Timed magnitude comparisons of numerical and nonnumerical expressions of uncertainty

Two experiments involving paired comparisons of numerical and nonnumerical expressions of uncertainty are reported. Subjects were timed under two opposing sets of instructions ("choose higher probability" vs. "choose lower probability"). Numerical comparisons were consistently faster and easier than their nonnumerical counterparts. Consistent distance and congruity effects were obtained, illustrating that both numerical and nonnumerical expressions of uncertainty contain subjective magnitude information, and suggesting that similar processes are employed in manipulating and comparing numerical and verbal terms. To account for the general pattern of results obtained, Holyoak's reference point model (1978) was generalized by explicitly including the vagueness of the nonnumerical expressions. This generalized model is based on the notion that probability expressions can be represented by membership functions (Wallsten, Budescu, Rapoport, Zwick, & Forsyth, 1986) from which measures of location for each word, and measures of overlap for each pair can be derived. A good level of fit was obtained for this model at the individual level.     

Dyadic decisions with numerical and verbal probabilities

The goal of the research was to compare decisions under risk in a situation in which forecasters (F) communicate to decision makers (DM) either numerically (e.g., .70) or verbally (e.g., likely) about the chances that a binary event will occur. Following each forecast, the DM bid for a winning or losing lottery based on the event. In Experiment 1 Fs and DMs also provided numerical translations of each verbal forecast after the DMs' bid. In Experiment 2 the DMs provided membership functions over the [0, 1] interval for each phrase used by the Fs. The primary results were: (a) extreme similarity in the DM's bids and rates of bidding under the two modes of communication; (b) greater variability in bids to specific verbal than numerical forecasts; (c) a pattern of bids, in which DMs demonstrated risk seeking for gains and risk neutrality for losses; (d) DMs' numerical translations in Experiment 1 were closer to .50 than were those of Fs; and (e) phrases selected by Fs had high membership values to DMs for the probabilities the Fs were attempting to describe. Points (a), (b), (d), and (e) are consistent with the ν-μ model which assumes that the vague meaning of a probability phrase can be represented by a membership function over the [0, 1] interval, and that in reaching a decision the DM focuses on a range of probabilities with sufficiently high membership. Point (c) is speculatively attributed to social aspects of the dyadic situation, and requires further investigation.     

The effects of averaging subjective probability estimates between and within judges

The average probability estimate of J > 1 judges is generally better than its components. Two studies test 3 predictions regarding averaging that follow from theorems based on a cognitive model of the judges and idealizations of the judgment situation. Prediction 1 is that the average of conditionally pairwise independent estimates will be highly diagnostic, and Prediction 2 is that the average of dependent estimates (differing only by independent error terms) may be well calibrated. Prediction 3 contrasts between- and within-subject averaging. Results demonstrate the predictions' robustness by showing the extent to which they hold as the information conditions depart from the ideal and as J increases. Practical consequences are that (a) substantial improvement can be obtained with as few as 2-6 judges and (b) the decision maker can estimate the nature of the expected improvement by considering the information conditions.     

A Constrained Linear Estimator for Multiple Regression

“Improper linear models” (see Dawes, Am. Psychol. 34:571–582, 1979), such as equal weighting, have garnered interest as alternatives to standard regression models. We analyze the general circumstances under which these models perform well by recasting a class of “improper” linear models as “proper” statistical models with a single predictor. We derive the upper bound on the mean squared error of this estimator and demonstrate that it has less variance than ordinary least squares estimates. We examine common choices of the weighting vector used in the literature, e.g., single variable heuristics and equal weighting, and illustrate their performance in various test cases.     

A Psychometric Analysis of the “Divide and Conquer” Principle in Multicriteria Decision Making

The principle of “Divide and Conquer” (DAC) suggests that: (1) complex decision problems should be decomposed into smaller, more manageable parts and (2) these smaller parts should be logically aggregated to derive an overall value for each alternative. Typically, decompositional procedures have been compared to holistic evaluations that require decision makers to simultaneously consider all of the relevant attributes in the evaluation of the objects under consideration. These comparisons between decompositional and holistic judgments have primarily used a variant of Multiattribute Utility Theory (MAUT).We presented a general experimental framework that allows for a more extensive assessment of the DAC principle, as well as the effects of decision complexity on both holistic and decompositional procedures. We illustrate this approach with a study that uses the Simple Multiattribute Rating Technique with Swing Weights (SMARTS; Edwards & Barron, 1994) and the Analytic Hierarchy Process (AHP; Saaty, 1980). We report data comparing the convergent validity (e.g the agreement between decompositional and holistic strategies) and the temporal stability for decompositional and holistic judgments on a variety of dependent measures. Decision complexity did not significantly affect the correspondence between decompositional and holistic judgments for both SMARTS and AHP judgments. Results from an ordinal measure of temporal stability indicated the DAC principle was violated for the AHP judgments. For a linear measure of temporal stability, trends in the data indicated that the predicted effects of decision complexity on the DAC principle was violated for the SMARTS judgments.     

Kinship Support and Academic Efficacy Among College Students: A Cross-Sectional Examination

The study examined whether relationships with extended kin were related to higher levels of mental health and academic functioning among college students. Specifically, the study tested whether perceived emotional support from extended (non-nuclear) family was related to self-esteem, psychological distress, and academic efficacy and dedication above and beyond relationships with one’s primary caregivers, and whether these associations varied by class year in college. The sample consisted of 530 students (average age = 20.82), at a public, four-year university. The results revealed that freshmen and seniors who reported high levels of positive relationships with their extended kin also reported higher levels of academic-efficacy and dedication, as well as lower levels of psychological distress. However, the relation between kin emotional support and these outcomes were not significant for sophomores and juniors. There was also a significant association between kinship support and self-esteem for participants in all four class levels. The study underscores the need to examine extended social support systems among college students, above and beyond those maintained with primary caregivers, as well as the dynamic nature of family support during young adulthood.     

Perceptions of Adequate Personal Time and Wellbeing among African American Families with Adolescents

The current study examines the perception of adequate personal or leisure time, and its association with family and caregiver functioning, among a sample of low-income African American families. The investigation is grounded in Conservation of Resources (COR) theory which predicts that caregivers who perceive more adequate personal time will also report higher levels of optimism and lower levels of depressive symptoms, and will have adolescents who report more household routines and less psychologically controlling parenting. A total of 115 caregiver-adolescent (age 14–18) dyads were recruited from a low-income, predominantly African American neighborhood in a major metropolitan center in the United States as part of a larger survey on African American family life. Results indicate that caregivers report perceiving inadequate amounts of time to sleep, get enough exercise, and relax. Caregivers also report comparatively less adequate personal time than time with children. Analyses reveal that caregivers who perceive having more adequate leisure or personal time, report fewer depressive symptoms and higher levels of optimism, after controlling for perceptions of adequate financial resources. Alternatively, there was no association between perceptions of free or leisure time and parenting behaviors, including maintenance of household routines and the use of psychological control. The results underscore the need to examine non-material resources, and their association with wellbeing.     

Demanding kin relations and depressive symptoms among low-income African American women: mediating effects of self-esteem and optimism

Association of demanding kin relations, depressive symptoms, self-esteem, and optimism was assessed among 130 low-income African American women. Demanding relations with kin were positively associated with depressive symptoms and negatively linked to self-esteem and optimism. Self-esteem and optimism were negatively associated with depressive symptoms and mediated the association of demanding relations with kin and women's depressive symptoms. Findings were discussed in terms of the detrimental effects of demanding social relations with kin and the possible role that other relationships may play in compensating for poor relations with extended family.