Variability of the MAX and MIN Statistic: A Theory of the Quantile Spread as a Function of Sample Size

The maximum and minimum of a sample from a probability distribution are extremely important random variables in many areas of psychological theory, methodology, and statistics. For instance, the behavior of the mean of the maximum or minimum processing time, as a function of the number of component random processing times (n), has been studied extensively in an effort to identify the underlying processing architecture (e.g., Townsend & Ashby, 1983; Colonius & Vorberg, 1994). Little is known concerning how measures of variability of the maximum or minimum change with n. Here, a new measure of random variability, the quantile spread, is introduced, which possesses sufficient strength to define distributional orderings and derive a number of results concerning variability of the maximum and the minimum statistics. The quantile spread ordering may be useful in many venues. Several interesting open problems are pointed out. This work was supported by an NIH Grant R01 MH57717 to the first author. Some of the collaboration took place during the year 2000 while J.T. Townsend was a Fellow at the Hanse Institute for Advanced Study (HWK), sponsored by H. Colonius at Oldenburg University.     

Sample Size Planning for Detecting Mediation Effects: A Power Analysis Procedure Considering Uncertainty in Effect Size Estimates

Abstract

When planning mediation studies, researchers are often interested in the sample size needed to achieve adequate power for testing mediation. Power depends on population effect sizes, which are unknown in practice. In conventional power analysis, effect size estimates, however, are often used as population values, which could result in underpowered studies. Uncertainty in effect size estimates has been considered in other sample size planning contexts (e.g., t-test, ANOVA), but has not been handled properly for planning mediation studies. In the current study, we proposed an easy-to-use sample size planning method for testing mediation with uncertainty in effect size estimates considered. We conducted simulation studies to demonstrate the impact of uncertainty in effect size estimates on power of testing mediation, and to provide sample size suggestions under different levels of uncertainty. Empirical examples were provided to illustrate the application of our method. R functions and a web application were developed to facilitate implementation.     

Differential Response to a Dysphoric Mood Induction Procedure as a Function of Level of Experiential Avoidance

The Psychological Record - Participants reporting high versus low levels of experiential avoidance as assessed by the Acceptance and Action Questionnaire (Hayes et al., 2004) were compared in their...     

Dispersion in Cognitive Ability as a Function of Age: A Longitudinal Study of an Elderly Community Sample

This longitudinal study investigated whether age is associated with increased dispersion among major domains of cognitive ability. Three samples were examined: the full sample of 760 elderly community dwellers aged 70 years and older who were tested in 1990; a subset of the original sample who died between testing occasions; and the sample of 426 who survived with full data sets in 1994 (followed up for a mean 3.5 years). Dispersion, as measured by the within-individual standard deviation of ability scores and by the within-individual deviations from crystallized intelligence for speed, memory and spatial functioning, was significantly correlated with age in all three samples at Wave 1 and at Wave 2 (for the longitudinal sample). The rate at which dispersion increased was not significantly correlated with age. In a more detailed analysis of the 426 survivors, dispersion as a function of age was similar for demented persons within this sample, those without dementia, those with poor and excellent educational levels, and those with a physical disability. Activities of daily living was a predictor of larger-than-average changes in dispersion – but not age, education, or activity. Greater dispersion was associated with faster deterioration in memory and speed performance. Contrary to some recent reports, there was evidence for greater within-individual variability among cognitive domains in older individuals.     

Empirical Correlates of Cosmopolitan Orientation: Etiology and Functions in a Worldwide Representative Sample

Psychology has begun contributing to social theory by providing empirical measures of actually existing cosmopolitanism that complements more purely theoretical conceptions of the construct common in philosophy and sociology. Drawing from two waves of research on representative adult samples from 19 countries (N = 8740), metric invariance was found for the three factors of cosmopolitan orientation (COS): cultural openness (CO), global prosociality (GP), and respect for cultural diversity (RCD). In terms of etiology, among Wave 1 measures, the personality factor of agreeableness was the best predictor of the cosmopolitan factors of GP and RCD at Wave 2, whereas openness of personality best predicted CO. Wave 1 measures of education, political liberalism, and self-reported social status independently also explained a small amount of variance in COS. Functionally, COS was shown to predict less prejudice against immigrants, and more support for global civil society, even after controlling for social dominance orientation. All three COS factors independently predicted better attitudes towards immigrants. GP was the best predictor of trust in the United Nations, whereas RCD was the best predictor of support for environmental protection. The three-factor model of COS appears well-calibrated for assessing actually existing cosmopolitanism across cultures.     

