A Bayesian Examines the Lady Tasting Tea

Abstract

This technical note accompanies the case/class on “The Lady Tasting Tea” (LTT). It describes how a Bayesian would update his or her prior probability for the probability the LTT can correctly distinguish cups of tea based on whether the milk was added first or last. This long-form note describes both a discrete model (LTT has p of 0.5 or 0.8) and a more complicated continuous model (p is beta distributed). The abridged note (UVA-QA-0768) describes only the discrete model. The case/class itself provides a very useful analogy with which students can explore the elements of statistical inference. Excerpt UVA-QA-0769 Jun. 13, 2011 A Bayesian Examines the Lady Tasting Tea Before I describe what Bayesian statistics can add to the discussion of the lady tasting tea (LTT), let me remind you where the classical statisticians left us. They used the binomial distribution to calculate the probability distribution of the number the LTT gets correct (in 10 trials) under two scenarios. The first scenario, called the null hypothesis, is that she is guessing. Guessing would mean P, the probability that she correctly identifies which of two cups has had milk poured into it first and which had tea in it first, is 0.5. The second scenario, called the alternative hypothesis, is that she is skilled. To keep things from getting too complicated, we assume that skilled means P = 0.8 for each trial. The resulting probability distributions are given in Table 1. With these probabilities, the classical statistician can make probability statements about what will happen undereither scenario. Table 1. Probability distributions for number correct in 10 trials. . . .