The algebra of factorial indeterminancy

Certain properties and consequences of factor indeterminancy are deduced from an orthogonal transformation derived by Ledermann [5]. The first deduction is the matrix of cosines between maximally distinct factor axes which represent the same factor solution. This result is used to investigate the indeterminancy of factor extensions.     

The geometry of factorial indeterminancy

TheN-dimensional geometry of a Spearman-Thurstone factor solution reveals two sources for the indeterminancy of factor scores: indeterminancy of total factor space and a rotational indeterminancy within a given total factor space. The analytical papers of Ledermann [4] and Guttman [2] on indeterminancy of factor scores are related to these findings and a simple vector model is developed to reveal the properties of rotational indeterminancy. The significance of factor-score indeterminancy is discussed in light of these findings.     

The factorial isolation of primary abilities

This is an experimental study of the isolation, by factor methods, of primary abilities from a battery of tests given to 240 students. The range and nature of the fifty-six tests is briefly described. Tentative interpretations of the twelve orthogonal primary factors are given.     

The factorial interpretation of test difficulty

This paper discusses the influence of test difficulty on the correlation between test items and between tests. The greater the difference in difficulty between two test items or between two tests the smaller the maximum correlation between them. In general, the greater the number of degrees of difficulty among the items in a test or among the tests in a battery, the higher the rank of the matrix of intercorrelations; that is, differences in difficulty are represented in the factorial configuration as additional factors. The suggestion is made that if all tests included in a battery are roughly homogeneous with respect to difficulty existing hierarchies will be more clearly defined and meaningful psychological interpretation of factors more readily attained.     

The factorial structure of sleep dissatisfaction

Research into sleep problems has been dominated by a number of theoretical perspectives from each of which useful treatment applications have been derived. However, the rich diversity of problems that are subsumed under insomnia or sleep disturbance often remain unappreciated. This paper reports the results of a factor analysis performed on the combined items of two questionnaires designed to assess sleep disturbance. Six factors are described, two of which relate to cognitive aspects of sleep disturbance; two which map onto sleep onset and sleep maintenance problems; and two which are drawn from dissatisfaction with poor sleep. Correlations of factor scores with measures of neuroticism, worry and various sleep history variables provide a strong level of construct validity. The results are discussed in terms of their treatment implications.     

The effects of reinforcement and social approval on conforming behaviour

The effects of reinforcement, social approval and sex on conformity were studied. Seventy-two male and 72 female college Ss were divided into equal high and low need for social approval groups. Each group was assigned to 1 of 3 experimental conformity conditions: (a) True-agree; (b) neutral; and (c) true-disagree. The groups were tested via a social conformity apparatus. It was found that: (a) Reinforcement for agreeing with a contrived group consensus (true-agree group) elicited more conformity than social pressure without reinforcement (neutral group), which in turn elicted more conformity than reinforcement for disagreeing with the consensus (trueA- disagree group); (b) females conformed more than males; (c) there was a slight tendency for high social approval Ss to conform more than low social approval Ss. Conformity was explained in terms of social learning, and it was suggested that the situational factor of reinforcement was a more important determinant of conformity than the motivational factor of social approval. The modified conformity scoring procedure used focuses on the conformity process.     

The mathematical theory of factorial invariance under selection

It is first demonstrated that Aitken's selection formulas are equivalent to a linear transformation in the factor space. On this basis the Thomson-Ledermann theorem concerning the invariance of the number of common factors under selection, and a theorem concerning the invariance of factor loadings under selection are derived. A mathematical proof of the results of Thurstone, which are concerned with the invariance of simple structure under selection, is given. The paper provides a conclusive answer to the question, considered by Thurstone and Thomson, whether a multivariate selection is always reducible to successive univariate selections.     

The factorial structure of individual differences in visual perception

Although at first glance the way we perceive the world is similar for most individuals and resembles a veridical interpretation of the environment, the persistent individual differences found in many perceptual processes continue to inspire and confuse researchers. Despite numerous attempts to map out the reliable factors and correlates of individual variance in perception, the factorial structure of vision has remained elusive. The current article reviews recent developments in the study of individual differences in perception with a focus on work that has applied latent variable techniques for analysing performance across multiple visual paradigms. As this overview reveals, studies that have attempted to answer the question whether one general or several specific factors best describe vision tend to reject the monolithic view. Some general notes are also provided regarding pitfalls that should be taken into account when designing such research in the future.     

Attentional characteristics of different types of individuals with high self-esteem in self-threatening situations

The high self-esteem (HSE) heterogeneity hypothesis provides a new research perspective for investigating differences in the quantity and quality of different types of self-esteem. The present study adopted the emotional Stroop paradigm and the odd-one-out search task to explore how individuals with different types of self-esteem process social information in self-threatening situations. The results showed that individuals with different types of self-esteem had an attentional bias toward negative information and had different attentional biases toward angry faces in self-threatening situations. Individuals with fragile HSE and low self-esteem showed facilitated attention to angry faces and had difficulty drawing attention away from them; secure HSE individuals only showed difficulty disengaging attention from angry faces.

     

The orthogonal transformations of a factorial matrix into itself

Certain matrix algebra, pertinent to multiple factor theory, is presented.     

Extensions of factorial solutions

A method is developed for extending any type of factor solution to new tests. The theoretical basis for this approximating scheme is thoroughly investigated, and then a simplification in the technique is introduced for practical purposes. An example is presented which illustrates the procedure of extending a factor solution to three new tests simultaneously.