A widely and readily applicable covariance structure modeling approach is outlined that allows point and interval estimation of scale reliability with fixed components. The procedure employs only linear constraints introduced in a congeneric model, which after reparameterization permit expression of composite reliability as a function of…

Curriculum-based measurement of oral reading fluency (CBM-R) is an established procedure used to index the level and trend of student growth. A substantial literature base exists regarding best practices in the administration and interpretation of CBM-R; however, research has yet to adequately address the potential influence of measurement error.…

The phenomenon of nonlinear resonance (sometimes called the "jump phenomenon") is examined and second-order van der Pol plane analysis is employed to indicate that this phenomenon is not a feature of the equation, but rather the result of accumulated round-off error, truncation error and algorithm error that distorts the true bounded solution onto…

A simple errors-in-variables regression model is given in this article for illustrating the method of marginal maximum likelihood (MML). Given suitable estimates of reliability, error variables, as nuisance variables, can be integrated out of likelihood equations. Given the closed form expression of the resulting marginal likelihood, the effects…

With respect to the often-present covariance between error terms of correlated variables, D. W. Zimmerman and R. H. Williams's (1977) adjusted correction for attenuation estimates the strength of the pairwise correlation between true scores without assuming independence of error scores. This article focuses on the derivation and analysis of…

Past estimates of the effect of family income on child development have often been plagued by endogeneity and measurement error. In this paper, we use two simulated instrumental variables strategies to estimate the causal effect of income on children's math and reading achievement. Our identification derives from the large, non-linear changes…

Full account of the latent regression model for the National Assessment of Educational Progress is given. The treatment includes derivation of the EM algorithm, Newton-Raphson method, and the asymptotic standard errors. The paper also features the use of the adaptive Gauss-Hermite numerical integration method as a basic tool to evaluate…

The procedures required to obtain the approximate posterior standard deviations of the parameters in the three commonly used item response models for dichotomous items are described and used to generate values for some common situations. The results were compared with those obtained from maximum likelihood estimation. It is shown that the use of…

"Choice and Education across the States," published by the Heartland Institute, is an advocacy document that assigns letter grades to states based on the extensiveness of each state's school choice system. The report asserts, based on a faulty use of past research, that an increase in school choice will strengthen accountability and improve…

In this study, the authors compare the validity of three nonverbal tests for the purpose of identifying academically gifted English-language learners (ELLs). Participants were 1,198 elementary children (approximately 40% ELLs). All were administered the Raven Standard Progressive Matrices (Raven), the Naglieri Nonverbal Ability Test (NNAT), and…

A series of computer programs was written for computing the conditional standard errors of measurement (CSEM) for both rights-scored and formula-scored tests based on a method suggested by F. M. Lord (1984), commonly known as Lord's Method IV or the compound binomial method. These programs estimate the CSEM for both raw and scaled scores, average…

Sampling error refers to variability that is unique to the sample. If the sample is the entire population, then there is no sampling error. A related point is that sampling error is a function of sample size, as a hypothetical example illustrates. As the sample statistics more and more closely approximate the population parameters, the sampling…

The modeling of longitudinal and multilevel data using a latent variable framework is reviewed. Particular emphasis is placed on growth modeling. Examples are discussed where repeated observations are made on students sampled within classrooms and schools. The concept of a latent variable is a convenient way to represent statistical variation not…

The use of multiple comparisons in analysis of variance (ANOVA) is discussed. It is argued that experimentwise Type I error rate inflation can be serious and that its influences are often unnoticed in ANOVA applications. Both classical balanced omnibus and orthogonal planned contrast tests inflate experimentwise error to an identifiable maximum.…

Methods to aid the statistical researchers in making arguments as to what constitutes minimal effect size (MES) are outlined. By selecting MES and determining power for that effect, the researcher communicates to the reader what the researcher considers to be important and what the researcher's chances are for finding that effect or a larger one.…