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doi: 10.1007/bf02288801pmid: N/A
Abstract A battery of 46 tests was given to 237 college men. A factor analysis using the Thurstone technique revealed eight clearly interpretable first-order factors, one dubious factor, and a residual factor. The factors were interpreted as induction, deduction, flexibility of closure, speed of closure, space, verbal comprehension, word fluency, and number. Four second-order factors were abstracted from the matrix of first-order correlations. The presence of induction, deduction, and flexibility of closure on the first second-order factor, interpreted as an analytic factor, confirmed previous indications of relationships between the reasoning and closure factors. A second bipolar factor is interpreted as a speed of association factor. The third factor is interpreted as facility in handling meaningful verbal materials—perhaps an ability to do abstract thinking. The fourth factor is possibly a second-order closure factor—perhaps an ability to do concrete thinking.
doi: 10.1007/bf02288802pmid: N/A
Abstract The nature of psychological measurements in relation to mathematical structures and representations is examined. Some very general notions concerning algebras and systems are introduced and applied to physical and number systems, and to measurement theory. It is shown that the classical intensive and extensive dimensions of measurements with their respective ordinal and additive scales are not adequate to describe physical events without the introduction of the notions of dimensional units and of dimensional homogeneity. It is also shown that in the absence of these notions, the resulting systems of magnitudes have only a very restricted kind of isomorphism with the real number system, and hence have little or no mathematical representations. An alternative in the form of an extended theory of measurements is developed. A third dimension of measurement, the supra-extensive dimension, is introduced; and a new scale, the multiplicative scale, is associated with it. It is shown that supra-extensive magnitudes do constitute systems isomorphic with the system of real numbers and that they alone can be given mathematical representations. Physical quantities are supra-extensive magnitudes. In contrast, to date, psychological quantities are either intensive or extensive, but never of the third kind. This, it is felt, is the reason why mathematical representations have been few and without success in psychology as contrasted to the physical sciences. In particular, the Weber-Fechner relation is examined and shown to be invalid in two respects. It is concluded that the construction of multiplicative scales in psychology, or the equivalent use of dimensional analysis, alone will enable the development of fruitful mathematical theories in this area of investigation.
doi: 10.1007/bf02288803pmid: N/A
Abstract A procedure for estimating the reliability of sets of ratings, test scores, or other measures is described and illustrated. This procedure, based upon analysis of variance, may be applied both in the special case where a complete set of ratings from each ofk sources is available for each ofn subjects, and in the general case wherek 1,k 2, ...,k n ratings are available for each of then subjects. It may be used to obtain either a unique estimate or a confidence interval for the reliability of either the component ratings or their averages. The relations of this procedure to others intended to serve the same purpose are considered algebraically and illustrated numerically.
doi: 10.1007/bf02288804pmid: N/A
Abstract Thesquare root method of selection has been explained in a previous article. In the present article a worked example is given which illustrates the compactness of the procedure. The square root method is compared with the Wherry-Doolittle method.
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