Cultural consensus theory (CCT) is a data aggregation technique with many applications in the social and behavioral sciences. We describe the intuition and theory behind a set of CCT models for continuous type data using maximum likelihood inference methodology. We describe how bias parameters can be incorporated into these models. We introduce…

A classic topic in the fields of psychometrics and measurement has been the impact of the number of scale categories on test score reliability. This study builds on previous research by further articulating the relationship between item response theory (IRT) and classical test theory (CTT). Equations are presented for comparing the reliability and…

In adolescence research, the treatment of measurement reliability is often fragmented, and it is not always clear how different reliability coefficients are related. We show that generalizability theory (G-theory) is a comprehensive framework of measurement reliability, encompassing all other reliability methods (e.g., Pearson "r,"…

There are three fundamental problems in Sijtsma ("Psychometrika," 2008): (1) contrary to the name, the glb is not the greatest lower bound of reliability but rather is systematically less than omega[subscript t] (McDonald, "Test theory: A unified treatment," Erlbaum, Hillsdale, 1999), (2) we agree with Sijtsma that when considering how well a test…

Hopelessness has become an increasingly important construct in palliative care research, yet concerns exist regarding the utility of existing measures when applied to patients with a terminal illness. This article describes a series of studies focused on the exploration, development, and analysis of a measure of hopelessness specifically intended…

Within a response to intervention model, educators increasingly use progress monitoring (PM) to support medium- to high-stakes decisions for individual students. For PM to serve these more demanding decisions requires more careful consideration of measurement error. That error should be calculated within a fixed linear regression model rather than…

An examinee-level (or conditional) reliability is proposed for use in both classical test theory (CTT) and item response theory (IRT). The well-known group-level reliability is shown to be the average of conditional reliabilities of examinees in a group or a population. This relationship is similar to the known relationship between the square of…

Because reliability is a function of scores, and not tests per se, it is inaccurate to hold that a given test will yield scores with the same reliability across samples. Therefore, score reliability should always be reported and interpreted in both measurement and substantive studies. In an effort to facilitate this outcome, this paper is intended…

Presents a model of tests and measurement that identifies test scores with Hilbert space vectors and true and error components of scores with linear operators. This geometric point of view brings to light relations among elementary concepts in test theory, including reliability, validity, and parallel tests. (Author/SLD)

Presents minimization and maximization models for parallel test construction under constraints. The minimization model constructs weakly and strongly parallel tests of minimum length, while the maximization model constructs weakly and strongly parallel tests with maximum test reliability. (Author/SLD)

This paper discusses the fact that reliability is about scores and not tests and how reliability limits effect sizes. The paper also explores the classical reliability coefficients of stability, equivalence, and internal consistency. Stability is concerned with how stable test scores will be over time, while equivalence addresses the relationship…