Barba's (2012) paper is a serious and thoughtful analysis of a vexing problem in behavior analysis: Just what should count as an operant class and how do people know? The slippery issue of a "generalized operant" or functional response class illustrates one aspect of this problem, and "variation" or "novelty" as an operant appears to fall into…

Since 1986, Marilyn Vos Savant, who is listed in the "Guinness Book of World Records Hall of Fame" for the highest IQ, has had a weekly column that is published in "Parade Magazine." In this column, she answers readers' questions on a wide variety of subjects including mathematics and particularly probability. Many of the mathematically oriented…

To compute the probability of having a disease, given a positive test result, is a standard probability problem. The sensitivity and specificity of the test must be given and the prevalence of the disease. We ask how a test-maker might determine the tradeoff between sensitivity and specificity. Adding hypothetical costs for detecting or failing to…

In the nonequivalent groups with anchor test (NEAT) design, the standard error of linear observed-score equating is commonly estimated by an estimator derived assuming multivariate normality. However, real data are seldom normally distributed, causing this normal estimator to be inconsistent. A general estimator, which does not rely on the…

Latent class regression models relate covariates and latent constructs such as psychiatric disorders. Though full maximum likelihood estimation is available, estimation is often in three steps: (i) a latent class model is fitted without covariates; (ii) latent class scores are predicted; and (iii) the scores are regressed on covariates. We propose…

Mutual support societies for problem gamblers have existed in Sweden for 20 years. They have helped more people with gambling problems than any other institution inside or outside the Swedish health care system. This paper outlines the background of these societies and describes the meetings of one of them. Data come from interviews with members…

We construct semigroups with any given positive rational commuting probability, extending a Classroom Capsule from November 2008 in this Journal.

Failure to initiate and remain engaged in academic tasks can have long-lasting effects for students. In this study, we investigated the effects of high-preference sequences on both digits correct per minute and latency to initiate nonpreferred mathematics problems for 3 students with emotional and behavioral disorders. We found that…

This multiple-study experiment evaluated the utility of assessing and treating severe self-injurious behavior (SIB) based on the outcomes of a functional analysis of precursor behavior. In Study 1, a precursor to SIB was identified using descriptive assessment and conditional probability analyses. In Study 2, a functional analysis of precursor…

Research on the high-probability (high-p) request sequence shows that compliance with low-probability (low-p) requests generally increases when preceded by a series of high-p requests. Few studies have conducted formal preference assessments to identify the consequences used for compliance, which may partly explain treatment failures, and still…

This article describes some misconceptions about random variables and related counter-examples, and makes suggestions about teaching initial topics on random variables in general form instead of doing it separately for discrete and continuous cases. The focus is on post-calculus probability courses. (Contains 2 figures.)

The main result of an experiment is typically an estimate of the average treatment effect (ATE) and its standard error. In most experiments, the number of covariates that may be moderators is large. One way this issue is typically skirted is by interpreting the ATE as the average effect for "some" population. Cornfield and Tukey (1956)…

Inverse probability weighting (IPW) estimates are widely used in applications where data are missing due to nonresponse or censoring or in observational studies of causal effects where the counterfactuals cannot be observed. This extensive literature has shown the estimators to be consistent and asymptotically normal under very general conditions,…

In this article we consider the random breakage of a rod into "L" unit elements and present a Markov chain based method that tracks intermediate breakage configurations. The probability of the time to final breakage for L = 3, 4, 5 is obtained and the method is shown to extend in principle, beyond L = 5.

Research on probability judgment has traditionally emphasized that people are susceptible to biases because they rely on "variable substitution": the assessment of normative variables is replaced by assessment of heuristic, subjective variables. A recent proposal is that many of these biases may rather derive from constraints on cognitive…