This study was an investigation of the use of manipulative materials in the mathematics classroom. The researcher guided students to create paper triangles, which were then used as a manipulative to calculate the sum of the interior angles of a triangle. On pre- and post-measures of quantitative data, although the data indicated a positive…

The variance formula derived for a two-stage sampling design without replacement employs the joint inclusion probabilities in the first-stage selection of clusters. One of the difficulties encountered in data analysis is the lack of information about such joint inclusion probabilities. One way to solve this issue is by applying Hájek's…

Test score distributions of schools or demographic groups are often summarized by frequencies of students scoring in a small number of ordered proficiency categories. We show that heteroskedastic ordered probit (HETOP) models can be used to estimate means and standard deviations of multiple groups' test score distributions from such data. Because…

The analysis of variance (ANOVA) is one of the most frequently used statistical analyses in practical applications. Accordingly, the single and multiple comparison procedures are frequently applied to assess the differences among mean effects. However, the underlying assumption of homogeneous variances may not always be tenable. This study…

Test scores are commonly reported in a small number of ordered categories. Examples of such reporting include state accountability testing, Advanced Placement tests, and English proficiency tests. This paper introduces and evaluates methods for estimating achievement gaps on a familiar standard-deviation-unit metric using data from these ordered…

Test scores are commonly reported in a small number of ordered categories. Examples of such reporting include state accountability testing, Advanced Placement tests, and English proficiency tests. This article introduces and evaluates methods for estimating achievement gaps on a familiar standard-deviation-unit metric using data from these ordered…

Large-scale assessment programs such as the National Assessment of Educational Progress (NAEP), Trends in International Mathematics and Science Study (TIMSS), and Programme for International Student Assessment (PISA) use a sophisticated assessment administration design called matrix sampling that minimizes the testing burden on individual…

In this article, we consider estimation of parameters of random effects models from samples collected via complex multistage designs. Incorporation of sampling weights is one way to reduce estimation bias due to unequal probabilities of selection. Several weighting methods have been proposed in the literature for estimating the parameters of…

Several complex sample standard error estimators based on linearization and resampling for the latent regression model of the National Assessment of Educational Progress (NAEP) are studied with respect to design choices such as number of items, number of regressors, and the efficiency of the sample. This paper provides an evaluation of the extent…

At present, although the percentages of students with disabilities (SDs) and/or students who are English language learners (ELL) excluded from a NAEP administration are reported, no statistical adjustment is made for these excluded students in the calculation of NAEP results. However, the exclusion rates for both SD and ELL students vary…

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…

A hierarchical latent regression model is suggested to estimate nested and nonnested relationships in complex samples such as found in the National Assessment of Educational Progress (NAEP). The proposed model aims at improving both parameters and variance estimates via a two-level hierarchical linear model. This model falls naturally within the…

Large-scale educational assessments such as the National Assessment of Educational Progress (NAEP) sample examinees to whom an exam will be administered. In most situations the sampling design is not a simple random sample and must be accounted for in the estimating model. After reviewing the current operational estimation procedure for NAEP, this…