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.