The TeachBayes package has several functions to facilitate working with a discrete prior for two proportions.

`library(TeachBayes)`

Start with a uniform prior on (p1, p2), where each proportion takes on values .05, .15, …, .95.

```
values <- seq(.05, .95, by=.1)
prior <- prior.two.parameters(values, values)
```

Construct a graph of this distribution.

`draw_two_p(prior)`

This finds the probability distribution of the difference in proportions p1 - p2.

`prob_plot(two_p_summarize(prior))`

Collect some data from two binomial samples.

```
y1n1 <- c(10, 20)
y2n2 <- c(8, 24)
```

Update (find posterior):

`post <- two_p_update(prior, y1n1, y2n2)`

Graph and summarize:

`draw_two_p(post)`

`prob_plot(two_p_summarize(post))`

`prior <- testing_prior(.05, .95, 10, .5)`

Construct a graph of this distribution and summarize.

`draw_two_p(prior)`

`prob_plot(two_p_summarize(prior))`

Collect some data from two binomial samples.

```
y1n1 <- c(10, 20)
y2n2 <- c(8, 24)
```

Update (find posterior):

`post <- two_p_update(prior, y1n1, y2n2)`

Graph and summarize:

`draw_two_p(post)`

`prob_plot(two_p_summarize(post))`