A Tableau Calculus for the Analysis of Experiments

Experimental analysis often involves analyzing groups containing varying numbers of elements; for example, a different number of units for each treatment assignment within each stratum. We therefore encounter objects that are like matrices, except they are not perfect rectangular blocks; i.e., they are not always “filled.” In this note, we define a new structure, called a tableau, which can be regarded as a partially filled matrix, and seek to formalize the operations on tableaus that are used in the analysis of experiment. We then show how tableau notation can be used to express the key equations in a variety of statistical contexts, including stratification, clustering, and the sum-of-squares decomposition. Moreover, we express these equations in both an invariant and index form: <a href="https://towardsdatascience.com/a-tableau-calculus-for-the-analysis-of-experiments-53655dd04eb8">Website</a>