A Bayesian Network Framework for Generalising the Lady Tasting Tea Experiment

The Lady Tasting Tea experiment is widely recognised as the origin of modern statistical hypothesis testing. In a previous study, we modelled this experiment using a Bayesian network (BN); however, that approach was constrained by a three-level ability scale and manually specified parameters. In this paper, we present a methodological advancement that enables BN modelling for more flexible experimental designs. A key contribution is the generation of simulated sample data for arbitrary designs with N cups (where N is even) and k ability levels ( k  ≥ 2). This simulation, implemented in R, enabled the construction of a 10-cup, 5-level BN model. Parameter estimation for this model, comprising 21 nodes and 22,511 conditional probability entries, was performed efficiently using the Expectation–Maximisation algorithm in Netica—an otherwise impractical task to complete manually. Although models with larger numbers of cups and ability levels exhibit exponential growth in parameter space, the proposed simulation–EM approach establishes a methodologically innovative and scalable procedure for generalising the Lady Tasting Tea experiment. Beyond Fisher’s test of significance, the framework retains posterior probability estimates for assessing a tester’s ability, thereby providing a more comprehensive perspective on statistical inference.