Criterion analysis; an application of the hypothetico-deductive method to factor analysis.

Among statistical methods now in common use in psychology, factor analysis presents certain interesting and paradoxical features. Although more and more psychologists, sociologists, and recently even physicists and chemists, have used factor analysis as their preferred statistical research tool, and although many experts, among whom we may mention Thurstone, Burt, Cattell, Guilford, and Vernon, have expressed their faith in its adequacy to solve some of our most pressing taxonomic problems, yet much criticism of this technique has been advanced by two schools of thought usually on opposite sides of the fence. Factor analysis has been criticized severely by those who, like Allport, Murray, and other adherents of the psychiatric, individualistic, idiopathic point of view believe its atomistic assumptions violate the holistic nature of human personality. It has equally suffered the onslaughts of professional statisticians who point out its formal deficiencies, and prefer the more rigorous methods of discriminant function analysis, analysis of variance, and regression equations. No other method in statistical psychology has suffered such a multiplicity of criticisms, and it behooves those of us who make use of it to look carefully at the various aspects of factor analysis which may be considered most vulnerable to such attacks. Truman L. Kelley has pointed out that statistics has three main functions. "The first function of statistics is to be purely descriptive, and its second function is to enable analysis in harmony with hypothesis, and its third function to suggest by the force of its virgin data analyses not earlier thought of" (9, pp. 22, 23). While most statisticians would agree to the descriptive purposes of many statistical constants, there is less agreement regarding the other two functions mentioned by Kelley. "We may say that there are two occasions for resort to statistical procedures, the one dominated by a desire to prove a hypothesis, and the other by a desire to invent one. This has led to distinct schools of statisticians, both lying within the general field of scientific endeavor" (9, p. 12). 1 Reference to this dichotomy of functions and purposes within the field of statistics gives us one hint as to the reasons for the general statistical criticisms of factorial methods. Unlike analysis of variance and covariance, discriminant function analysis, or even the humble C.R. or t form of analysis, factor analysis does not in general attempt to prove or disprove a hypothesis; it does not set out to disprove any form of null hypothesis at some critical level of significance. Its function appears to be far more dominated by the desire to "invent" a theory, and in spite of Kelley's words this function of statistics is not generally recognized by statisticians as being truly within the purview of this particular branch of science. Holzinger describes the nature of factor analysis thus: "Factor analysis is a branch of statistical theory concerned with the resolution of a set of descrip-