Conceptual Models for Visualizing Contingency Table Data

Michael Friendly
Psychology Department
York University

Conference on Visualization of Categorical Data
Cologne, May 17-19, 1995


This paper reviews several graphical methods for visualizing n-way contingency table data: parquet diagrams (Reidwyl & Schüpach, 1994), mosaic displays (Friendly, 1994) and fourfold displays (Friendly, 1995a), which all display counts by area or observation density, and asks why visualization methods for categorical data are relatively ill-developed, while analogous methods for quantitative data are both well-developed and highly used.

An answer is suggested by a physical model for categorical data (Friendly, 1995b) which likens categorical observations to gas molecules in pressure chambers, and provides a conceptual model for the use of area or observation density to display frequency data. The physical model provides concrete interpretations of a surprising number of results in the analysis of categorical data, from degrees of freedom and likelihood ratios, to iterative proportional fitting and Newton-Raphson iteration.