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.     

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.     

A Response to G. Scott Davis

This defense of my essay on Vitoria and Suárez argues that my use of the term “religious war” is based on religious authority at least as much as religious cause, and that Davis’s decision to discuss only Vitoria limits his ability to come to terms with my thesis. To Davis’s argument that for Vitoria war was justified against the Indians only as a necessity of simple justice and to protect the innocent, I argue that his disjunction between simple justice and religious cause is a false one that fails to come to term with the church’s primary reason for approaching Indians, with the Thomistic understanding of the relation between nature and grace and between reason and revelation, and with the distinction between what justice requires in relation to the church and Christians and what it requires for others. I explain finally that my claim is not that the Catholic political rulers readily responded to papal calls for war except when it was in their interest, but that papal war was central to the normative just‐war tradition of the church in canon law and among major theologians like Vitoria and Suárez.     

Communication of Genetic Risk Information to Daughters in Families with Fragile X Syndrome: The Parent’s Perspective

Parental approaches to communicating information about genetic disorders to their children may be an important determinant in how the children manage stress as well as their adjustment and adaptation to that information. We explored communication patterns through structured interviews with 46 parents of daughters who learned about their genetic risk status as minors. Three different levels of knowledge about fragile X syndrome were explored: 1) informing that it has been diagnosed in the family and is an inherited disorder, 2) informing about the possibility of a daughter being a carrier, and 3) if testing had been done, informing the daughter of her actual carrier status. Additionally, parental perceptions of their daughter’s understanding of the information were explored along with frequency of discussions. We found that communication about genetic risk was initiated by the parents. Five disclosure patterns were identified with variations in style, content, and frequency of communication related to the information that was being disclosed. Aspects of resilient communication were present for all levels of disclosure; however, as the information became more personally relevant for the daughter such as disclosure about the possibility of “being a carrier” for fragile X syndrome and there was uncertainty regarding potential outcomes, the conversations included fewer resilient characteristics. Uncertainty about what and how to present information may negatively affect a parent’s ability to include elements of resilient communication when disclosing genetic risk information.