NULL, cred.mass = 0.95, n.iter = 15000, progress.bar = "none", p, conf.level) ```

## Arguments

 `x` number of successes, or a vector of length 2 giving the numbers of successes and failures, respectively. `n` number of trials; ignored if x has length 2. `comp.theta` a fixed relative frequency of success to compare with the estimated relative frequency of success. This argument fills a similar role as `p` in `binom.test`. `alternative` ignored and is only retained in order to mantain compatibility with `binom.test`. `cred.mass` the amount of probability mass that will be contained in reported credible intervals. This argument fills a similar role as `conf.level` in `binom.test`. `n.iter` The number of iterations to run the MCMC sampling. `progress.bar` The type of progress bar. Possible values are "text", "gui", and "none". `p` same as `comp.theta` and is only retained in order to mantain compatibility with `binom.test`. `conf.level` same as `cred.mass` and is only retained in order to mantain compatibility with `binom.test`.

## Details

Given data on the number of successes and failures `bayes.binom.test` estimates θ, the relative frequency of success, assuming the following model:

x ~ Binomial(θ, n)

θ ~ Beta(1, 1)

Here the prior on θ is a non-informative Beta(1, 1) distribution which is identical to a Uniform(0, 1) distribution. By `plot`ing and looking at a `summary` of the object returned by `bayes.binom.test` you can get more information about the shape of the posterior and the posterior predictive distribution. `model.code` prints out the corresponding R code underlying `bayes.binom.test` which can be copy-n-pasted into an R script and modified, for example, changing the prior on θ.

## Value

A list of class `bayes_binom_test` that contains information about the analysis. It can be further inspected using the functions `summary`, `plot`, `diagnostics` and `model.code`.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18``` ```# A college dormitory recently sponsored a taste comparison between # two major soft drinks. Of the 64 students who participated, 39 selected # brand A, and only 25 selected brand B. Example from # http://www.elderlab.yorku.ca/~aaron/Stats2022/BinomialTest.htm bayes.binom.test(x = 39, n = 64) # Save the return value in order to inspect the model result further. fit <- bayes.binom.test(x = 39, n = 64, cred.mass=0.8) summary(fit) plot(fit) # MCMC diagnostics (should not be necessary for such a simple model) diagnostics(fit) # Print out the R code to run the model. This can be copy n' pasted into # an R-script and further modified. model.code(fit) ```

rasmusab/bayesian_first_aid documentation built on May 27, 2019, 2:03 a.m.