Bayesian statistics and biased procedures

A comparison of Neyman's theory of interval estimation with the corresponding subjective Bayesian theory of credible intervals shows that the Bayesian approach to the estimation of statistical parameters allows experimental procedures which, from the orthodox objective viewpoint, are clearly biased and clearly inadmissible. This demonstrated methodological difference focuses attention on the key difference in the two general theories, namely, that the orthodox theory is supposed to provide a known average frequency of successful estimates, whereas the Bayesian account provides only a coherent ordering of degrees of belief and a subsequent maximization of subjective expected utilities. To rebut the charge of allowing biased procedures, the Bayesian must attack the foundations of orthodox, objectivist methods. Two apparently popular avenues of attack are briefly considered and found wanting. The first is that orthodox methods fail to apply to the single case. The second is that orthodox methods are subject to a typical Humean regress. The conclusion is that orthodox objectivist methods remain viable in the face of the subjective Bayesian alternative — at least with respect to the problem of statistical estimation.     

Variables underlying the recognition of random shapes

Speed of sorting decks of 32 cards with two alternative stimuli was measured. The stimuli were pairs of dots with attributes of distance between dots, angle of orientation of the pair, and position of the pair to the right or left of center. The attributes varied in relative discriminability and were used in all possible pair- and triple-correlated (redundant) combinations. Results showed an increase in speed of sorting with either an increase in discriminability or an increase in number of redundant attributes. It is argued that the increased speed with addition of redundant attributes is due both to a selective serial processing of attributes (requiring attribute separability) and to an increased discriminability with combined attributes (requiring attribute integrality).     

Rehabilitation of the Culturally Different: A Model of the Individual in Cultural Change

Services of rehabilitation agencies and facilities tend to be structured to the needs of the larger American culture. It is important, however, to reconsider our social service programs in view of the needs of different cultural groups when providing services that will aid these individuals to move across cultural boundaries. An attempt is made in this paper to develop a model of the individual who undergoes such cultural transition. Such a model should help define problems in service programs, assess the value of current service activities, and identify areas for developing new services that will aid the overall process of cultural transition. A model of behavior development is outlined, followed by a formulation of a model of the individual in cultural change.     

Student Attendance at University Co-curricular Activities

Over 18,000 students at Michigan State University reported their attendance at 46 campus events. Student characteristics were analyzed in terms of student attendance patterns. The 46 events were grouped into 4 independent categories that were attended by students with different characteristics. Students who attended cultural events were mostly single upperclassmen majoring in liberal arts; musical events were attended mostly by music majors; those attending athletic events tended to be single male undergraduates from the more applied disciplines; and social events were attended mostly by undergraduate girls.     

The number of ways to label a structure

It has been observed that the number of different ways in which a graph withp points can be labelled isp! divided by the number of symmetries, and that this holds regardless of the species of structure at hand. In this note, a simple group-theoretic proof is provided.This work was supported by Grant MH 10834 from the National Institute of Mental Health.     

Orlo Strunk Jr.

Pastoral Psychology -     

Serial discrimination-reversal learning with and without errors by the California sea lion

A sea lion under water performed virtually without errors on a series of three form-discrimination reversals. Significant training requirements were the combining of a previously well-established size cue preference with the nonpreferred form cue, followed by the gradual reduction of the size cue until it was completely eliminated. Orienting responses reached a peak and then decreased during progressive-dimensional-change training, suggesting critical stages in the transition of attention from the size dimension to the form dimension. Further experimentation revealed that intensive training during these critical stages obviated the need to reduce very gradually the size cue. Without special training sea lions make perseverative errors on a series of form-discrimination reversals. "Emotional" or nontest-oriented behavior was associated only with the occurrence of successive errors.     

The minimal transformation to orthonormality

The solution is presented to the problem of finding that orthonormal matrix closest in the least-square sense to a given matrix of full rank. An application is shown to the problem in multiple regression analysis of determining the importance of each independent variable.