Topic 17: Learning About a Proportion Using Continuous Models

Minitab Local Macro p_beta

Summarizes beta distribution for a proportion p.

TO RUN:

Suppose 10 and 20 are the numbers of the beta curve that represents your prior beliefs about the proportion. Put in column c1 the values of p for which you want to compute "less than" probabilities. In column c2, put the probability value for which you wish to compute percentiles. To compute the "less than" probabilities and the percentiles, type the following in the Minitab Session Window. The graph of the beta curve is automatically displayed.

MTB > %p_beta 10 20;

SUBC> cprob c1;

SUBC> quan c2.

CUMULATIVE PROBABILITIES:

Row P PROB_LT

1 0.1 0.00033

2 0.2 0.04926

3 0.3 0.36400

4 0.4 0.78532

5 0.5 0.96929

6 0.6 0.99848

7 0.7 0.99998

8 0.8 1.00000

9 0.9 1.00000

QUANTILES:

Row PROB QUANTILE

1 0.05 0.200496

2 0.95 0.479014

Other subcommands:

The full macro command is

%p_beta a b;

data s f;

cprob pvalue;

quan qvalue.

In Activity 17-5, our prior about p, the proportion of cards that Frank identifies correctly, is modeled by a beta(2.5, 7.5) curve. We observe 7 successes and 13 failures in the experiment.

We can get a plot of the prior, likelihood, and posterior densities by typing the command

%p_beta 2.5 7.5;

data 7 13.