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

TLDR

The intraclass correlation coefficient (ICC) and the standard error of measurement (SEM) are commonly reported reliability coefficients, with ICC measuring discriminability among subjects and SEM quantifying measurement error in original units, yet most physical‑therapy literature focuses on ICC. This study aims to demonstrate how to estimate a confidence interval for the SEM, use its width to calculate required sample size, and compare error variances in elbow flexor strength data. The authors apply these methods to actual elbow flexor make‑and‑break strength measurements, illustrating confidence‑interval estimation, a priori sample‑size determination, and variance‑comparison techniques.

Abstract

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).