The lady tasting tea: how it changed research forever!
As the story unfolds into a summer afternoon in Cambridge in the early 20th century. There are several guests enjoying the tea party in the classical English fashion, indulging into the creamy milk-tea that Britishers are famous for. It so happens that one of the ladies claims that she can differentiate whether tea was added to milk or the other way around. Since most of the people are from the scientific community they don’t believe her. She happens to be Muriel Bristol (Ph.D. in Psychology) could not sufficiently defend herself on this.
There is one particular researcher at the party, who happens to be a statistician. He refuses to merely shun her claim. He says he can test it out. However, it was not an easy task, since he had to devise a test that would not require too much difficulty in conducting and analyzing. Classical Chi-Square tests and G-test could not be used on smaller and skewed samples so he plans to use the Fisher’s Exact Test(that time it was not called by this name). Readers interested in this can look up the footnotes[1].
Here the null hypothesis was that ‘She cannot discern between both types of tea’. The two types of tea ( milk-over-tea and tea-over-milk) are prepared incognito and presented to her in form of 4 cups of the variety each. Here just for the reference, we should note that Fisher was one of the early proponents of methodical scientific experiments[2]. He made sure that the cups were randomized too. It means that it was not four cups of type1 then four cups of type2. It was such that they were kept and offered randomly for the lady to try. Here, as an advanced reader would note, the treatment was the ‘tea preparation’ process which is a categorical variable. You cannot appropriately assign ‘number’ to whether you poured tea-over-milk and vice-versa. On the other hand, the outcome of the experiment was that she could correctly classify the method of preparation. This reduced to a problem of classification with the classification result being either correct or incorrect. All Dr. Bristol had to do was to say which four came from the same method. A combinatorial approach was taken to enlist all the outcomes, which in this case is 70[3]. There is only one possibility among 70 to get all of them right. There are 16 ways to choose 3 correct and 1 incorrect cup, similarly, 16 ways to choose 1 correct and 3 incorrect cups[4]. Now, for rejection of Null Hypothesis, there is a standard cut-ff in the scientific community. Conservative significance level of 1% means that it should such that there is only a 1% chance that the Null Hypothesis could be rejected by ‘chance’. While a liberal and a more common cutoff for social sciences lie at 5%. If we take the case of her getting 1 cup right out of 4 then she getting it right by chance would be 1/70 of the possible ways of classifying the cups which is just 1.4%, which if we accept her to discern the cups by classifying at least 3 out of 4 cups correctly, then she could have guessed it correctly just by chance at 22.86% plus 1.4% chance of guessing all four right which makes it 24.2%. This would not be acceptable. Hence, for her claim to be accepted that she could indeed discern just by taste, the two types of mixing of tea, she would have to correctly classify all four cups from the eight cups.
As it turns out, she did exactly that. She got all four cups right! [5]
Footnotes:
[1] Interested readers may look up Fisher’s Exact Test, Barnard’s Exact Test for 2x2 matrix situations and Cochran–Mantel–Haenszel test for stratified samples.
[2] Suggested readings :
Fisher, R. A. (1937). The design of experiments. Oliver And Boyd; Edinburgh; London.
Campbell, D. T., & Stanley, J. C. (1967). Experimental and quasi-experimental designs for research (2. print). Boston: Houghton Mifflin Comp.
Dunning, T. (2012). Natural Experiments in the Social Sciences: A Design-Based Approach. Cambridge: Cambridge University Press. https://doi.org/10.1017/CBO9781139084444
Kempthorne, O. (1977). Why randomize? Journal of Statistical Planning and Inference, 1(1), 1–25. https://doi.org/10.1016/0378-3758(77)90002-7
[3] There is a total of 8 cups of which one has to choose 4 cups. It can be done in NCk ways or 8C4 ways = 8!/4!(8–4)! = 70
[4]Choosing 1 correct and 3 incorrect or another way round can be possible in following ways: 4C1 = 4C3 = 4!/1!(4–3)!= 4 and there are 4 ways to choose them so total is 16
[5] Salsburg, D. (2001). The lady tasting tea. Henry Holt and Company, LLC, New York, NY.
[6] https://en.wikipedia.org/wiki/Lady_tasting_tea ( for the lazy ones, check out this source)
Stock image source : Pexels.com
