On the Alias Method for Generating Random Variables from a Discrete Distribution

The alias method of Walker is a clever, new, fast method for generating random variables from an arbitrary, specified discrete distribution. A simple probabilistic proof is given, in terms of mixtures, that the method works for any discrete distribution with a finite number of outcomes. A more efficient version of the table-generating portion of the method is described. Finally, a brief discussion on efficiency of the method is given. We believe that the generality, speed, and simplicity of the method make it attractive for use in generating discrete random variables.     

New Developments in Statistical Computing: New Bias Evaluation Features of EXPLOR—A Program for Assessing Experimental Design Properties

Longitudinal investigations play an increasingly prominent role in biomedical research. Much of the literature on specifying and fitting linear models for serial measurements uses methods based on the standard multivariate linear model. This article proposes a more flexible approach that permits specification of the expected response as an arbitrary linear function of fixed and time-varying covariates so that mean-value functions can be derived from subject matter considerations rather than methodological constraints. Three families of models for the covariance function are discussed: multivariate, autoregressive, and random effects. Illustrations demonstrate the flexibility and utility of the proposed approach to longitudinal analysis.     

Use of the Correlation Coefficient with Normal Probability Plots

The use of the correlation coefficient is suggested as a technique for summarizing and objectively evaluating the information contained in probability plots. Goodness-of-fit tests are constructed using this technique for several commonly used plotting positions for the normal distribution. Empirical sampling methods are used to construct the null distribution for these tests, which are then compared on the basis of power against certain nonnormal alternatives. Commonly used regression tests of fit are also included in the comparisons. The results indicate that use of the plotting position p_i = (i - .375)/(n + .25) yields a competitive regression test of fit for normality.     

On constructing T 2 control charts for retrospective examination

In this paper we consider the issue of constructing retrospective T ² control chart limits so as to control the overall probability of a false alarm at a specified value. We describe an exact method for constructing the control limits for retrospective examination. We then consider Bonferroni-adjustments to Alt's control limit and to the standard x ² control limit as alternatives to the exact limit since it is computationally cumbersome to find the exact limit. We present the results of some simulation experiments that are carried out to compare the performance of these control limits. The results indicate that the Bonferroni-adjusted Alt's control limit performs better that the Bonferroni-adjusted x ² control limit. Furthermore, it appears that the Bonferroni-adjusted Alt's control limit is more than adequate for controlling the overall false alarm probability at a specified value.     

Creating a Consensus: Psychologists, the Supreme Court, and School Desegregation, 1952–1955

SPSSI psychologists' involvement in the early civil rights movement in the postwar United States was epitomized by their involvement in the case of Brown v. Board of Education. This article examines how social scientists sought to maintain the persona of objective, scientific expert when asked to prepare briefs for the U.S. Supreme Court for the Brown case. The social scientists believed that only by collapsing what they saw as an artificial distinction between objectivity and advocacy could the social scientist become a social activist. This article is based on extensive research in numerous archives, including the papers of Gordon W. Allport, Kenneth B. Clark, Stuart W. Cook, David Krech, the National Association for the Advancement of Colored People, Theodore M. Newcomb, Robert Redfield, and the Society for the Psychological Study of Social Issues.     

Career decision-making,career exploration behaviors,and self-regulated learning

Helping individuals make a career decision is a key aim of career counseling. Determining how to encourage self-regulated learning and behaviors needed to achieve this goal often underlies career interventions. The English version of the Career Exploration Behavior survey (CEB-E) measures activities individuals engage in to learn about career options. The present study explored the psychometric properties of the CEB and its impact on various career outcomes. In the first study (N = 498), a good-fitting second-order factor model with four group-level scales and loadings was retained as the best model. In the second study (N = 143), convergent validity and incremental validity of the CEB dimensions were explored through correlation and regression analyses. The CEB predicted commitment making, metacognitions, and vocational identity. Results suggest the CEB-E is a psychometrically sound assessment of career exploration behaviors with potential utility for theory development, program evaluation, and monitoring client progress.     

Stability analysis using mixed models: A critique of tolerance interval methods and a probabilistic solution

Recently, tolerance interval approaches to the calculation of a shelf life of a drug product have been proposed in the literature. These address the belief that shelf life should be related to control of a certain proportion of batches being out of specification. We question the appropriateness of the tolerance interval approach. Our concerns relate to the computational challenges and practical interpretations of the method. We provide an alternative Bayesian approach, which directly controls the desired proportion of batches falling out of specification assuming a controlled manufacturing process. The approach has an intuitive interpretation and posterior distributions are straightforward to compute. If prior information on the fixed and random parameters is available, a Bayesian approach can provide additional benefits both to the company and the consumer. It also avoids many of the computational challenges with the tolerance interval methodology.