How to calculate standard error of measurement

Where ICC is the intraclass correlation coefficient as described previously and SD is the standard deviation of all the scores about the grand mean. The first formula is the most common and estimates the standard error of measurement as

Standard error of measurement can be estimated with two common formulas. Further, the standard error of measurement is an index of the precision of the test, or the trial-to-trial noise of the test. The standard error of measurement is an absolute estimate of the reliability of a test, meaning it has the units of the test being evaluated and is not sensitive to the between-subjects variability of the data. However, it is not particularly informative for practitioners such as clinicians, coaches, and educators who wish to make inferences about individuals from a test result.Р”Р‡or practitioners, a more useful tool is the standard error of measurement ( SEM not to be confused with the standard error of the mean). As such, the intraclass correlation coefficient is helpful to researchers when assessing the utility of a test for use in a study involving multiple subjects. It is useful for assessing sample size and statistical power and for estimating the degree of correlation attenuation. Because the general form of the intraclass correlation coefficient is a ratio of variabilities (see equation 13.04), it is reflective of the ability of a test to differentiate between subjects. The intraclass correlation coefficient provides an estimate of the relative error of the measurement that is, it is unitless and is sensitive to the between-subjects variability. This is an excerpt from Statistics in Kinesiology 5th Edition With Web Resource by Joseph Weir & William Vincent.

How to calculate standard error of measurement