Investigating the Impact of Equating on Measurement Error Using Generalizability Theory

The paper discusses the relationship between equating error and measurement error in educational measurement research, which are traditionally treated as independent sources of error with potential differential impacts on individual scores and group means. This paper proposes a perspective shift using generalizability theory. It argues that equating, when integrated into the measurement process, should be viewed as one among various sources contributing to measurement error. The key assertion is that the impact of equating can be assessed alongside other sources of error through appropriate generalizability study designs. The paper acknowledges potential challenges and offers a framework for classifying applications of generalizability theory, providing empirical examples of study designs to investigate the impact of equating and other errors either separately or simultaneously. The paper also delves into the differential impact of equating error on individual scores and group means by decomposing the variance components in generalizability theory, particularly when individuals or schools are the object of measurement. By adopting a unified view of equating error and measurement error within the generalizability theory framework, the paper aims to facilitate both the conceptual discussions and practical estimation of various error sources. Ultimately, this approach is expected to enhance interpretation of scores in educational measurement.