A note on partitioned determinants

A formula for the determinant of a partitioned matrix, possibly with singular submatrices, is derived and applied to some psychometric and numerical problems.     

Generalized eigenvalue problems with positive semi-definite matrices

In a recent paper in this journal McDonald, Torii, and Nishisato show that generalized eigenvalue problems in which both matrices are singular can sometimes be solved by reducing them to similar problems of smaller order. In this paper a more extensive analysis of such problems is used to sharpen and clarify the results of McDonald, Torii, and Nishisato. Possible extensions are also indicated. The relevant mathematical literature is reviewed briefly.     

Toward understanding sex differences in pay allocation: Agency,communion, and reward distribution behavior

This research examined the extent to which the personality characteristics of agency and communion are sex linked, and the extent to which differences in these orientations can account for sex differences in reward distribution behavior. In two studies, the agency and communion level of large samples of male and female undergraduates were assessed. As expected, males were more agentic and females were more communal. Moreover, when subjects who scored high or low on agency and high or low on communion were asked to allocate rewards between themselves and a co-worker, these personality differences were related to their allocation decisions. These results were used as the basis for discussing the role that sex-linked personality differences might play in distributive justice judgments.This article is an adaptation of a colloquium presentation at the meeting of the American Psychological Association, Los Angeles, August 1981. The research reported here was supported by NIMH grant MH29987-1, Goals, Motives, and Norms of Reward Distribution, and by NIMH Biomedical Research Support Grant from the College of Social Science, Michigan State University. The authors wish to thank Andrea Doughty for her valuable advice, and to gratefully acknowledge the help of Mark Teicher, Julie B. Klein, Sue Schnelbach, Pat Loepp, Barb Allen, Gavin Goodrich, Bob O'Hara, Kelly Bowen, Rod Hollenstein, Steve Schultz, and Mary Hurst.     

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.     

Evidence that a factor besides progesterone, prolactin, or plasma-estradiol-binding protein inhibits estrogen-induced sexual receptivity in pregnant rats.

Daily administration of estradiol benzoate stimulated significantly less lordotic behavior in rats during the second half of pregnancy than in ovariectomized females that received subcutaneous progesterone implants, pituitary grafts that raised plasma prolactin, or both treatments combined. Following an initial facilitation of receptivity, females with progesterone implants showed only moderate reductions in lordosis quotients over 3 test days. The capacity of plasma from pregnant rats to bind estradiol was found to increase significantly during the second half of pregnancy. However, daily administration to pregnant rats of a synthetic estrogen, R 2858, which is not bound by plasma protein, was no more effective than estradiol benzoate in stimulating receptive behavior. Administration of estradiol benzoate also stimulated significantly lower levels of sexual behavior in pregnant females than in females in which pseudopregnancy had been prolonged by previous hysterectomy or induction of uterine decidualization. These findings suggest that some endocrine factor other than progesterone, prolactin, or estradiol-binding protein is primarily responsible for the potent suppression of behavioral responsiveness to estrogen which occurs in pregnant rats. It is suggested that 5 alpha-reduced androgens may cause these behavioral effects.     

Demonstration of an aftereffect occurring in the tactile-kinesthetic domain

Summary The aim of this work is the demonstration of a tactile-kinesthetic aftereffect. A sequence of stimuli was offered to adult subjects whose task was to compare two weights presented simultaneously to both hands by means of a Piéron gravimeter. In Experiment 1 the inspection stimuli consisted of two successive presentations of unequal weights for a period of 2 × 10 s. The test stimuli consisted of two equal weights rapidly following an inspection stimulus. Control stimuli consisting of two equal weights not preceded by an inspection stimulus were interspersed in the sequence. The results obtained confirm the existence of a contrast effect after presentation of an inspection stimulus. In Experiment 2 the inspection stimuli consisted of a single presentation of two unequal weights for a period of 20 s. The results confirm those of the first experiment and provide data enabling the contrast effect obtained to be interpreted as a Köhler-type aftereffect. In order to avoid confusion with the kinesthetic-figural aftereffect, we propose to call the effect demonstrated here the Gravimetric Aftereffect.     

Correctness of Kruskal's algorithms for monotone regression with ties

Kruskal has proposed two modifications of monotone regression that can be applied if there are ties in nonmetric scaling data. In this note we prove Kruskal's conjecture that his algorithms give the optimal least squares solution of these modified monotone regression problems. We also propose another (third) approach for dealing with ties.Comments by Dr. J. B. Kruskal have been most helpful.