THIS NOTE IS CONCERNED WITH IDEAS AND PROBLEMS INVOLVED IN CROSS-CLASSIFICATION OF OBSERVATIONS ON A GIVEN POPULATION, ESPECIALLY TWO-DIMENSIONAL CROSS-CLASSIFICATIONS. MAIN OBJECTIVES OF THE NOTE INCLUDE--(1) ESTABLISHMENT OF A CONCEPTUAL FRAMEWORK FOR CHARACTERIZATION AND COMPARISON OF CROSS-CLASSIFICATIONS, (2) DISCUSSION OF EXISTING METHODS FOR CHARACTERIZING CROSS-CLASSIFICATIONS, (3) PROPOSAL OF A NEW APPROACH TO AND A NEW METHOD FOR CHARACTERIZING AND MAKING INFERENCES FROM CROSS-CLASSIFICATIONS, AND (4) INDICATION OF HOW MARKOV PROCESSES CAN BE TREATED AS CROSS-CLASSIFICATIONS. THREE KINDS OF PROBABILITIES (UNCONDITIONAL, CONDITIONAL, AND JOINT) ARE DISCUSSED IN TERMS OF STATISTICAL INDEPENDENCE. MEASURES OF ASSOCIATION, ESPECIALLY THE Z-MEASURE OF ASSOCIATION AND ITS RELATION TO THE PHI COEFFICIENT IN VARIOUS SITUATIONS, ARE DISCUSSED AS MEANS OF INVESTIGATING NON-INDEPENDENCE. AN EXAMPLE OF THE Z-MEASURE APPLICATION IS PRESENTED. THE PROCESS OF DERIVING JOINT PROBABILITIES FROM Z-MEASURES AND THE INTERPRETATION OF MARKOV PROCESSES AS CROSS-CLASSIFICATIONS ARE ILLUSTRATED. (HW)