Matrix derivatives with chain rule and rules for simple,Hadamard, and Kronecker products

The differential calculus for scalars is used to develop theorems for a calculus of functions of matrices. No appeal to scalar notation is necessary in the resulting calculus, so that the given chain and matrix product rules have wide applicability to matrix theory and models. The chain and product rules of scalar calculus become a special case of the matrix rules. The methods are illustrated by application to a generalized stochastic process model potentially relevant to long- and short-term memory.     

Sex-role behaviors and personality traits of male day care teachers

It was hypothesized that male day care teachers who had adopted the feminine role of caregiver would score feminine in their personality traits and would reinforce children for feminine behaviors and punish them for masculine behaviors. A random sample of 20 male caregivers was contrasted to 20 male engineers on personality traits as assessed by The Adjective Checklist (ACL). Twenty female caregivers were also contrasted to the personality traits and the sex-typed contingency behaviors of the male caregivers. Feminine traits were defined by raw scores on the Abasement, Nurturance, Affiliation, Succorance, and Deference scales of the ACL. Masculine traits were represented by raw scores on the Achievement, Dominance, Endurance, and Autonomy scales. The Fagot-Patterson Checklist was employed to determine sex-typed contingency behaviors. Both male and female caregivers reinforced children significantly more for feminine behaviors than masculine behaviors (as defined by The Fagot-Patterson Checklist) and punished masculine behaviors more than feminine behaviors. The personalities of the male caregivers corresponded to the feminine direction of their female counterparts, but they were not significantly more feminine than the male engineers. The female caregivers, however, scored significantly more feminine in personality than the male engineers.This study is based on a dissertation submitted by Bryan E. Robinson to the Department of Child Development — Family Relations, University of North Carolina at Greensboro, in partial fulfillment of the requirements for the Ph.D.     

Debunking a stereotype: The female medical student

The combined research of Horner (1972) and Monahan, Kuhn, and Shaver (1974) has demonstrated the existence of a stereotype of the female medical student as sex-role deviant and disinterested in sex. The present study examined the validity of this stereotype. Male and female medical students' scores on two psychometric measures were compared with the male and female college norms. The stereotype was not supported. Female medical students demonstrated no greater sex-role deviance than did their male counterparts. Furthermore, only male medical students indicated significantly less heterosexual interest than their same-sex norm.The authors wish to thank Dr. David G. Fish, who was involved in the original data collection. Support for the analyses of these data was obtained from Grant Number 607-1034-21 and from a Career Scientist Award, Number 607-1001-22, to the Junior Author.     

Young adults' perceptions of social sex roles across the life span

Fifty male and 50 female undergraduates rated 10 age-sex targets (Boy, Girl, Adolescent Boy, Adolescent Girl, Young Man, Young Woman, Middle-aged Man, Middle-Aged Woman, Old Man and Old Woman) on 12 semantic differential scales. Compared with female targets, male targets were rated higher on potency and activity scales and lower on evaluative scales. Semantic distance between male and female targets showed a curvilinear relationship with target age. Results suggested that young adult subjects perceive that sex-role differences first increase and then decrease across the life span.An earlier version of this article was presented at the convention of the Western Psychological Association in Los Angeles, California, April 1976.     

Multidimensional same--different judgments: evidence against independent comparisons of dimensions

Commonly discussed models of performance in the multidimensional same-different task are based on the assumption that independent same-different decisions are reached for each of the stimulus dimensions used in an experiment. In these models, a higher level mechanism examines th outcome of these independent decisions in order to determine whether the stimuli are the same or different overall. Previous evidence indicating that these models are inconsistent with results from same trials is summarized, and a new test of the above assumption using data from different trials is proposed. Detailed analysis of reaction times from different trials is shown, at least for some pairs of dimensions, to be incompatible with the view that separate same-different decisions are reached for each dimension. The major finding is that there are more relatively fast responses in a condition with two dimensions different, compared with the two conditions with only one of the dimensions different, than any processing model treating the dimensions separately could predict. The results suggest that partial information may be combined across dimensions in order to reach a "different" judgment.     

Sex and cultural differences in the factorial structure of the self-directed search

Holland's Self-Directed Search was administered to 247 male and 252 female high school students, aged 16 to 18 years, attending state schools in New Zealand. Principal factor analysis was used in an attempt to identify six orthogonal factors analogous to Holland's six personality types. The Social and Enterprising scales could not be split into two factors in either sample, and the Investigative and Realistic scales defined a single factor for the female students. Computed distances between pairs of the six personality types in five dimensional factorial space were compared with the relative ordering of the distances expected from Holland's hexagonal model. The positions of the types in space corresponded more closely with the model for the males than they did for the females. The results, in conjunction with those of similar studies in Israel and the United States, imply that the correspondence between some summary codes on the SDS and existing occupational classifications based on Holland's types may be less than perfect, particularly for females. Also, care should be taken when using codes on the SDS to calculate Holland's indices of “consistency,” especially for females.