In insurance, the analyst is often faced with a large number of inter-related variables for which correlations need to be estimated. Clearly, all correlations lie in the interval [-1, 1], but the numbers cannot be assigned independently. Here, the choices left to the analyst are considered from both a geometric and a probabilistic viewpoint. In…

The national lottery is often portrayed as a game of pure chance with no room for strategy. This misperception seems to stem from the application of probability instead of expectancy considerations, and can be utilized to introduce the statistical concept of expectation.

In this article, we define the inversion vector of a permutation of the integers 1, 2,..., n. We set up a particular kind of permutation, called a partial random permutation. The sum of the elements of the inversion vector of such a permutation is a random variable of interest.

Four experiments are presented that competitively test rule- and exemplar-based models of human categorization behavior. Participants classified stimuli that varied on a unidimensional axis into 2 categories. The stimuli did not consistently belong to a category; instead, they were probabilistically assigned. By manipulating these assignment…

The authors provide evidence that people typically evaluate conditional probabilities by subjectively partitioning the sample space into n interchangeable events, editing out events that can be eliminated on the basis of conditioning information, counting remaining events, then reporting probabilities as a ratio of the number of focal to total…

The relationship between luminance (i.e., the photometric intensity of light) and its perception (i.e., sensations of lightness or brightness) has long been a puzzle. In addition to the mystery of why these perceptual qualities do not scale with luminance in any simple way, "illusions" such as simultaneous brightness contrast, Mach bands,…

Mr. Johnson has discovered that the higher the level of student engagement and creativity, the lower the probability of plagiarism. For teachers who would like to see such desirable results, he describes the characteristics of assignments that are most likely to produce them. Two scenarios of types of assignments that avoid plagiarism are…

We studied preparatory attention in patients suffering from frontotemporal dementia in the beginning stages of the disease, using an experimental test developed by LaBerge, Auclair, and Sieroff (2000). In this experimental test, a distracter can appear while subjects have to prepare to respond to a simple target. The probability that a distracter…

In this paper, we apply sequential one-sided confidence interval estimation procedures with beta-protection to adaptive mastery testing. The procedures of fixed-width and fixed proportional accuracy confidence interval estimation can be viewed as extensions of one-sided confidence interval procedures. It can be shown that the adaptive mastery…

The ability to identify schematic knowledge is an important goal for both assessment and instruction. In the current paper, schematic knowledge of statistical probability theory is explored from the declarative-procedural framework using multiple methods of assessment. A sample of 90 undergraduate introductory statistics students was required to…

A clinical trial needs a carefully structured, written plan in order not only to ensure its smooth running and successful conclusion but also to gain the compulsory agreement of an ethical committee. Such a plan is called a protocol. It consists of several stages. These are: (1) An introduction; (2) A statement of aims, objectives, hypotheses and…

Punctuated equilibrium theory (PET) is an agenda-based theory that offers a theoretical foundation for large budget shifts. PET emphasizes that the static, incremental nature of agendas is occasionally interrupted by punctuations. These punctuations indicate shifts in priority among the agenda items, and with those agenda shifts come trade-offs.…

The Centre for the Economics of Education was asked to bring together a wide range of academic evidence (primarily England-based) to investigate the extent to which academic and non-academic childhood outcomes are complementary to each other, or are in some way traded-off against each other. The report also investigates the drivers of both…

This study considers the importance of contextual effects on the quality of assessments on item bias and differential item functioning (DIF) in measurement. Often, in educational studies, students are clustered in teachers or schools, and the clusters could impact psychometric issues yet are largely ignored by traditional item analyses. A…

Differential Item Functioning (DIF) occurs when there is a greater probability of solving an item based on group membership after controlling for ability. Following administration of a 50-item scientific and quantitative reasoning exam to 286 two-year and 1174 four-year students, items were evaluated for DIF. Two-year students performed…