Revisiting Fisher's 'Lady Tasting Tea' from a perspective of sensory discrimination testing

- Fisher's Lady Tasting Tea is just an 'M + N' test.
- The 'M + N' tests with larger M and N are a new kind of discrimination test.
- Statistical significance can be reached based on only one set of 'M + N' samples.
- The relationship between the odds ratio and Cohen's d was discussed.
- The new methods are applicable to assessing performance of panelists and panels.

The Lady Tasting Tea is a famous real story in the history of development of statistics, related to R.A. Fisher, one of the greatest statisticians and founders of modern statistics. The main learning and insight offered by this paper from revisiting the story are that the methodology of conventional sensory difference tests can be and should be expanded to cover the 'M + N' method with larger M and N. Unlike the conventional discrimination tests, which use multiple sets of 'M + N' samples with small M and N based on a binomial model, the 'M + N' tests with larger M and N can reach a statistical significance in a single trial using only one set of 'M + N' samples based on a hypergeometric distribution in Fisher's exact test. This paper explores the applications of the new methods particularly in assessing performance of trained sensory panels and panelists. The connection of the odds ratio or common odds ratio with Cohen's standardized mean difference d is also discussed.