Conditional Difference Asymmetry Model for Square Contingency Tables with Nominal Categories

Abstract

This paper proposes a model, which is an extension-of-symmetry model, for square contingency tables with the same nominal row and column classifications. The model states that the absolute values of difference between the conditional probability that an observation will fall in cell (i, j) on condition that it falls in cell (i, j) or (j, i) and the conditional probability that it falls in cell (j, i) on the same condition, are constant for every i≠j. The model describes a structure of asymmetry (not symmetry), and it is applied to the data on a nominal scale. An example is given.

Keywords:

• Asymmetry
• conditional distribution
• nominal category
• model
• square table
• symmetry

Acknowledgments

The authors thank a referee for the many helpful comments on improving the paper.