Coefficient alpha reliability persists as the most common reliability coefficient reported in research. The assumptions for its use are, however, not well-understood. The current paper challenges the commonly used expressions of coefficient alpha and argues that while these expressions are correct when estimating reliability for summed scores,…

Vertical scales are frequently developed using common item nonequivalent group linking. In this design, one can use upper-grade, lower-grade, or mixed-grade common items to estimate the linking constants that underlie the absolute measurement of growth. Using the Rasch model and a dataset from Curriculum Associates' i-Ready Diagnostic in math in…

Credentialing examination developers rely on task (job) analyses for establishing inventories of task and knowledge areas in which competency is required for safe and successful practice in target occupations. There are many ways in which task-related information may be gathered from practitioner ratings, each with its own advantage and…

In this digital ITEMS module, we introduce the framework of nonparametric item response theory (IRT), in particular Mokken scaling, which can be used to evaluate fundamental measurement properties with less strict assumptions than parametric IRT models. We walk through the key distinction between parametric and nonparametric models, introduce the…

The Programme for International Student Assessment (PISA) is an important international study of 15-olds' knowledge and skills. New results are released every 3 years, and have a substantial impact upon education policy. Yet, despite its influence, the methodology underpinning PISA has received significant criticism. Much of this criticism has…

Mokken scale analysis (MSA) is a probabilistic-nonparametric approach to item response theory (IRT) that can be used to evaluate fundamental measurement properties with less strict assumptions than parametric IRT models. This instructional module provides an introduction to MSA as a probabilistic-nonparametric framework in which to explore…

Previous research has established that SAT scores and high school grade point average (HSGPA) differ in their predictive power and in the size of mean differences across racial/ethnic groups. However, the SAT is scaled nationally across all test takers while HSGPA is scaled locally within a school. In this study, the researchers propose that this…

This module describes and extends X-to-Y regression measures that have been proposed for use in the assessment of X-to-Y scaling and equating results. Measures are developed that are similar to those based on prediction error in regression analyses but that are directly suited to interests in scaling and equating evaluations. The regression and…

Some writers in the measurement literature have been skeptical of the meaningfulness of achievement standards and described the standard-setting process as blatantly arbitrary. We argue that standard setting is more appropriately conceived of as a measurement process similar to student assessment. The construct being measured is the panelists'…

"Scaling" is the process of constructing a score scale that associates numbers or other ordered indicators with the performance of examinees. Scaling typically is conducted to aid users in interpreting test results. This module describes different types of raw scores and scale scores, illustrates how to incorporate various sources of…

Most growth models implicitly assume that test scores have been vertically scaled. What may not be widely appreciated are the different choices that must be made when creating a vertical score scale. In this paper empirical patterns of growth in student achievement are compared as a function of different approaches to creating a vertical scale.…

Practice analyses are routinely used in support of the development of occupational and professional certification and licensure examinations. These analyses usually survey incumbents to obtain importance ratings of (1) specific tasks and (2) knowledge, skill, and ability (KSA) statements deemed by subject matter experts as essential to safe and…