Michael Smithson

Correct confidence intervals for various regression effect sizes and parameters: The importance of noncentral distributions in computing intervals

The advantages that confidence intervals have over null-hypothesis significance testing have been presented on many occasions to researchers in psychology. This article provides a practical introduction to methods of constructing confidence intervals for multiple and partial R 2 and related parameters in multiple regression models based on “noncentral”F and χ2 distributions. Until recently, these techniques have not been widely available due to their neglect in popular statistical textbooks and software. These difficulties are addressed here via freely available SPSS scripts and software and illustrations of their use. The article concludes with discussions of implications for the interpretation of findings in terms of noncentral confidence intervals, alternative measures of effect size, the relationship between noncentral confidence intervals and power analysis, and the design of studies.

A comparison of an electronic version of the SF-36 General Health Questionnaire to the standard paper version

Because of its sound psychometric properties the SF-36 General Health Questionnaire is used throughout the world, yet it is difficult to analyse and score. Using a newly developed software package, onto which any questionnaire can be loaded, we developed an electronic version of the SF-36 General Health Questionnaire. The purpose of this study is test the effect of the electronic mode of administration on the measurement properties of the SF-36. In a randomised cross-over design study 79 healthy individuals and 36 chronic pain patients completed both electronic and paper versions of the SF-36. Seventy-one percent preferred the electronic SF-36, 7% stated no preference, and 22% preferred the paper version. Completion time for the electronic SF-36 was slightly less, and there were no missing or problematical responses, whereas 44% of participants had at least one missing or problematical response in the paper version. Data entry and auditing time was 8 hours. There was less than 4% inter-version difference for any of the SF-36 sub-scales. The electronic SF-36 was well accepted and slightly quicker to complete than the paper version. We conclude that the electronic SF-36 is equivalent in performance and more effective than the paper version.

Can gender inequalities be eliminated

In previous work we used a conceptualization of double standards to develop a theory explaining how similar performances may lead to different levels of attributed ability when performers belong to different status groups (e.g., gender, ethnicity). The theory predicts that the effect of double standards will be reduced when objective standards are presented explicitly. Using the dyadic influence paradigm from status characteristics research, we tested three hypotheses: (1) In the absence of performance information, people hold higher performance expectations for males than for females on a male task; (2) contradictory information on performance with explicit standards for ability cancels the effect of gender-based expectations; and (3) the size of the performance difference (magnitude of contradiction) is related to the magnitude of difference in expectations. We measured expectation advantage/disadvantage both directly and through its effect on behavior, namely rejection or acceptance of influence. The results support the hypotheses.

Mixed and mixture regression models for continuous bounded responses using the beta distribution

Doubly bounded continuous data are common in the social and behavioral sciences. Examples include judged probabilities, confidence ratings, derived proportions such as percent time on task, and bounded scale scores. Dependent variables of this kind are often difficult to analyze using normal theory models because their distributions may be quite poorly modeled by the normal distribution. The authors extend the beta-distributed generalized linear model (GLM) proposed in Smithson and Verkuilen (2006) to discrete and continuous mixtures of beta distributions, which enables modeling dependent data structures commonly found in real settings. The authors discuss estimation using both deterministic marginal maximum likelihood and stochastic Markov chain Monte Carlo (MCMC) methods. The results are illustrated using three data sets from cognitive psychology experiments.

Relative ability, paths of relevance, and influence in task-oriented groups

In task-oriented groups, people accept influence more from others whom they believe, on the basis of diffuse and specific status characteristics as well as prior performances, to have greater ability at the task. Past research has treated difference in ability as a binary variable (better or worse); it is not known whether magnitude of difference in performances translates into relative magnitude of inferred ability, and thence into degrees of differentiation in the status structure of decision-making groups. We conducted an experiment to examine the relative impact of three aspects of task performance on the inference of ability: absolute level of performance, relative performance (better/worse), and the degree of difference in performances by two group members. These variables then were used to predict acceptance of influence in a two-person decision task. Simple binary difference in ability explained 35 per cent of the variance in influence accepted. Degree of difference in ability significantly increased level of prediction, particularly for subjects in the lower range of performance scores, thus supporting the claim that relative and absolute levels of performance create additional differences in expectations. Finally, we propose that a concept of graded status characteristics should be incorporated into status characteristics theory.

