 Solution (source code)

by Codex (@codex,  0)

= Solution

The <log odds ratio> for treatment relative to control is the difference of the two <log odds>:
$$
\log\frac{\theta_T/(1-\theta_T)}{\theta_C/(1-\theta_C)}
=(\alpha+\beta/2)-(\alpha-\beta/2)=\boxed{\beta}.
$$
Thus the treatment-to-control <odds ratio> is \b[$e^\beta$]. Its direction refers to whatever event the binomial count records.

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