Given an arbitrary proximity matrix that is cross-classified according to two dimensions, a nonparametric strategy generalizing Friedman's (randomized blocks) analysis-of-variance method is suggested for testing the salience of the dimensions. Straightforward extensions of the approach can be given for more than two dimensions or when only the ordering of the proximity values is of interest. The major contribution of the study is its use of arbitrary proximity measures and the development of a strategy for blocking on the levels of one or more a priori dimensions when evaluating the differences over a second. The strategy proposed is very general, even though the illustration used contains three explicit classification dimensions of space, time, and crime type. Since any two of the dimensions could have been considered the major classification facets of interest, proximity measures could have been obtained between profiles over the cities and the interest in crime type and time. The basic inference principles would remain the same, and the analyses would be conducted as before. The analysis features presented should permit researchers to assess dimensional salience in data sets that are not easily studied by more standard analysis-of-variance schemes because of an unusual proximity measure. Moreover, the possibility of relying on only nonmetric comparisons among proximities should provide a tie-in to the current emphasis on nonmetric clustering and scaling in the social and behavioral sciences. Tabular data, mathematical equations, and eight references are provided. (Author summary modified)