3.25 For comparing two binomial samples with fixed sample sizes, show that the stan-

dard error (3.1) of a log odds ratio increases when, for either sample, the absolute difference of proportions of successes and failures increases. [Hint: Show that the asymptotic variance is minimized when each binomial probability is 0.50. In partic-
ular, when an outcome is relatively uncommon, estimates of the log odds ratio tend to be imprecise.]