The reliability of data is a critical issue in decision-making for practitioners in the school. Percent Agreement and Cohen's kappa are the two most widely reported indices of inter-rater reliability, however, a recent Monte Carlo study on the reliability of multi-category scales found other indices to be more trustworthy given the type of data…

Thermodynamic quantities such as the average energy, heat capacity, and entropy are calculated using a Monte Carlo method based on the Metropolis algorithm. This method is illustrated with reference to the harmonic oscillator but is particularly useful when the partition function cannot be evaluated; an example using a one-dimensional spin system…

Monte Carlo simulations are a classical tool to analyse physical systems. When unlikely events are to be simulated, the importance sampling technique is often used instead of Monte Carlo. Importance sampling has some drawbacks when the problem dimensionality is high or when the optimal importance sampling density is complex to obtain. In this…

The Pareto 80/20 Rule, also known as the Pareto principle or law, states that a small number of causes (20%) is responsible for a large percentage (80%) of the effect. Although widely recognized as a heuristic rule, this proportion has not been theoretically based. The article considers derivation of this 80/20 rule and some other standard…

In this article, we discuss the effect of removing the independence assumptions between the residuals in two-level random effect models. We first consider removing the independence between the Level 2 residuals and instead assume that the vector of all residuals at the cluster level follows a general multivariate normal distribution. We…

Despite many articles reporting the problems of dichotomizing continuous measures, researchers still commonly use this practice. The authors' purpose in this article was to understand the reasons that people still dichotomize and to determine whether any of these reasons are valid. They contacted 66 researchers who had published articles using…

The material in this module introduces students to some of the mathematical tools used to examine molecular evolution. This topic is standard fare in many mathematical biology or bioinformatics classes, but could also be suitable for classes in linear algebra or probability. While coursework in matrix algebra, Markov processes, Monte Carlo…

Bayesian multidimensional scaling (MDS) has attracted a great deal of attention because: (1) it provides a better fit than do classical MDS and ALSCAL; (2) it provides estimation errors of the distances; and (3) the Bayesian dimension selection criterion, MDSIC, provides a direct indication of optimal dimensionality. However, Bayesian MDS is not…

When two or more univariate population means are compared, the proportion of variation in the dependent variable accounted for by population group membership is eta-squared. This effect size can be generalized by using multivariate measures of association, based on the multivariate analysis of variance (MANOVA) statistics, to establish whether…

The Functional Measurement approach, proposed within the theoretical framework of Information Integration Theory (Anderson, 1981, 1982), can be a useful multi-attribute analysis tool. Compared to the majority of statistical models, the averaging model can account for interaction effects without adding complexity. The R-Average method (Vidotto &…

This article describes SIMREL, a software program designed for the simulation of alpha coefficients and the estimation of its confidence intervals. SIMREL runs on two alternatives. In the first one, if SIMREL is run for a single data file, it performs descriptive statistics, principal components analysis, and variance analysis of the item scores…

The recent literature on computerized adaptive testing (CAT) has developed methods for creating CAT item pools from a large master pool. Each CAT pool is designed as a set of nonoverlapping forms reflecting the skill levels of an assumed population of test takers. This article presents a Monte Carlo method to obtain these CAT pools and discusses…

Traditional estimators of fit measures based on the noncentral chi-square distribution (root mean square error of approximation [RMSEA], Steiger's [gamma], etc.) tend to overreject acceptable models when the sample size is small. To handle this problem, it is proposed to employ Bartlett's (1950), Yuan's (2005), or Swain's (1975) correction of the…

Our pig game involves a series of tosses of a die with the possibility of a player's score improving with each additional toss. With each additional toss, however, there is also the chance of losing the entire score accumulated so far. Two different strategies for deciding how many tosses a player should attempt are developed and then compared in…

Problems requiring numerical solutions of differential equations or the use of agent-based modeling are presented for use in a course on mass transfer. These problems were solved using the popular technical computing language MATLABTM. Students were introduced to MATLAB via a problem with an analytical solution. A more complex problem to which no…