We present and discuss three examples of misapplication of the notion of conditional probability. In each example, we present the problem along with a published and/or well-known incorrect--but seemingly plausible--solution. We then give a careful treatment of the correct solution, in large part to show how careful application of basic probability…

The experiments reported in this article used a delayed same/different sentence matching task with concurrent measurement of eye movements to investigate the nature of the plausibility effect. The results clearly show that plausibility effects are not due to low level lexical associative processes, but arise as a consequence of the processing of…

Although previous research has not consistently shown that uncertainty about academic major negatively impacts graduation, commitment is largely believed to affect college students' success. We investigated the impact of institutional commitment, commitment to an educational goal, and commitment to an academic major on the probabilities of…

A large literature has developed in which labor market contracts are used to estimate the value of a statistical life (VSL). Reported estimates of the VSL vary substantially, from less than $100,000 to more than $25 million. This research uses meta-analysis to quantitatively assess the VSL literature. Results from existing studies are pooled to…

The number Pi has a rich and colorful history. The origin of Pi dates back to when Greek mathematicians realized that the ratio of the circumference to the diameter is the same for all circles. One is most familiar with many of its applications to geometry, analysis, probability, and number theory. This paper demonstrates several examples of how…

This study investigates sequential dependencies in interresponse times (IRTs) produced by human subjects under random-ratio (RR) and staircase stochastic reinforcement of waiting (staircase SRW) schedules using autocorrelation and relative frequencies of IRT[subscript n] *IRT[subscript n+1] pairs. In the first of two experiments conducted for this…

In this issue's "Classroom Notes" section, the following papers are described: (1) "Sequences of Definite Integrals" by T. Dana-Picard; (2) "Structural Analysis of Pythagorean Monoids" by M.-Q Zhan and J. Tong; (3) "A Random Walk Phenomenon under an Interesting Stopping Rule" by S. Chakraborty; (4) "On Some Confidence Intervals for Estimating the…

Comprehension of moral reasoning is important both for successful moral education and for Kohlbergian claims that moral reasoning development is cognitive in nature. Because a psychometrically appropriate moral comprehension instrument does not appear to exist, the Moral Comprehension Questionnaire (MCQ) was constructed in Study 1 and displayed…

This article introduces prediction as a useful tool to promote mathematical reasoning. First, the article addresses prediction expectations in state standards and gives examples. It also provides a classroom example and activities to illustrate what prediction can look like and how it can serve as a building block for the development of students'…

Instructional strategies for teaching concepts have long been identified. Less commonly studied is a learner's level of confidence and certitude in their knowledge based upon exposure to these instructional treatments. This experimental research study used an instrument referred to as the Spatial Probability Measure (SPM) to solicit levels of…

In an Angoff standard setting procedure, judges estimate the probability that a hypothetical randomly selected minimally competent candidate will answer correctly each item in the test. In many cases, these item performance estimates are made twice, with information shared with the panelists between estimates. Especially for long tests, this…

Many statistical tests are designed to test the different assumptions of the Rasch model, but only few are directed at detecting multidimensionality. The Martin-Lof test is an attractive approach, the disadvantage being that its null distribution deviates strongly from the asymptotic chi-square distribution for most realistic sample sizes. A Monte…

The value of reciprocity in social exchange potentially comprises both instrumental value (the value of the actual benefits received from exchange) and communicative or symbolic value (the expressive and uncertainty reduction value conveyed by features of the act of reciprocity itself). While all forms of exchange provide instrumental value, we…

This article reports on a subset of results from a larger study which examined middle and high school students' probabilistic reasoning. Students in grades 5, 7, 9, and 11 at a boys' school (n = 173) completed a Probability Inventory, which required students to answer and justify their responses to ten items. Supplemental clinical interviews…

In the standard Iowa Gambling Task (IGT), participants have to choose repeatedly from four options. Each option is characterized by a constant gain, and by the frequency and amount of a probabilistic loss. Crone and van der Molen (2004) reported that school-aged children and even adolescents show marked deficits in IGT performance. In this study,…