Given a set of urns, each filled with a mix of black chips and white chips, what is the probability of drawing a black chip from the last urn after some sequential random shifts of chips among the urns? The Total Probability Formula (TPF) is the common tool to solve such a problem. However, when the number of urns is more than two and the number…

This article examines how numerical intuition for prices develops after a major change in currency. University students in Portugal (Study 1) and Austria (Study 2) made price estimates for 40 different items from November 2001 to June 2002, surrounding the time at which these countries switched to the euro. Overall results are more in accordance…

The starting point for this discussion of error estimates is the fact that integrals that arise in Fourier series have properties that can be used to get improved bounds. This idea is extended to more general situations.

As the title says, this article considers the dog-on-the-beach problem from the perspective of the calculus of variations, making connections with the brachistochrone problem and Snell's law.

Do people tend to underestimate time when their attention is engaged? Studies supporting this idea have routinely confounded attentional manipulations with changes in other factors, such as response complexity and memory load. The aim of the present study was to obtain the first direct evidence that attentional engagement mediated by cortical…

Neater representations for variance are given for small sample sizes, especially for 3 and 4. With these representations, variance can be calculated without a calculator if sample sizes are small and observations are integers, and an upper bound for the standard deviation is immediate. Accessible proofs of lower and upper bounds are presented for…

This article illustrates that not all statistical software packages are correctly calculating a "p"-value for the classical "F" test comparison of two independent Normal variances. This is illustrated with a simple example, and the reasons why are discussed. Eight different software packages are considered.

The authors introduce subset conjunction as a classification rule by which an acceptable alternative must satisfy some minimum number of criteria. The rule subsumes conjunctive and disjunctive decision strategies as special cases. Subset conjunction can be represented in a binary-response model, for example, in a logistic regression, using only…

In hierarchical linear models we often find that group indicator variables at the cluster level are significant predictors for the regression slopes. When this is the case, the average relationship between the outcome and a key independent variable are different from group to group. In these settings, a question such as "what range of the…

The notion of an impact factor was first posited by Eugene Garfield (1972) to study the use, prestige, and status of scientific journals. The Institute for Scientific Information created the impact factor as a means to measure the number of times an "average article" published in a journal was cited over a particular time period ("The impact…

This paper investigates a general identity which expresses an apparently complicated and intriguing sum of fractions as an elegant and straightforward sum of simple terms.

A method for the numerical evaluation of the error term in Gaussian quadrature rules is derived by means of Chebyshev polynomials of the first kind.

This article considers skills and abilities of young children with number in the areas of cardinality and ordinality. Responses to number tasks by a sample of 3- and 4-year-old children are described to outline their differing approaches to determining the numerosity of a set, and to establish their application of ordinality language to describe…

An alternative formulation of the multigroup common factor model with minimal uniqueness constraints is considered. This alternative formulation is based on a simple identification constraint that is related to the standard maximum likelihood constraint used in single-group common factor analysis. It is argued that the alternative formulation…

Eggerth and Andrew (2006 [this issue]) provide a valuable contribution to researchers and practitioners using the C index to measure congruence when person or environment codes contain fewer than three letters. However, the computational procedures outlined by Eggerth and Andrew may be more complex than they need be. A simpler alternative to…