Abstract
We have shown that the SEM (typical error) and LOA are very similar when defined at the same level of abstraction. The calculation of these sample statistics does not depend on sample size, but the precision of their estimate for the population parameter does. Only the latter concept involves the t-statistic. They do differ in the type of measurement error that is described (true score error versus test-retest error) and the coverage probability of the reference interval (0.6 versus 0.95). Bland and Altman and Atdinson and Nevill have promoted the citation of either the SEM or the LOA to help researchers in their discussion of the impact of error to real uses of the measurement tol. What is vital in this discussion is the researcher having a thorough understanding of the underlying theory behind the measurement error statistic(s) that is/are employed, especially the definition of error and the coverage probability that is selected. Such issues have been built into the title of the 95% LOA statistic, and are also an inherent part of SEM. Whilst the concept of typical error appears to be easy to understand and teach, this is only because the underlying theory and definition of what the statistic actually represents is not communicated. Only if all researchers adopt one single statistic (e.g. typical error) for measurement error is it remotely possible to push underlying theory into the background, since there would be a baseline of comparison for all. Because this scenario is highly unlikely, it is important that any measurement error statistic is well defined and understood by researchers.