Aggregate-level conditional status metrics (ACSMs) describe the status of a group by referencing current performance to expectations given past scores. This article provides a framework for these metrics, classifying them by aggregation function (mean or median), regression approach (linear mean and nonlinear quantile), and the scale that supports…

Generalized linear mixed models are frequently applied to data with clustered categorical outcomes. The effect of clustering on the response is often difficult to practically assess partly because it is reported on a scale on which comparisons with regression parameters are difficult to make. This article proposes confidence intervals for…

A common strategy for estimating treatment effects in observational studies using individual student-level data is analysis of covariance (ANCOVA) or hierarchical variants of it, in which outcomes (often standardized test scores) are regressed on pretreatment test scores, other student characteristics, and treatment group indicators. Measurement…

In this article, the change in examinee effort during an assessment, which we will refer to as persistence, is modeled as an effect of item position. A multilevel extension is proposed to analyze hierarchically structured data and decompose the individual differences in persistence. Data from the 2009 Program of International Student Achievement…

This article addresses likely error rates for measuring teacher and school performance in the upper elementary grades using value-added models applied to student test score gain data. Using a realistic performance measurement system scheme based on hypothesis testing, the authors develop error rate formulas based on ordinary least squares and…

Regression methods can locate student test scores in a conditional distribution, given past scores. This article contrasts and clarifies two approaches to describing these locations in terms of readily interpretable percentile ranks or "conditional status percentile ranks." The first is Betebenner's quantile regression approach that results in…

It is often assumed that a vertical scale is necessary when value-added models depend upon the gain scores of students across two or more points in time. This article examines the conditions under which the scale transformations associated with the vertical scaling process would be expected to have a significant impact on normative interpretations…

Value-added models have been widely used to assess the contributions of individual teachers and schools to students' academic growth based on longitudinal student achievement outcomes. There is concern, however, that ignoring the presence of missing values, which are common in longitudinal studies, can bias teachers' value-added scores.…

Test-based accountability as well as value-added asessments and much experimental and quasi-experimental research in education rely on achievement tests to measure student skills and knowledge. Yet, we know little regarding fundamental properties of these tests, an important example being the extent of measurement error and its implications for…

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…

For RCTs of education interventions, it is often of interest to estimate associations between student and mediating teacher practice outcomes, to examine the extent to which the study's conceptual model is supported by the data, and to identify specific mediators that are most associated with student learning. This article develops statistical…

It has been known for some time that item response theory (IRT) models may exhibit a likelihood function of a respondent's ability which may have multiple modes, flat modes, or both. These conditions, often associated with guessing of multiple-choice (MC) questions, can introduce uncertainty and bias to ability estimation by maximum likelihood…

Nonparametric or kernel regression estimation of item response curves (IRCs) is often used in item analysis in testing programs. These estimates are biased when the observed scores are used as the regressor because the observed scores are contaminated by measurement error. Accuracy of this estimation is a concern theoretically and operationally.…

Researchers often compare the relationship between an outcome and covariate for two or more groups by evaluating whether the fitted regression curves differ significantly. When they do, researchers need to determine the "significance region," or the values of the covariate where the curves significantly differ. In analysis of covariance (ANCOVA),…

This paper examines the impact of quality-score weights in meta-analysis. A simulation examines the roles of study characteristics such as population effect size (ES) and its variance on the bias and mean square errors (MSEs) of the estimators for several patterns of relationship between quality and ES, and for specific patterns of systematic…