DIMENSIONS INVOLVED IN DIFFERENCES AMONG SCHOOL MEANS OF COGNITIVE MEASURES

The widespread use of multiple factor analysis has pushed the concept of general intelligence into the background of the thinking of many psychologists. It is true, of course, when any large number of ability tests are intercorrelated and factored, that multiple first order factors are described. Thurstone (1938) called these factors "primary," which connotes "important. " Guilford's research (1967) has multiplied the number of so-called primary factors to perhaps 120, although many fewer factors than this have been described in any one analysis. Nevertheless, multiple factors are obviously present in any large scale test battery. One must carefully select a small subset of heterogeneous ability tests in order to demonstrate Spearman's concept of hierarchical order and the use of a single factor to describe their intercorrelations. Another ubiquitous phenomenon also is present. In the full range of human talent there are few if any negative correlations between measures of abilities. This is particularly true if one restricts the domain to the cognitive area. Also, if one has a reliable, valid criterion measure of proficiency in an activity having cognitive content, almost any cognitive measure will show a nonzero predictive validity with that criterion. The only reservation required for this statement is that the sample be large enough to avoid large negative sampling errors. Differential validity of a predictor for different criteria can be found, but in the full range of talent the differences required are not readily demonstrated. These observations indicate that there is generality in human cognitive performance underlying the multiple factors. A hierarchical model of the factors in human abilities reconciles multiple first order factors with the evidence for a general factor. This model has been more popular among British psychometricians than among American and is well represented in the writings of Vernon (1950). A number of American psychologists, on the other hand, have factored in more than one order and perhaps most accept higher order factors in principle. Schmid and Leiman (1967) joined these two factor models by means of a transformation that allows one to translate factors in higher orders into the hierarchical model of Vernon. Although recognizing that the hierarchical model might not fit the complexities of the interrelationships of human abilities perfectly, Humphreys (1962) recommended it as a useful approximation. The problem with the model is not with the concept of the general factor but with the lack of neatness with which factors are broken out of the hierarchy as one proceeds from the general to the specific. Humphreys (1974) has also discussed the importance of the general factor in research on heritability. Although accepting the reality of Spearman's "g" for descriptive purposes, Humphreys (1971) defines the construct behaviorally rather than as an entity within the organism. With this as background it occurred to the present authors that the variances and intercorrelations of test means of groups that had experienced unplanned social selection of a cognitive sort would be relevant to the importance of the concept of a general factor