Bad Probability, Good Statistics, and Group Testing for Binomial Estimation

This article examines some improperly stated but often used textbook probability problems.Moving from a probabilistic to a statistical setting provides insight into group testing (i.e., observing only whether one or more of a group responds and not the response of each individual).Exact methods are used to construct tables showing (i) that group testing n times to estimate p can be more efficient than n individual tests even for small n and large p, (ii) optimal grouping strategies for various (n, p) combinations, and (iii) the efficiencies and biases achieved.