This article studies the Type I error, false positive rates, and power of four versions of the Lagrange multiplier test to detect measurement noninvariance in item response theory (IRT) models for binary data under model misspecification. The tests considered are the Lagrange multiplier test computed with the Hessian and cross-product approach,…

Modeling the distribution of site level effects is an important problem, but it is also an incredibly difficult one. Current methods rely on distributional assumptions in multilevel models for estimation. There it is hoped that the partial pooling of site level estimates with overall estimates, designed to take into account individual variation as…

Measures of classroom environments have become central to policy efforts that assess school and teacher quality. This has sparked a wide interest in using multilevel factor analysis to test measurement hypotheses about classroom-level variables. One approach partitions the total covariance matrix and tests models separately on the…

This study investigated the levels of possession of science process skills by final year Nigerian Certificate in Education (NCE) Students in colleges of Education in South-Eastern States of Nigeria. The skills that were assessed were observation, experimentation, measurement, communication, and inference. The research was guided by five research…

Considerable discrepancies between the mean and median often occur in data sets that are skewed left, skewed right, or have other unusual features. In such cases, it is important to analyze the data and context carefully to decide how best to describe centers of distributions. The importance of this type of statistical thinking is acknowledged in…

We propose a new limited-information goodness of fit test statistic C[subscript 2] for ordinal IRT models. The construction of the new statistic lies formally between the M[subscript 2] statistic of Maydeu-Olivares and Joe (2006), which utilizes first and second order marginal probabilities, and the M*[subscript 2] statistic of Cai and Hansen…

Written by a social worker for social work students, this is a nuts and bolts guide to statistics that presents complex calculations and concepts in clear, easy-to-understand language. It includes numerous examples, data sets, and issues that students will encounter in social work practice. The first section introduces basic concepts and terms to…

Provides a short BASIC program, RANVAR, which generates random variates for various theoretical probability distributions. The seven variates include: uniform, exponential, normal, binomial, Poisson, Pascal, and triangular. (MVL)