5.6 Comparison of two proportions; the $2\times 2$ table
5.6.1 Methods based on the log-odds ratio
In this section, we are concerned with another two sample problem, but this time one arising from the binomial rather than the normal distribution. Suppose
and that we are interested in the relationship between π and ρ. Another way of describing this situation is in terms of a 2 × 2 table (sometimes called a 2 × 2 contingency table)
We shall suppose that the priors for π and ρ are such that and , independently of one another. It follows that the posteriors are also beta distributions, and more precisely if
then
We recall from Section 3.1 on the binomial distribution that if
then , so that
Get Bayesian Statistics: An Introduction, 4th Edition now with the O’Reilly learning platform.
O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.