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Use of the Standard Error as a Reliability Index of Interest: An Applied Example Using Elbow Flexor Strength Data

PW Stratford, PT, is Assistant Professor, School of Rehabilitation Science, and Associate Member, Department of Clinical Epidemiology and Biostatistics, McMaster University, Hamilton, Ontario, Canada.
CH Goldsmith, PhD, is Professor of Clinical Epidemiology and Biostatistics. McMaster University, and Honorary Professor of Physical Therapy. Department of Physical Therapy, University of Western Ontario, London, Ontario, Canada.

The intraclass correlation coefficient (ICC) and the standard error of measurement (SEM) are two reliability coefficients that are reported frequently. Both measures are related; however, they define distinctly different properties. The magnitude of the ICC defines a measure's ability to discriminate among subjects, and the SEM quantifies error in the same units as the original measurement. Most of the statistical methodology addressing reliability presented in the physical therapy literature (eg, point and interval estimations, sample size calculations) focuses on the ICC. Using actual elbow flexor make and break strength measurements, this article illustrates a method for estimating a confidence interval for the SEM, shows how an a priori specification of confidence interval width can be used to estimate sample size, and provides several approaches for comparing error variances (and square root of the error variance, or the SEM).

Key Words: Measurement error • Reliability • Variance components

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