Aggregate item response analysis

A stochastic postulate is given for the multiple-item, successive-intervals scaling of populations. The logistic equivalent of this postulate provides an aggregate item response model in which a unidimensional submodel may be nested. This reduction provides a subtractive conjoint measurement of several items and stimuli on the same latent scale. Generalized-least-squares methods are used to estimate and test the multiple-item model, and its unidimensional reduction, on aggregate survey responses. The entire procedure is illustrated with an analysis of semantic-differential attitude data. This analysis exhibits an item selection procedure that is applicable to various social constructs.The authors dedicate this paper to the memory and contributions of Clyde Coombs.The programming and data analyses for the present paper were carried out by José Ventura of the Department of Industrial and Systems Engineering, and Jerry Meiten of the Department of Statistics, University of Florida.The study was also supported by the College of Business Administration, University of Florida, and the Faculty of Social Sciences, Hebrew University of Jerusalem.     

Confidence depends on level of aggregation

The credible intervals that people set around their point estimates are typically too narrow (cf. Lichtenstein, Fischhoff, & Phillips, 1982). That is, a set of many such intervals does not contain the actual values of the criterion variables as often as it should given the probability assigned to this event for each estimate. The typical interpretation of such data is that people are overconfident about the accuracy of their judgments. This paper presents data from two studies showing the typical levels of overconfidence for individual estimates of unknown quantities. However, data from the same subjects on a different measure of confidence for the same items, their own global assessment for the set of multiple estimates as a whole, showed significantly lower levels of confidence and overconfidence than their average individual assessment for items in the set. It is argued that the event and global assessments of judgment quality are fundamentally different and are affected by unique psychological processes. Finally, we discuss the implications of a difference between confidence in single and multiple estimates for confidence research and theory.     

Interval estimation for linear functions of medians in within-subjects and mixed designs

The currently available distribution-free confidence interval for a difference of medians in a within-subjects design requires an unrealistic assumption of identical distribution shapes. A confidence interval for a general linear function of medians is proposed for within-subjects designs that do not assume identical distribution shapes. The proposed method can be combined with a method for linear functions of independent medians to provide a confidence interval for a linear function of medians in mixed designs. Simulation results show that the proposed methods have good small-sample properties under a wide range of conditions. The proposed methods are illustrated with examples, and R functions that implement the new methods are provided.     

Algebras of Intervals and a Logic of Conditional Assertions

Intervals in boolean algebras enter into the study of conditional assertions (or events) in two ways: directly, either from intuitive arguments or from Goodman, Nguyen and Walker's representation theorem, as suitable mathematical entities to bear conditional probabilities, or indirectly, via a representation theorem for the family of algebras associated with de Finetti's three-valued logic of conditional assertions/events. Further representation theorems forge a connection with rough sets. The representation theorems and an equivalent of the boolean prime ideal theorem yield an algebraic completeness theorem for the three-valued logic. This in turn leads to a Henkin-style completeness theorem. Adequacy with respect to a family of Kripke models for de Finetti's logic, ukasiewicz's three-valued logic and Priest's Logic of Paradox is demonstrated. The extension to first-order yields a short proof of adequacy for Körner's logic of inexact predicates.     

Standard errors and confidence intervals for correlations corrected for indirect range restriction: A simulation study comparing analytic and bootstrap methods

A frequent topic of psychological research is the estimation of the correlation between two variables from a sample that underwent a selection process based on a third variable. Due to indirect range restriction, the sample correlation is a biased estimator of the population correlation, and a correction formula is used. In the past, bootstrap standard error and confidence intervals for the corrected correlations were examined with normal data. The present study proposes a large-sample estimate (an analytic method) for the standard error, and a corresponding confidence interval for the corrected correlation. Monte Carlo simulation studies involving both normal and non-normal data were conducted to examine the empirical performance of the bootstrap and analytic methods. Results indicated that with both normal and non-normal data, the bootstrap standard error and confidence interval were generally accurate across simulation conditions (restricted sample size, selection ratio, and population correlations) and outperformed estimates of the analytic method. However, with certain combinations of distribution type and model conditions, the analytic method has an advantage, offering reasonable estimates of the standard error and confidence interval without resorting to the bootstrap procedure's computer-intensive approach. We provide SAS code for the simulation studies.     

Comparing What to What,on What Scale? The Impact of Item Comparisons and Reference Points in Communicating Risk and Uncertainty

The mandated public availability of individual hospital's audit data for children's heart surgery in the UK creates a challenging scenario for communicating these complex and sensitive data to diverse audiences. On the basis of this scenario, we conducted three experiments with the aim of understanding how best to help lay people understand these data and the practical goal of improving the public presentation of these data. The experiments compared different outcome measures for displaying the survival rate (percentage scale versus the ratio of the predicted/observed rates) and presentation formats (individual hospital versus all hospitals shown) for outcomes data presented relative to prediction intervals generated by a risk model that adjusts for case mix. Our data highlight how easily inappropriate comparisons can influence evaluations of complex data: for instance, both a survival ratio of 1 and the presence of other hospitals seemingly provided reference points that resulted in inappropriately harsh evaluations of some hospitals. By drawing on evaluability theory, we demonstrate how to enhance people's understanding of these complex data while also discouraging inappropriate comparisons, which has implications for communicating risk and uncertainty and for choice architecture design in a range of contexts. Copyright © 2018 John Wiley & Sons, Ltd.     

Regional brain activity change predicts responsiveness to treatment for stuttering in adults

Developmental stuttering is known to be associated with aberrant brain activity, but there is no evidence that this knowledge has benefited stuttering treatment. This study investigated whether brain activity could predict progress during stuttering treatment for 21 dextral adults who stutter (AWS). They received one of two treatment programs that included periodic H₂¹⁵O PET scanning (during oral reading, monologue, and eyes-closed rest conditions). All participants successfully completed an initial treatment phase and then entered a phase designed to transfer treatment gains; 9/21 failed to complete this latter phase. The 12 pass and 9 fail participants were similar on speech and neural system variables before treatment, and similar in speech performance after the initial phase of their treatment. At the end of the initial treatment phase, however, decreased activation within a single region, L. putamen, in all 3 scanning conditions was highly predictive of successful treatment progress.