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.     

Scene perception: Detecting and judging objects undergoing relational violations

Five classes of relations between an object and its setting can characterize the organization of objects into real-world scenes. The relations are (1) Interposition (objects interrupt their background), (2) Support (objects tend to rest on surfaces), (3) Probability (objects tend to be found in some scenes but not others), (4) Position (given an object is probable in a scene, it often is found in some positions and not others), and (5) familiar Size (objects have a limited set of size relations with other objects). In two experiments subjects viewed brief (150 msec) presentations of slides of scenes in which an object in a cued location in the scene was either in a normal relation to its background or violated from one to three of the relations. Such objects appear to (1) have the background pass through them, (2) float in air, (3) be unlikely in that particular scene, (4) be in an inappropriate position, and (5) be too large or too small relative to the other objects in the scene. In Experiment I, subjects attempted to determine whether the cued object corresponded to a target object which had been specified in advance by name. With the exception of the Interposition violation, violation costs were incurred in that the detection of objects undergoing violations was less accurate and slower than when those same objects were in normal relations to their setting. However, the detection of objects in normal relations to their setting (innocent bystanders) was unaffected by the presence of another object undergoing a violation in that same setting. This indicates that the violation costs were incurred not because of an unsuccessful elicitation of a frame or schema for the scene but because properly formed frames interfered with (or did not facilitate) the perceptibility of objects undergoing violations. As the number of violations increased, target detectability generally decreased. Thus, the relations were accessed from the results of a single fixation and were available sufficiently early during the time course of scene perception to affect the perception of the objects in the scene. Contrary to expectations from a bottom-up account of scene perception, violations of the pervasive physical relations of Support and Interposition were not more disruptive on object detection than the semantic violations of Probability, Position and Size. These are termed semantic because they require access to the referential meaning of the object. In Experiment II, subjects attempted to detect the presence of the violations themselves. Violations of the semantic relations were detected more accurately than violations of Interposition and at least as accurately as violations of Support. As the number of violations increased, the detectability of the incongruities between an object and its setting increased. These results provide converging evidence that semantic relations can be accessed from the results of a single fixation. In both experiments information about Position was accessed at least as quickly as information on Probability. Thus in Experiment I, the interference that resulted from placing a fire hydrant in a kitchen was not greater than the interference from placing it on top of a mail ? in a street scene. Similarly, violations of Probability in Experiment II were not more detectable than violations of Position. Thus, the semantic relations which were accessed included information about the detailed interactions among the objects—information which is more specific than what can be inferred from the general setting. Access to the semantic relations among the entities in a scene is not deferred until the completion of spatial and depth processing and object identification. Instead, an object's semantic relations are accessed simultaneously with its physical relations as well as with its own identification.     

Perception of autonomic reactions and actual heart rate in phobic patients

The relationship between perceived physiological arousal and actual heart-rate reactions was studied in two behavioral test situations. The subjects were 70 phobic patients (34 social phobics and 36 claustrophobics) who were given the general form of the Autonomic Perception Questionnaire about 1 month before the respective behavioral test and the specific form immediately after the test. The results showed significant correlations between APQ and actual heart rate for the social phobics, while the picture was more complicated for the claustrophobics. The implications of these results are discussed.This research was supported by Grant 05452 from the Swedish Medical Research Council.     

The influence of relative frequencies of pure and mixed stimuli on mixture suppression in taste

In experiments on saltiness suppression in NaCL-sucrose mixtures, the amount of suppression depends not only on the suppressing sucrose component in the mixture, but also on the relative frequencies of pure NaCL stimuli and mixed stimuli in the series. The observed variation of mixture suppression as a function of these frequencies can be explained by Helson’s adaptation level theory.     

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.     

TRAINING CONSERVATION OF QUANTITY (LIQUIDS) IN WEST AFRICAN (BAOULE) CHILDREN

A developmental ‘lag’ is found in the Conservation of Quantity (Liquids) in a sample of 73 rural, schooled Baoulé children (Ivory Coast, West Africa) aged 7 to 14 years. This study was designed to investigate if this ‘lag’ could be reduced or bridged through training and whether it could be attributed to differences in ‘performance’ or in ‘competence’. A sub-sample of 28 children aged 7 to 9 years was divided into two matched groups, one being trained for Conservation of Liquids and the other for Class Inclusion (Lavallée and Dasen in press). Statistically significant training effects were observed, which generalized to other concrete operational concepts and remained stable over at least one month. Since no ‘actualization’ or very fast learning occurred, the ‘lag’ was attributed to differences in competence; the training was sufficient to bridge the developmental lag.