The overall aim was to examine effects of differences in group ability and features of the anchor test form on equating bias and the standard error of equating (SEE) using both real and simulated data. Chained kernel equating, Postratification kernel equating, and Circle-arc equating were studied. A college admissions test with four different…

In this study, Kernel test equating methods were compared under NEAT and NEC designs. In NEAT design, Kernel post-stratification and chain equating methods taking into account optimal and large bandwidths were compared. In the NEC design, gender and/or computer/tablet use was considered as a covariate, and Kernel test equating methods were…

A latent variable modeling method for studying measurement invariance when evaluating latent constructs with multiple binary or binary scored items with no guessing is outlined. The approach extends the continuous indicator procedure described by Raykov and colleagues, utilizes similarly the false discovery rate approach to multiple testing, and…

Path models with observed composites based on multiple items (e.g., mean or sum score of the items) are commonly used to test interaction effects. Under this practice, researchers generally assume that the observed composites are measured without errors. In this study, we reviewed and evaluated two alternative methods within the structural…

In a typical differential item functioning (DIF) analysis, a significance test is conducted for each item. As a test consists of multiple items, such multiple testing may increase the possibility of making a Type I error at least once. The goal of this study was to investigate how to control a Type I error rate and power using adjustment…

ACT reporting categories and ACT Readiness Ranges are new features added to the ACT score reports starting in fall 2016. For each reporting category, the number correct score, the maximum points possible, the percent correct, and the ACT Readiness Range, along with an indicator of whether the reporting category score falls within the Readiness…

Tucker and chained linear equatings were evaluated in two testing scenarios. In Scenario 1, referred to as rater comparability scoring and equating, the anchor-to-total correlation is often very high for the new form but moderate for the reference form. This may adversely affect the results of Tucker equating, especially if the new and reference…

The paper develops a two-stage robust procedure for structural equation modeling (SEM) and an R package "rsem" to facilitate the use of the procedure by applied researchers. In the first stage, M-estimates of the saturated mean vector and covariance matrix of all variables are obtained. Those corresponding to the substantive variables…

This article contrasts 2 approaches to analyzing transitivity of preference and other behavioral properties in choice data. The approach of Regenwetter, Dana, and Davis-Stober (2011) assumes that on each choice, a decision maker samples randomly from a mixture of preference orders to determine whether "A" is preferred to "B." In contrast, Birnbaum…

After many equatings have been conducted in a testing program, equating errors can accumulate to a degree that is not negligible compared to the standard error of measurement. In this paper, the author investigates the asymptotic accumulative standard error of equating (ASEE) for linear equating methods, including chained linear, Tucker, and…

The objective of this study was to provide empirical evidence to support psychometric properties of a modified four-dimensional model of the Leadership Scale for Sports (LSS). The study tested invariance of all parameters (i.e., factor loadings, error variances, and factor variances-covariances) in the four-dimensional measurement model between…

Standard least squares analysis of variance methods suffer from poor power under arbitrarily small departures from normality and fail to control the probability of a Type I error when standard assumptions are violated. This article describes a framework for robust estimation and testing that uses trimmed means with an approximate degrees of…

A new formula is developed for the relative efficiency of two tests measuring the same trait. The formula expresses relative efficiency solely in terms of the standard errors of measurement and, surprisingly, the frequency distributions of true scores. Approximate methods for estimating relative efficiency may make this function routinely…

A simple, usefully accurate approximation of the standard error of measurement is proposed for use by classroom teachers. An empirical comparison with Lord's approximation indicated that, though not as easy to calculate as Lord's, this approximation is more practical because it is useful at any point in the score distribution. (BW)

Current usage and theory of standard error of measurement calls for one standard error of measurement figure to be used across all levels of scoring. The study revealed that scoring variance across scoring levels is not constant. As scoring ability increases scoring variance decreases. The assertion that low and high scoring subjects will…