Data analysis: good but ...

Abstract

In the 1950s Tukey and Benzécri led the Data Analysis movement, opposed to the perceived mathematisation of statistics. This has flourished but we perceive some troubling
problems (Greenacre prefers challenges or opportunities) which are addressed in the paper. These problems are manifest in the simplest analyses of two-way arrays of data
(Sections 2 - 3) and become worse with higher order arrays (Section 4). The most important thing about Data Analysis is the Data, its type (e.g. how data is collected, the physical kinds of variable, categories, counts, etc.) and the data structure (e.g. arrays, multiway tables, symmetry etc.). Analysis is concerned with models, distances, norms, measures of
approximation and algorithms. Perhaps Data Analysis is in some danger of replicating the kind of mathematisation it was designed to supplant.