A large number of correlational models for cross-tabular analysis are available for utilization by social scientists for data description. Criteria for selection (such as levels of measurement and proportional reduction in error) do not lead to conclusive model choice. Moreover, such criteria may be irrelevant. More pertinent criteria are operational characteristics of a model. Operational criteria examined in this research include sensitivity to changes in population convariance; and insensitivity to sample size, table dimensions, and variable distributional characteristics. A complete facit or factorial design of 384 elements is generated to include cross-slassification conditions of typical social science utilization. A Monte Carlo computer program is then utilized to generate a cross-tabulation table as specified by the parameters of each of its design elements. Twenty-five correlational models are then applied to each of the tables. Because the tables are generated by design and their characteristics known, a priori, changes in the value of a given correlation coefficient can be explained. Analysis over all the facits lends to a description of the operational characteristics of each of the models. Finally, a factorial analysis leads to a reduction of the 25 models into four types of correlational models. (Author)