The Comedy of Measurement Errors: Standard Error of Measurement and Standard Error of Estimation

Abstract

Testing is used to inform a range of critical decisions that help structure much of contemporary society. An unavoidable aspect of testing is that test scores are not infallible. As a result, individual test scores should be accompanied by an interval that indicates the uncertainty surrounding the score. There are a number of different test-score intervals that can be created from different error terms. Unfortunately, there are pervasive misinterpretations of these errors and their intervals. Many of these interpretations can be found in authoritative sources on psychological measurement, which has resulted in stubborn and persistent confusion about what these intervals mean. In the current article, we clarify two important error terms and their intervals: (a) the Standard Error of Estimation and (b) the Standard Error of Measurement. We explicate the meaning and interpretation of these errors by examining their statistical foundations. Specifically, we detail how these terms are formulated from different statistical models and the implications of these models for their different interpretations. We use classical test theory, bivariate linear regression, R activities, and algebra to illustrate the key concepts and differences.