Several articles deal with tilings with squares and dominoes on 2-dimensional boards, but only a few on boards in 3-dimensional space. We examine a tiling problem with coloured cubes and bricks on a (2 × 2 × "n")-board in three dimensions. After a short introduction and the definition of breakability we show a way to get the number of…

Predictive processing (PP) has been repeatedly presented as a unificatory account of perception, action, and cognition. In this paper, we argue that this is premature: As a unifying theory, PP fails to deliver general, simple, homogeneous, and systematic explanations. By examining its current trajectory of development, we conclude that PP remains…

The Program for the International Assessment of Adult Competencies (PIAAC) is a multicycle survey of adult skills and competencies sponsored by the Organization for Economic Cooperation and Development (OECD). The survey examines a range of basic skills in the information age and assesses these adult skills consistently across participating…

Two questions about certainty in mathematics are asked. First, is mathematical knowledge known with certainty? Second, why is the belief in the certainty of mathematical knowledge so widespread and where does it come from? This question is little addressed in the literature. In explaining the reasons for these beliefs, both cultural-historical and…

Although randomized studies have high internal validity, generalizability of the estimated causal effect from randomized clinical trials to real-world clinical or educational practice may be limited. We consider the implication of randomized assignment to treatment, as compared with choice of preferred treatment as it occurs in real-world…

There have been many discussions of how Type I errors should be controlled when many hypotheses are tested (e.g., all possible comparisons of means, correlations, proportions, the coefficients in hierarchical models, etc.). By and large, researchers have adopted familywise (FWER) control, though this practice certainly is not universal. Familywise…

In the field of cognitive psychology, the "p"-value hypothesis test has established a stranglehold on statistical reporting. This is unfortunate, as the "p"-value provides at best a rough estimate of the evidence that the data provide for the presence of an experimental effect. An alternative and arguably more appropriate measure of evidence is…

In this chapter, the authors discuss the issue of research design in conducting inquiry on college impact and demonstrate the importance of longitudinal pretest-posttest designs in maximizing the internal validity of findings. They begin by discussing the strengths and weaknesses of different types of research design in the college impact…

This article compares Donald Campbell's and Donald Rubin's work on causal inference in field settings on issues of epistemology, theories of cause and effect, methodology, statistics, generalization, and terminology. The two approaches are quite different but compatible, differing mostly in matters of bandwidth versus fidelity. Campbell's work…

On August 14, 2010, the "Los Angeles Times" published the results of a statistical analysis of student test data to provide information about elementary schools and teachers in the Los Angeles Unified School District (LAUSD). The analysis, covering the period from 2003 to 2009, was put forward as an evaluation of the effects of schools…

Value-added models have become popular in research and pay-for-performance plans. While scholars have focused attention on some aspects of their validity (e.g., scoring procedures), others have received less scrutiny. This article focuses on the extent to which value-added scores correspond to other indicators of teacher and teaching quality. The…

Imposed time limits on computer adaptive tests (CATs) can result in examinees having difficulty completing all items, thus compromising the validity and reliability of ability estimates. In this study, the effects of speededness were explored in a simulated CAT environment by varying examinee response patterns to end-of-test items. Expectedly,…

The purpose of the performance study was to review a proposed U.S. Navy Learning Center instructor computation (ICOMP) model for calculating the number of instructors required for teaching courses at Navy training sites. Based on recommendations from the initial analysis, a workweek breakdown was conducted for facilitated self-paced instructors.…

The examination of measurement invariance in polytomous items is complicated by the possibility that the magnitude and sign of lack of invariance may vary across the steps underlying the set of polytomous response options, a concept referred to as differential step functioning (DSF). This article describes three classes of nonparametric DSF effect…

Curriculum-based measurement of mathematics (CBM-M) comprises a set of procedures and instrumentation to assess the level and trend of student achievement in early mathematics. The purpose of this article is to review the recent research and psychometric evidence for CBM-M. Although recent developments in CBM-M include procedures to assess early…