Even so, for the reasons already outlined, the methods exployed by experimental psychology are incapable of accommodating differential variables and the methods of correlational psychology are incapable of revealing the critical features of individual processes. Many have hinted that efforts to resolve the conflict between experimentalists and correlationists have been hampered by the lack of an appropriate methodology for embedding individual performance within a model of individual differences, one that will support predictions of behavior of the organism under specified situations. Suggestions are aplenty. Noting the success of correlational methods such as factor analysis for the problems of inter-individual differences, Brower (1949) called for the elaboration of new methods, perhaps an inverted factor model, to deal with the problems of intra-individual variation. No such method has been presented but encouraging signposts on the road to an integrated model have appeared.
In 1945, Clark Hull boldly suggested that a natural-science approach to behavior theory must bridge the concerns of traditional academic psychology with the efforts of differential psychology. He proposed that this may be accomplished by estimating natual laws with individualized empirical constants. The variation in the empirical constants accounts for individual differences in behavior. He assumed that
the forms of the equations representing the behavioral laws of both individuals and species to be identical, and the differences between animals and species will be found in the empirical constants which are essential components of the equations (p. 60).However, Hull's attempts to demonstrate his approach were inconclusive but he continued to voice the need for an appropriate addition to experimental methodology which would deal with individual differences.
Later efforts have pursued a mixed analytic strategy. Cronbach (1957) held as a prominent example of research in this direction Piaget's (1950) discovery (by relating the emergence of stages of reasoning processes with age) of the developmental structure of operational thought. Another example is found in cognitive psychology. Componential analysis builds individual models of cognitive processes by experimental manipulation of task components. The procedure for detecting individual differences in problem solving strategy calls for intuitive comparisons of individual-level regressions with a model based on group-averaged data (Sternberg, 1985). Indices of individual performance are then correlated with external individual difference measures to gain insights into the character of information processing strategies. Like Burstein's (1980) slopes-as-outcomes approach to educational data, componential analysis attempts to address the issue of heterogeneity in cognitive performance. It represents a major analytical innovation but serious methodological problems arise when unit-level models are combined in a naive manner. The need to detect heterogeneity in performance also sparked the earlier search for stable aptitude-treatment interactions (ATIs) in educational research (Cronbach, 1957; Cronbach and Snow, 1977). Although ATI effects pertain to processes within individuals, inferences are frequently based on data aggregated over students or treatments (Phillips, 1985). It is clear that while all these investigators appreciate the proper role of individual variation in psychology, the difficult issues relating the precision of measurement, the effects of data aggregation, or the heterogeneous performance among subjects will be impossible to refine without a rational, integrative approach.