Delayed Matching to Sample: Probability of Responding in Accord with Equivalence as a Function of Different Delays

The Psychological Record - The present series of 4 experiments investigated the probability of responding in accord with equivalence in adult human participants as a function of increasing or...     

Scaling Judgments of Lifted Weight: Lifter Size and the Role of the Standard

Animals generally seek to avoid potentially harmful collisions. To perform successful avoidance, actors must correctly perceive the approach of an object and produce an appropriate motor response. Objects can approach from any part of the visual field, but avoidance skills are particularly relevant when threatening approaches occur in peripheral vision. This type of behavior has so far received little attention. Stoffregen and Riccio (1990) found that participants are sensitive to visually simulated impending collision at 0 or 90°. However, motor behavior produced in response to a real object approaching at various angles of eccentricity and at various speeds has not been investigated.

In this study, participants were asked to dodge a ball approaching at 0, 20, 40, 60, or 80° of eccentricity. The ball was travelling at a constant speed of 1.0, 1.5, or 2.0 m/sec. Results showed that time to contact (TTC) at initiation of the avoidant response was similar for 0 and 20° but increased from 20 to 80°. Angle of approach had no effect on participants' movement velocity. Ball speed had an effect on both variables. TTC decreased and participants' movement velocity increased with eccentricity. No interaction was observed between ball speed and eccentricity. These results show that a successful motor response to impending physical collision is possible across a wide range of approach eccentricities. It appears that the speed of the approach was accurately perceived. The speed of avoidant responses was consistent, suggesting that intensity coupling, that is, a coupling of movement velocity with stimulus speed, was not affected by the eccentricity.     

Probability of Stimulus Equivalence as a Function of Class Size vs. Number of Classes

The Psychological Record - Two experiments were conducted to study stimulus equivalence as a function of class size and number of classes. In the first experiment, equivalence was tested in 50...     

Sample Size in Factor Analysis: The Role of Model Error

This article examines effects of sample size and other design features on correspondence between factors obtained from analysis of sample data and those present in the population from which the samples were drawn. We extend earlier work on this question by examining these phenomena in the situation in which the common factor model does not hold exactly in the population. We present a theoretical framework for representing such lack of fit and examine its implications in the population and sample. Based on this approach we hypothesize that lack of fit of the model in the population will not, on the average, influence recovery of population factors in analysis of sample data, regardless of degree of model error and regardless of sample size. Rather, such recovery will be affected only by phenomena related to sampling error which have been studied previously. These hypotheses are investigated and verified in two sampling studies, one using artificial data and one using empirical data.     

Attention Problems as a Mediator of the Relation between Executive Function and Social Problems in a Child and Adolescent Outpatient Sample

Social functioning is critical for the successful navigation of everyday life for children, adolescents, and adults. Recent theories have postulated a neuropsychological basis for social functioning with particularly strong links with the executive functioning (EF) system. The current study examined attention problems as a mediator between EF (e.g., working memory, planning, and response inhibition) and social functioning in a child and adolescent outpatient sample. Participants were 218 children ages 6–16 (M = 10.23; SD = 2.52; 68.8 % males) who were referred to an outpatient clinic for psychoeducational assessment. Bias-corrected bootstrapping mediation analyses were used to examine the hypothesized models. The effects of working memory and planning (but not response inhibition) on social problems were mediated by attention problems in both teacher- and mother-reported models. These findings also held up in cross-source models (e.g., mother-reported attention problems as a mediator in a model predicting teacher-reported social problems). These findings have implications for dimensional models of social functioning and conceptual models for specific clinical populations (e.g., attention-deficit/hyperactivity disorder).     

The Trapezoidal Illusion as a Function of Age,Intellectual Status,Size Constancy,and Form Discrimination

One hundred twenty-two, middle-class white boys and girls aged 3 through 12 years were interviewed to determine the nature and the development of their concepts of death and the impact of experience on those concepts.

Five conclusions were drawn from the results of this inquiry: (a) children's concepts of death were found to be constituted of components which were suggested prior to the study; (b) children's understanding of each of the components developed from absence to incomplete presence to complete presence; (c) children's concepts of death developed as a function of age maturity; (d) children's experiences with death accelerated death concept development only in 6-year-olds and below; and (e) children's concepts of death developed in three stages clearly related to the preoperational, concrete operations, and formal operations stages suggested by Piaget. In contrast with Nagy's results, children did not reify death; furthermore, children 8-years-old and above were consistent in showing adult ideas of death.     