The theory of uncertainty orientation: a mathematical reformulation

In this paper, we present a mathematical formulation derived from the theory of uncertainty orientation (In R.M. Sorrehtino, & E.T. Higgins (Eds.), the handbook of motivation and cognition: Foundations of social behaviour, Vol. 1 (pp. 379-403). New York: The Guilford press; The uncertain mind: Individual differences in facing the unknown. London: Erlbaum (UK), Taylor & Francis). This formulation integrates affective and informational influences on thought and action. It is a model of self-regulation where the need to maintain clarity and the need to attain clarity are considered as two independent informational tendencies. These informational tendencies are influenced by the degree of self-relevance and the amount of perceived situational uncertainty. In addition, they are multiplicative with affective approach and avoidance tendencies, leading to accentuation or inhibition of behaviours expressed in action. It is further demonstrated that when the nondominant action tendency is instigated, secondary source of motivation are expressed. This model not only accounts for past data, but also permits exploration using computer simulation. In addition, many new and testable hypotheses, including those related to affect and dynamical decision theory, are generated.

Scientific uncertainty and climate change: Part I. Uncertainty and unabated emissions

Uncertainty forms an integral part of climate science, and it is often used to argue against mitigative action. This article presents an analysis of uncertainty in climate sensitivity that is robust to a range of assumptions. We show that increasing uncertainty is necessarily associated with greater expected damages from warming, provided the function relating warming to damages is convex. This constraint is unaffected by subjective or cultural risk-perception factors, it is unlikely to be overcome by the discount rate, and it is independent of the presumed magnitude of climate sensitivity. The analysis also extends to “second-order” uncertainty; that is, situations in which experts disagree. Greater disagreement among experts increases the likelihood that the risk of exceeding a global temperature threshold is greater. Likewise, increasing uncertainty requires increasingly greater protective measures against sea level rise. This constraint derives directly from the statistical properties of extreme values. We conclude that any appeal to uncertainty compels a stronger, rather than weaker, concern about unabated warming than in the absence of uncertainty.

Variables Affecting the Perception of Self-Disclosure Appropriateness

Summary The perception of appropriate self-disclosure was examined as a function of sex of the interactants, intimacy, and valence of self-disclosure. Dependent variables investigated in addition to perceived appropriateness were perceived friendliness, maturity, warmth, psychological adjustment, openness, emotional stability, and sensitivity of the discloser; and mutual liking of, and desire for future contact with, the discloser. Normative evaluations of male or female confederate disclosure where intimacy level and valence had been experimentally manipulated, were provided by 64 male and 64 female volunteer undergraduate Ss, who were randomly assigned to the 16 cells of a 2(sex of discloser/confederate) × 2(sex of recipient/subject) × 2(intimacy) × 2(valence) factorial design. Interpersonal evaluations of the discloser occurred in the context of a structured acquaintance session. Female recipients were more receptive to disclosure thus viewing it as appropriate. Positive disclosure in contrast to negat...

Generalized Linear Models for Categorical and Continuous Limited Dependent Variables

Introduction and Overview The Nature of Limited Dependent Variables Overview of GLMs Estimation Methods and Model Evaluation Organization of This Book Discrete Variables Binary Variables Logistic Regression The Binomial GLM Estimation Methods and Issues Analyses in R and Stata Exercises Nominal Polytomous Variables Multinomial Logit Model Conditional Logit and Choice Models Multinomial Processing Tree Models Estimation Methods and Model Evaluation Analyses in R and Stata Exercises Ordinal Categorical Variables Modeling Ordinal Variables: Common Practice versus Best Practice Ordinal Model Alternatives Cumulative Models Adjacent Models Stage Models Estimation Methods and Issues Analyses in R and Stata Exercises Count Variables Distributions for Count Data Poisson Regression Models Negative Binomial Models Truncated and Censored Models Zero-Inflated and Hurdle Models Estimation Methods and Issues Analyses in R and Stata Exercises Continuous Variables Doubly Bounded Continuous Variables Doubly Bounded versus Censored The beta GLM Modeling Location and Dispersion Estimation Methods and Issues Zero- and One-Inflated Models Finite Mixture Models Analyses in R and Stata Exercises Censoring and Truncation Models for Censored and Truncated Variables Non-Gaussian Censored Regression Estimation Methods, Model Comparison, and Diagnostics Extensions of Censored Regression Models Analyses in R and Stata Exercises Extensions Extensions and Generalizations Multilevel Models Bayesian Estimation Evaluating Relative Importance of Predictors in GLMs

Human judgment under sample space ignorance

This paper surveys results of a research program investigating human judgments of imprecise probabilities under sample-space ignorance (i.e., ignorance of what the possible outcomes are in a decision). The framework used for comparisons with human judgments is primarily due to Walley (1991, 1996). Five studies are reported which test four of Walleys prescriptions for judgment under sample-space ignorance, as well as assessing the impact of the number of observations and types of events on subjective lower and upper probability estimates. The paper concludes with a synopsis of future directions for empirical research on subjective imprecise probability judgments.