These authors have previously described how to use the "t" test to compare two groups. In this article, they describe the use of a different test, analysis of variance (ANOVA) to compare more than two groups. ANOVA is a test of group differences: do at least two of the means differ from each other? ANOVA assumes (1) normal distribution…

In this study we compared five item selection procedures using three ability estimation methods in the context of a mixed-format adaptive test based on the generalized partial credit model. The item selection procedures used were maximum posterior weighted information, maximum expected information, maximum posterior weighted Kullback-Leibler…

Though much research and attention has been directed at assessing the correlation coefficient under range restriction, the assessment of reliability under range restriction has been largely ignored. This article uses item response theory to simulate dichotomous item-level data to assess the robustness of KR-20 ([alpha]), [omega], and test-retest…

It is shown that deviations of estimated from true values of item difficulty parameters, caused for example by item calibration errors, the neglect of randomness of item difficulty parameters, testlet effects, or rule-based item generation, can lead to systematic bias in point estimation of person parameters in the context of adaptive testing.…

Evidence is presented for the immediate apprehension of exact small quantities. Participants performed a quantification task (are the number of items greater or smaller than?), and carry-over effects were examined between numbers requiring the same response. Carry-over effects between small numbers were strongly affected by repeats of pattern and…

In acquiring number words, children exhibit a qualitative leap in which they transition from understanding a few number words, to possessing a rich system of interrelated numerical concepts. We present a computational framework for understanding this inductive leap as the consequence of statistical inference over a sufficiently powerful…

This article investigates the numbers [image omitted], originally studied by Catalan. We re-confirm that they are indeed integers. Using the close relationship between them and the Catalan numbers C[subscript n], we develop some divisibility properties for C[subscript n]. In particular, we establish that [image omitted], where f[subscript k]…

Structural equation models with interaction and quadratic effects have become a standard tool for testing nonlinear hypotheses in the social sciences. Most of the current approaches assume normally distributed latent predictor variables. In this article, we present a Bayesian model for the estimation of latent nonlinear effects when the latent…

Archimedes calculated the centre of gravity of the cone but the proof of this theorem is not extant in his works. Knorr made a reconstruction of this proof utilizing geometrical arguments. This paper proves this theorem by means of a physical demonstration utilizing the law of the lever, and by adapting from Archimedes the method of mechanical…

By following learned rules rather than reasoning, students often fall into common error patterns, something every experienced teacher has observed in the classroom. In their effort to circumvent the developing common error patterns of their students, the authors decided to supplement their math text with two weeklong investigations. The first was…

This article summarizes research conducted on calculator block items from the 2007 fourth- and eighth-grade National Assessment of Educational Progress Main Mathematics. Calculator items from the assessment were categorized into two categories: problem-solving items and noncomputational mathematics concept items. A calculator has the potential to…

Nonreading tasks that share some (but not all) of the task demands of reading have often been used to make inferences about how cognition influences when the eyes move during reading. In this article, we use variants of the E-Z Reader model of eye-movement control in reading to simulate eye-movement behavior in several of these tasks, including…

Objective: Sample size and statistical power calculation should consider clustering effects when schools are the unit of randomization in intervention studies. The objective of the current study was to investigate how student outcomes are clustered within schools in an obesity prevention trial. Method: Baseline data from the Food, Health &…

Students with learning disabilities score lower than other at-risk groups on state standardized assessment tests. Educators are searching for intervention strategies to improve math achievement for students with learning disabilities. The study examined the effects of a mathematics intervention known as Cover, Copy, and Compare for learning basic…

Improving foundational academic skills for elementary level students continues to be a challenge for classroom teachers. This study implemented weekly progress monitoring procedures using curriculum-based measurement assessments in conjunction with weekly individual student-teacher graphing and goal-setting conferences to determine the effect the…