Mathematics of a Lady Tasting Tea

Mathematics of a Lady Tasting Tea Wed, 22 Jun 2022 09:13:48 GMT 2022-06-22T09:13:48Z In the <a style="text-decoration-line: none; color: #0b0080; background: none;" title="Design of experiments" href="https://en.wikipedia.org/wiki/Design_of_experiments">design of experiments</a> in <a style="text-decoration-line: none; color: #0b0080; background: none;" title="Statistics" href="https://en.wikipedia.org/wiki/Statistics">statistics</a>, the lady tasting tea is a <a style="text-decoration-line: none; color: #0b0080; background: none;" title="Randomized experiment" href="https://en.wikipedia.org/wiki/Randomized_experiment">randomized experiment</a> devised by <a style="text-decoration-line: none; color: #0b0080; background: none;" title="Ronald Fisher" href="https://en.wikipedia.org/wiki/Ronald_Fisher">Ronald Fisher</a> and reported in his book <a style="text-decoration-line: none; color: #0b0080; background: none;" title="The Design of Experiments" href="https://en.wikipedia.org/wiki/The_Design_of_Experiments">The Design of Experiments</a> (1935).<sup id="cite_ref-FOOTNOTEFisher1971II._The_Principles_of_Experimentation,_Illustrated_by_a_Psycho-physical_Experiment_1-0" class="reference" style="line-height: 1; unicode-bidi: isolate; white-space: nowrap; font-size: 11.2px;"><a style="text-decoration-line: none; color: #0b0080; background: none;" href="https://en.wikipedia.org/wiki/Lady_tasting_tea#cite_note-FOOTNOTEFisher1971II._The_Principles_of_Experimentation,_Illustrated_by_a_Psycho-physical_Experiment-1">[1]</a> The experiment is the original exposition of Fisher's notion of a <a style="text-decoration-line: none; color: #0b0080; background: none;" title="Null hypothesis" href="https://en.wikipedia.org/wiki/Null_hypothesis">null hypothesis</a>, which is "never proved or established, but is possibly disproved, in the course of experimentation".<sup id="cite_ref-FOOTNOTEFisher1971Chapter_II._The_Principles_of_Experimentation,_Illustrated_by_a_Psycho-physical_Experiment,_Section_8._The_Null_Hypothesis_2-0" class="reference" style="line-height: 1; unicode-bidi: isolate; white-space: nowrap; font-size: 11.2px;"><a style="text-decoration-line: none; color: #0b0080; background: none;" href="https://en.wikipedia.org/wiki/Lady_tasting_tea#cite_note-FOOTNOTEFisher1971Chapter_II._The_Principles_of_Experimentation,_Illustrated_by_a_Psycho-physical_Experiment,_Section_8._The_Null_Hypothesis-2">[2]</a><a style="text-decoration-line: none; color: #0b0080; background: none;" href="https://en.wikipedia.org/wiki/Lady_tasting_tea#cite_note-oed-3">[3]</a> The lady in question (<a style="text-decoration-line: none; color: #0b0080; background: none;" title="Muriel Bristol" href="https://en.wikipedia.org/wiki/Muriel_Bristol">Muriel Bristol</a>) claimed to be able to tell <a style="text-decoration-line: none; color: #0b0080; background: none;" title="Tea in the United Kingdom" href="https://en.wikipedia.org/wiki/Tea_in_the_United_Kingdom#The_question_of_milk">whether the tea or the milk was added first to a cup</a>. Fisher proposed to give her eight cups, four of each variety, in random order. One could then ask what the probability was for her getting the specific number of cups she identified correct, but just by chance. Fisher's description is less than 10 pages in length and is notable for its simplicity and completeness regarding terminology, calculations and design of the experiment Info