Geometrical representation of two methods of linear least squares multiple correlation

Geometrical properties and relationships of the Doolittle and square root methods of multiple correlation, as represented in the variable subspace of an orthogonal person space, are shown. The method of representation is also useful for depicting zero-order and partial correlations, as well as for the more general problem of the combination of variables.     

Some multiple correlation and predictor selection methods

The Doolittle, Wherry-Doolittle, and Summerfield-Lubin methods of multiple correlation are compared theoretically as well as by an application in which a set of predictors is selected. Wherry's method and the Summerfield-Lubin method are shown to be equivalent; the relationship of these methods to the Doolittle method is indicated. The Summerfield-Lubin method, because of its compactness and ease of computation, and because of the meaningfulness of the interim computational values, is recommended as a convenient least squares method of multiple correlation and predictor selection.     

NÉCESSITÉ ET SIGNIFICATION DES RECHERCHES COMPARATIVES EN PSYCHOLOGIE GÉNÉTIQUE

Need and meaning of comparative studies in genetic psychology. — The comparative studies in the field of genetic psychology are indispensable for Psychology in general and also for Sociology, because only such studies allow us to separate the effects of biological or mental factors from those of social and cultural influences on the formation and the socialization of individuals. Relevant to this discussion is the well-known issue between culturalistic psychoanalysts like Fromm, Horney, etc., and classical freudian psychoanalysts who reduce the whole individual development to an endogenous evolution of « instinct ». In the field of cognitive functions to which this paper is devoted, at least four kinds of various factors must be distinguished, the respective influences of which can be separated through comparative studies : I. Biological factors depending on the “epigenetic” system (maturation of nervous system, etc.). These factors probably explain the sequential aspects (constant and necessary order) of the stages in the development of operative intelligence. However, if only these factors were acting, the stages would not only appear in a sequence, but at the same ages, whereas in fact, the ages where a stage appears differ from one environment to another. 2. Equilibration or autoregulation factors, determining behavior and thought in their various specific activities. They correspond to the sequential forms in general coordination of the actions of individuals as interacting with their physical environment; such intervening regulations are probably at the origin of the mental operations themselves, especially logical - mathematical operations. 3. General socialization factors, which are identical for all societies : cooperations - discussions - oppositions - exchanges, etc., between children or between adults or between adults and children. These factors 3 are closely related with the factors 2, because the general coordination of actions concerns inter-individual as so as intra-individual actions. 4. Factors related to educational and cultural transmission, which differ from one society to another; they are those we usually have in mind when we say briefly “social factors”. To discuss the influence of these four factors, Mohseni's study on Teheran school children and illiterate rural children is given as an example. Three results were obtained : (1) For “conservation” tasks, the same stages of intellectual development are observed for urban and rural children, in Iran as well as in Europe. (2) For these same tasks, a systematic delay of two to three years is observed among rural children with respect to Teheran children. (3) For performance tests (i.e. Porteus, Goodenough, etc.) there is a delay of four and primarily five years. These data seem to show that there is some sequential order of the stages which depends partially on the factors I. But, the ages for each stage are not constant, showing the factors 2 and 3 are intervening in a probably inseparable way. On the other hand, the difference between the actual operative results and the performance tests seems to indicate that a distinction might be made between the factors of general coordination (factors 2 and 3) and the educational transmissions (factors 4). About these last factors, the three and four year delays observed by Canadian psychologists working in Martinique with school children (French curriculum) in operative tasks (like conservations) seem to indicate that the general operations depend less on school than on the activities themselves of children or in general on the adult stimulations in the environment. We must pay special attention to the problems raised by language. In some precise and systematic experiments in Geneva, Sinclair shows children on the “preoperative” level (i.e. with no conservation…) do not spontaneously use the same language as operative children : the former use chiefly “scale” words (“much” or “many”, “little” or “few”, “large”, “small”) and the latter use chiefly “vector” words (“more”, “less”). If the younger subjects are submitted to a verbal training, they do learn to use the older children's language, but it only results in very little operative improvement (about one case out of 10 subjects on the average). Therefore, replicating the same experiments in countries speaking different languages would be very interesting. For instance, in the Turkish language, there is only one “vector” word, i.e. “again”; so that the Turk says “again much, again many” to say “more”. Then, the question is to know whether a change will be observed for the stages of logical-mathematical operations or whether these operations will be found everywhere with their identical common background; it seems that this last conclusion has already been observed in Aden (Hyde), Hong Kong (Goodnow), South Africa (Price-Williams). In conclusion, the kind of psychology we develop in our social environments, remains conjectural as long as comparative extensive and systematical research is not available; a great effort is still to be made in this direction.