A procedure modelling ideal classical and quantum gases is discussed. The proposed approach is mainly based on the idea that modelling and algorithm analysis can provide a deeper understanding of particularly complex physical systems. Appropriate representations and physical models able to mimic possible pseudo-mechanisms of functioning and having…

Research pertaining to the distortion of the squared canonical correlation coefficient has traditionally been limited to the effects of sampling error and associated correction formulas. The purpose of this study was to compare the degree of attenuation of the squared canonical correlation coefficient under varying conditions of score reliability.…

Rational models of cognition typically consider the abstract computational problems posed by the environment, assuming that people are capable of optimally solving those problems. This differs from more traditional formal models of cognition, which focus on the psychological processes responsible for behavior. A basic challenge for rational models…

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…

Several previous studies have examined the ability to judge the relative mass of objects in idealized collisions. With a newly developed technique of psychological Markov chain Monte Carlo sampling (A. N. Sanborn & T. L. Griffiths, 2008), this work explores participants; perceptions of different collision mass ratios. The results reveal…

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…

In the first part of the study, nine estimators of the first-order autoregressive parameter are reviewed and a new estimator is proposed. The relationships and discrepancies between the estimators are discussed in order to achieve a clear differentiation. In the second part of the study, the precision in the estimation of autocorrelation is…

Cluster sampling results in response variable variation both among respondents (i.e., within-cluster or Level 1) and among clusters (i.e., between-cluster or Level 2). Properly modeling within- and between-cluster variation could be of substantive interest in numerous settings, but applied researchers typically test only within-cluster (i.e.,…

Relative weight analysis is a procedure for estimating the relative importance of correlated predictors in a regression equation. Because the sampling distribution of relative weights is unknown, researchers using relative weight analysis are unable to make judgments regarding the statistical significance of the relative weights. J. W. Johnson…

The vertical scales of large-scale achievement tests created by using item response theory (IRT) models are mostly based on cluster (or correlated) educational data in which students usually are clustered in certain groups or settings (classrooms or schools). While such application directly violated assumption of independent sample of person in…

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…

Most inter-rater reliability studies using nominal scales suggest the existence of two populations of inference: the population of subjects (collection of objects or persons to be rated) and that of raters. Consequently, the sampling variance of the inter-rater reliability coefficient can be seen as a result of the combined effect of the sampling…

Simulating multivariate nonnormal data with specified correlation matrices is difficult. One especially popular method is Vale and Maurelli's (1983) extension of Fleishman's (1978) polynomial transformation technique to multivariate applications. This requires the specification of distributional moments and the calculation of an intermediate…

One of the main objectives in meta-analysis is to estimate the overall effect size by calculating a confidence interval (CI). The usual procedure consists of assuming a standard normal distribution and a sampling variance defined as the inverse of the sum of the estimated weights of the effect sizes. But this procedure does not take into account…

This article presents an application of Monte Carlo methods for developing and assembling multistage adaptive tests (MSTs). A major advantage of the Monte Carlo assembly over other approaches (e.g., integer programming or enumerative heuristics) is that it provides a uniform sampling from all MSTs (or MST paths) available from a given item pool.…