Comparing Rectangular Data Matrices

A procedure is discussed for comparing two rectangular n × m data matrices. The two matrices would typically represent data on the same n objects (for example, cities or subjects) and the same m attributes (for example, crime rates or attitudinal variables). An index that measures the degree to which both matrices are similar is presented along with a significance testing strategy that takes into account the possible dependency among the m attributes. To illustrate the strategy, a numerical example is given that compares the seven index crime rates for a set of twenty standard metropolitan statistical areas for the years 1976 and 1977. In addition to giving several possible generalizations of the basic comparison method, including a natural procedure for comparing three or more data matrices, we show in some detail how the matrix comparison strategy encompasses and extends the work of Tjøtheim on measuring association for spatially related variables.