Problem 26
Fisher and the Lady Tasting Tea (1935)
Problem. At a tea party, a lady claims she can discriminate by tasting a cup of tea whether the milk (M) or the tea (T) was poured first. To verify her claim, a statistician presents her in random order with eight cups of tea, and tells her there are four of each type M and T. The lady correctly identifies the four M types (and thus also correctly identifies the four T types). How can the statistician verify if her claim is true?
Solution. Consider Table 26.1, which shows the lady's response in the tea-tasting experiment.
Table 26.1 The Lady's Response in Fisher's Tea-Tasting Experiment.
Conditional on the true states T and M, suppose the lady responds T with probabilities 
and 
, respectively. The lady's claim is false if 
, that is, the odds ratio 
. Under the null hypothesis 
, the probability of correctly answering T for each of the four ...
