It seems that just when we are about to lay P-technique factor analysis finally to rest as obsolete because of newer, more sophisticated multivariate time-series models using latent variables--dynamic factor models--it rears its head to inform us that an obituary may be premature. We present the results of some simulations demonstrating that even…

Null distributions of permutation tests for two-sample, paired, and block designs are simulated using the R statistical programming language. For each design and type of data, permutation tests are compared with standard normal-theory and nonparametric tests. These examples (often using real data) provide for classroom discussion use of metrics…

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…

Computing the mean and covariance matrix of some multivariate distributions, in particular, multivariate normal distribution and Wishart distribution are considered in this article. It involves a matrix transformation of the normal random vector into a random vector whose components are independent normal random variables, and then integrating…

Scale score measures are ubiquitous in the psychological literature and can be used as both dependent and independent variables in data analysis. Poor reliability of scale score measures leads to inflated standard errors and/or biased estimates, particularly in multivariate analysis. Reliability estimation is usually an integral step to assess…

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 currently available meta-analytic methods for correlations have restrictive assumptions. The fixed-effects methods assume equal population correlations and exhibit poor performance under correlation heterogeneity. The random-effects methods do not assume correlation homogeneity but are based on an equally unrealistic assumption that the…

Recursive partitioning methods have become popular and widely used tools for nonparametric regression and classification in many scientific fields. Especially random forests, which can deal with large numbers of predictor variables even in the presence of complex interactions, have been applied successfully in genetics, clinical medicine, and…

This article describes the Knowledge Discovery and Data Mining (KDD) process and its application in the field of educational data mining (EDM) in the context of a digital library service called the Instructional Architect (IA.usu.edu). In particular, the study reported in this article investigated a certain type of data mining problem, clustering,…

A variance-to-range ratio variable weighting procedure is proposed. We show how this weighting method is theoretically grounded in the inherent variability found in data exhibiting cluster structure. In addition, a variable selection procedure is proposed to operate in conjunction with the variable weighting technique. The performances of these…

This paper discusses the use of interactive graphics to teach multivariate data analysis to Psychology students. Three techniques are explored through separate activities: parallel coordinates/boxplots; principal components/exploratory factor analysis; and cluster analysis. With interactive graphics, students may perform important parts of the…

In a 2010 address to the College Board, U.S. Secretary of Education Arne Duncan laid out a vision for high school that advances the Obama administration's goal of the U.S. once again leading the world in educational attainment. There is no grade in which the magnitude and complexity of this shift becomes clearer than in senior year. Historically,…

Community college students typically have access to a large selection of courses and programs, and therefore the student transcripts at any one college or college system tend to be very diverse. As a result, it is difficult for faculty, administrators, and researchers to understand the course-taking patterns of students in order to determine what…

The design of computer science curricula should rely on central concepts of the discipline rather than on technical short-term developments. Several authors have proposed lists of basic concepts or fundamental ideas in the past. However, these catalogs were based on subjective decisions without any empirical support. This article describes the…

Using the divergence theorem technique of L. Eifler and N.H. Rhee, "The n-dimensional Pythagorean Theorem via the Divergence Theorem" (to appear: Amer. Math. Monthly), we extend the law of cosines for a triangle in a plane to an "n"-dimensional simplex in an "n"-dimensional space.