Mathematical structures and psychological measurements

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.The editors of this journal should perhaps point out that unanimous agreement with the arguments and points of view expressed in this article is not anticipated. They believe, however, that its publication may stimulate needed thinking and clarification of problems basic to psychological measurement and thus serve the purpose for which the journal was founded.     

A l'occasion du renouvellement de l'annee

Sans résumé     

Punishment of Schedule-Induced Drinking by Lick-Dependent Delays in Food Presented at Different Frequencies

The Psychological Record - Three food-deprived rats (80% of their free-feeding weights) developed schedule-induced drinking after being exposed to a multiple fixed-time schedule (FT 60-s FT 18-s)...     

Does awareness of speech as a sequence of phones arise spontaneously?

It was found that illiterate adults could neither delete nor add a phone at the beginning of a non-word; but these tasks were rather easily performed by people with similar environment and childhood experiences, who learned to read rudimentarily as adults. Awareness of speech as a sequence of phones is thus not attained spontaneously in the course of general cognitive growth, but demands some specific training, which, for most persons, is probably provided by learning to read in the alphabetic system.     

Generalized approaches to the maxbet problem and the maxdiff problem,with applications to canonical correlations

Van de Geer has reviewed various criteria for transforming two or more matrices to maximal agreement, subject to orthogonality constraints. The criteria have applications in the context of matching factor or configuration matrices and in the context of canonical correlation analysis for two or more matrices. The present paper summarizes and gives a unified treatment of fully general computational solutions for two of these criteria, Maxbet and Maxdiff. These solutions will be shown to encompass various well-known methods as special cases. It will be argued that the Maxdiff solution should be preferred to the Maxbet solution whenever the two criteria coincide. Horst's Maxcor method will be shown to lack the property of monotone convergence. Finally, simultaneous and successive versions of the Maxbet and Maxdiff solutions will be treated as special cases of a fully flexible approach where the columns of the rotation matrices are obtained in successive blocks.The author is obliged to Henk Kiers for computational assistance and helpful comments.     

Impact of parenting styles on adolescents' self-esteem and internalization of values in Spain

The relationship of parenting styles with adolescents' outcomes was analyzed within a sample of Spanish adolescents. A sample of 1456 teenagers from 13 to 16 years of age, of whom 54.3% were females, reported on their parents' child-rearing practices. The teenagers' parents were classified into one of four groups (authoritative, authoritarian, indulgent, or neglectful). The adolescents were then contrasted on two different outcomes: (1) priority given to Schwartz's self-transcendence (universalism and benevolence) and conservation (security, conformity, and tradition) values and (2) level of self-esteem (appraised in five domains: academic, social, emotional, family and physical). The results show that Spanish adolescents from indulgent households have the same or better outcomes than adolescents from authoritative homes. Parenting is related with two self-esteem dimensions--academic and family--and with all the self-transcendence and conservation values. Adolescents of indulgent parents show highest scores in self-esteem whereas adolescents from authoritarian parents obtain the worst results. In contrast, there were no differences between the priority given by adolescents of authoritative and indulgent parents to any of the self-transcendence and conservation values, whereas adolescents of authoritarian and neglectful parents, in general, assign the lowest priority to all of these values.     

Trait emotional intelligence and leadership self-efficacy: their relationship with collective efficacy

In this article, a leadership model is presented, with which to investigate the relationship of trait emotional intelligence (trait EI), leadership self-efficacy and leader's task self-efficacy with collective task efficacy and group performance. The sample was made up of 217 undergraduate students, randomly assigned to work teams of 1 leader and 2 followers that were requested to perform a production task. An adapted version of the Schutte Self-Report Inventory (SSRI; Schutte et al., 1998) was used to measure trait EI. Structural equation modeling was used to test the hypothesized relationships. Results indicated that task self-efficacy was a mediator between leadership self-efficacy and collective task efficacy; the latter, in turn, was the best predictor of group performance. No significant relationship was found between trait EI and collective task efficacy although, unexpectedly, trait EI was positively associated with leadership self-efficacy. Implications of the results are discussed.     

Temperamental dimension and anxiety problems in a clinical sample of three- to six-year old children: a study of variables

In the last few years, many researchers have studied the presence of common dimensions of temperament in subjects with symptoms of anxiety. The aim of this study is to examine the association between temperamental dimensions (high negative affect and activity level) and anxiety problems in clinical preschool children. A total of 38 children, ages 3 to 6 years, from the Infant and Adolescent Mental Health Center of Girona and the Center of Diagnosis and Early Attention of Sabadell and Olot were evaluated by parents and psychologists. Their parents completed several screening scales and, subsequently, clinical child psychopathology professionals carried out diagnostic interviews with children from the sample who presented signs of anxiety. Findings showed that children with high levels of negative affect and low activity level have pronounced symptoms of anxiety. However, children with anxiety disorders do not present different temperament styles from their peers without these pathologies.     

Concept learning,memory and transfer of dot pattern categories

In the first experiment, subjects rated the similarity of a sample of pairs of random dot patterns generated from 3 prototypes consisting of either 4, 6, or 9 dots. The results of the experiment tended to confirm the structure imposed on the patterns by the construction method. In the second experiment, subjects learned to classify random patterns generated from 2 prototypes with either short or long interprototype distance and consisting of either 4, 6, or 9 dots in a traditional concept identification task. After acquisition, memory for old and new distortions and the prototype, which was not presented during learning, was assessed. The tendency to call a pattern “new” increased with the distance between the pattern and its prototype. In a subsequent transfer test, all subjects saw patterns of either 4, 6, or 9 dots. Performance was above chance and the transfer from larger to smaller patterns tended to be greater than the transfer from smaller to larger patterns. This is consistent with a process of schema formation based on features common to most exemplars of the category. The results are discussed in relation to several theories of concept learning and schema abstraction.