Reply to Somers and Smith

The central points in my paper are two. First, it is meaningful to compute and make substantive use of a descriptive statistic only insofar as one can interpret it, that is, specify precisely what information it gives concerning the extent to which data support claims about some specified relation between variables. Second, in the ordinal multivariate case, we have no clear, rationally acceptable formulation of what a relation between three or more ordinal variables is. Consequently, at the present time the calculation of so-called "product-moment statistics" for the ordinal multivariate case depends entirely on analogy with the interval level additive model, and without this analogy these calculations would be entirely unmotivated and the results quite obviously devoid of clear meaning. The fundamental problem of ordinal multivariate analysis, then, is to give a clear, rationally acceptable account of what an ordinal multivariate relation is, and on this basis to develop appropriate, interpreted descriptive statistics. Whether a solution of this problem would result in a structure isomorphic to the "product-moment algebra," however, is not at all obvious.