Examination of the Hierarchical Structure of the Brief COPE in a French Sample: Empirical and Theoretical Convergences

This study aimed to determine whether the various factors of coping as measured by the Brief COPE could be integrated into a more parsimonious hierarchical structure. To identify a higher structure for the Brief COPE, several measurement models based on prior theoretical and hierarchical conceptions of coping were tested. First, confirmatory factor analysis (CFA) results revealed that the Brief COPE's 14 original factors could be represented more parsimoniously with 5 higher order dimensions: problem-solving, support-seeking, avoidance, cognitive restructuring, and distraction (N = 2,187). Measurement invariance across gender was also shown. Second, results provided strong support for the cross-validation and the concurrent validity of the hierarchical structure of the Brief COPE (N = 584). Results indicated statistically significant correlations between Brief COPE factors and trait anxiety and perceived stress. Limitations and theoretical and methodological implications of these results are discussed.     

Functional Somatic Syndromes and Childhood Physical Abuse in Women: Data From a Representative Community-Based Sample

This study investigated whether childhood physical abuse was associated with functional somatic syndromes (FSS) in women while controlling for age, race, and four clusters of potentially confounding factors: (a) Other childhood adversities, (b) adult health behaviors, (c) socioeconomic status and stressors, and (d) mental health. A regional subsample of the 2005 Canadian Community Health Survey of 7,342 women was used. Women reported whether they had been diagnosed with chronic fatigue syndrome (CFS), fibromyalgia (Fm), irritable bowel syndrome (IBS), or multiple chemical sensitivities (MCS). Fully 749 reported having been physically abused by someone close to them during their youth. When controlling for potentially confounding factors, childhood physical abuse was significantly associated with CFS (OR = 2.11; 95% CI = 1.22, 3.65), Fm (OR = 1.65; 95% CI = 1.08, 2.52), and MCS (OR = 2.82; 95% = CI 1.90, 4.17). Clinicians using reattribution and stepped care approaches in the management of FSS should assess for a history of abuse.     

A Rigorous Test of the Fit of the Circumplex Model to Big Five Personality Data: Theoretical and Methodological Issues and Two Large Sample Empirical Tests

Our objective was to apply the rigorous test developed by Browne (1992) to determine whether the circumplex model fits Big Five personality data. This test has yet to be applied to personality data. Another objective was to determine whether blended items explained correlations among the Big Five traits. We used two working adult samples, the Eugene-Springfield Community Sample and the Professional Worker Career Experience Survey. Fit to the circumplex was tested via Browne's (1992) procedure. Circumplexes were graphed to identify items with loadings on multiple traits (blended items), and to determine whether removing these items changed five-factor model (FFM) trait intercorrelations. In both samples, the circumplex structure fit the FFM traits well. Each sample had items with dual-factor loadings (8 items in the first sample, 21 in the second). Removing blended items had little effect on construct-level intercorrelations among FFM traits. We conclude that rigorous tests show that the fit of personality data to the circumplex model is good. This finding means the circumplex model is competitive with the factor model in understanding the organization of personality traits. The circumplex structure also provides a theoretically and empirically sound rationale for evaluating intercorrelations among FFM traits. Even after eliminating blended items, FFM personality traits remained correlated.     

Size contrast as a function of figural similarity

Size contrast occurs in numerous configurations where a test figure appears apparently larger when surrounded by small elements and apparently smaller when surrounded by large elements. Using the Ebbinghaus illusion, the magnitude of this effect is shown to vary as a function of apparent similarity between test and inducing element.     

Accuracy of Pace Count as a Distance Estimation Procedure

The purpose of this study was to assess the accuracy of pace counting under varying conditions and to resolve discrepancies between U.S. Army Field Manual 21-26 (FM 21-26; Department of the Army, 1987) and pace-counting research conducted by Powers (1964). Two experiments were designed to measure accuracy of distance estimations from pace counting on-road and off-road under conditions of daylight and darkness. In both experiments, male soldiers enrolled in One Station Unit Training (OSUT) were trained to estimate distances based on pace counts performed on a flat road during daylight. In Experiment 1, the soldiers were tested on a flat road during both daylight and darkness; in Experiment 2, soldiers were tested off-road on hilly terrain during both daylight and darkness. The general finding in both experiments was that soldiers tended to underestimate distance during day- light and to overestimate distance during darkness. These errors became greater as the test conditions became less like the training condition. It was concluded that pace count should be adjusted, as indicated by FM 21-26, either by opportunities for more training time or by standard pace-count adjustment formulas. Also, because of inherent inaccuracies, pace count should be used as a backup and/or in conjunction with other land navigation techniques.