A PARTITIONING OF ORDINAL INFORMATION IN A THREE-WAY CROSS-CLASSIFICATION

In summarizing ordinal data with many tied rankings, generally pre- sented in the form of a cross-tabulation, there are many considerations that enter into the selection of a statistic summarizing the degree of association. When more than two variables are analyzed simultaneously the situation is even more complex. This paper considers, for the joint distribution of three ordinal variables, the interpretation of a set of summary statistics having product-moment characteristics. This interpretation sheds some light on general problems of analysis of causal relations and relates these summary statistics to other procedures for analyzing attribute data. They are illustrated by re-analyzing some data used by Siege1 to illustrate a similar procedure.