The estimation of proportions inm groups

In many applications, it is desirable to estimate binomial proportions inm groups where it is anticipated that these proportions are similar but not identical. Following a general approach due to Lindley, a Bayesian Model II aposteriori modal estimate is derived that estimates the inverse sine transform of each proportion by a weighted average of the inverse sine transform of the observed proportion in the individual group and the average of the estimated values. Comparison with a classical method due to Jackson spotlights some desirable features of Model II analyses. The simplicity of the present formulation makes it possible to study the behavior of the Bayesian Model II approach more closely than in more complex formulations. Also, it is possible to estimate the amount of gain afforded by the Model II analyses.     

Teaching gender-related material: The effect of group sex composition on perceptions of a female instructor

This study investigated how group sex composition affects female and male students' perceptions of female instructors who teach in the area of counseling women. Three components of person perception were assessed: cognitive, affective, and behavioral. The cognitive domain included evaluations of the instructor and the subject matter presented; the affective domain included emotional responses to the instructor and the subject matter; and the behavioral domain included actions in response to the instructor, operationalized as the number of questions asked by students. Students with some interest in a career in the helping professions viewed one of two videotapes either with a group of same-sex peers or in a group in which they were the only male or female. One tape described a gender-neutral topic (psychology and the law) and the other described a female gender-related topic (sex bias in counseling women). The same female instructor made both presentations. Students then completed the measures. As predicted, the sex composition of the student group affected person perception, especially in the affective and behavior domains. Recommendations are made for future research.This study was supported by a small grant from the University Research Institute, University of Texas at Austin. Appreciation is expressed to Sherry Fowler, Bob Haverstick, and Kathy Thomas for help with data collection and to Carolyn Bates and Ken Wilgus for coding the open-ended responses. A paper based on this research was presented at the meetings of the American Psychological Association, August 1987.     

Computing the von Neumann-Morgenstern characteristic functionυ(S) for cooperativen-person transferable utility normal form games: LP and saddlepoint solutions

An APL computer program is described for computing the von Neumann-Morgensterncharacteristic function of cooperativen-person transferable utility games in normal form. The program is designed to stand alone, or it can be used in conjunction with other programs for game theoretic computation that will be introduced in future articles.     

Statistics as psychometrics

In this paper, modern statistics is considered as a branch of psychometrics and the question of how the central problems of statistics can be resolved using psychometric methods is investigated. Theories and methods developed in the fields of test theory, scaling, and factor analysis are related to the principle problems of modern statistical theory and method. Topics surveyed include assessment of probabilities, assessment of utilities, assessment of exchangeability, preposterior analysis, adversary analysis, multiple comparisons, the selection of predictor variables, and full-rank ANOVA. Reference is made to some literature from the field of cognitive psychology to indicate some of the difficulties encountered in probability and utility assessment. Some methods for resolving these difficulties using the Computer-Assisted Data Analysis (CADA) Monitor are described, as is some recent experimental work on utility assessment.1980 Psychometric Society presidential address.I am indebted to Paul Slovic and David Libby for valuable consultation on the issues discussed in this paper and to Nancy Turner and Laura Novick for assistance in preparation.Research reported herein was supported under contract number N00014-77-C-0428 from the Office of Naval Research to The University of Iowa, Melvin R. Novick, principal investigator. Opinions expressed herein reflect those of the author and not those of sponsoring agencies.     

Bayesian inference and the classical test theory model: Reliability and true scores

A general one-way analysis of variance components with unequal replication numbers is used to provide unbiased estimates of the true and error score variance of classical test theory. The inadequacy of the ANOVA theory is noted and the foundations for a Bayesian approach are detailed. The choice of prior distribution is discussed and a justification for the Tiao-Tan prior is found in the particular context of the “n-split” technique. The posterior distributions of reliability, error score variance, observed score variance and true score variance are presented with some extensions of the original work of Tiao and Tan. Special attention is given to simple approximations that are available in important cases and also to the problems that arise when the ANOVA estimate of true score variance is negative. Bayesian methods derived by Box and Tiao and by Lindley are studied numerically in relation to the problem of estimating true score. Each is found to be useful and the advantages and disadvantages of each are discussed and related to the classical test-theoretic methods. Finally, some general relationships between Bayesian inference and classical test theory are discussed. Supported in part by the National Institute of Child Health and Human Development under Research Grant 1 PO1 HDO1762. Reproduction, translation, use or disposal by or for the United States Government is permitted.     

Francisco de Vitoria and Francisco Suárez on Religious Authority and Cause for Justified War: The Centrality of Religious War in the Christian Just War Tradition

Contrary to the received understanding that Francisco de Vitoria and Francisco Suárez ruled out religious war by grounding just cause in natural law, they supported a robust view of papal authority for war when necessary for the defense of the church against heretics, schismatics, and pagans as well as for the spread of Christianity and Christendom throughout the world. They believed that religious wars were in accord with natural law as a means to its fulfillment in Christianity, as a justification for the defense of the church as the one true faith, and as a moral obligation to provide all of humanity with the opportunity to receive Christian truth and grace. The neo‐Thomists' vigorous support for religious war was in the mainstream of the Christian just war tradition from the time of the wars against pagans in the early middle ages through their own time. This finding and the continuation into the modern era of sanctified patriotism stemming from the mixing of church and state especially during war that began in early Middle Ages, along with the historic roots of the recently prominent presumption against war, argue for a more complex understanding of the normative Christian just war tradition than that found among supporters of the classic interpretation of that tradition.