I am working on SEM, and I am now at that stage where I got to think on what are the functions of SEM? where does it fit in?
@Yusuf Yes Standard Error of Measurement (SEM) is directly related to a test’s reliability: The larger the SEM, the lower the test’s reliability.
If test reliability = 0, the SEM will equal the standard deviation of the observed test scores.
If test reliability = 1.00, the SEM is zero.
The standard error of measurement is a concept of classical test theory (CTT). It is the standard deviation of the measurement error variable as defined in CTT. As such, it is directly related to (un)reliability as explained by Imran Anwar. The SEM can be used to construct a confidence interval (CI) around individual observed test scores to express uncertainty associated with individual test scores. The lower the reliability of test scores, the larger the SEM and the wider the CI around individual test scores.
A related concept is the standard error of the estimate (SEE) in linear regression analysis (the standard deviation of the residual variable in regression). The SEE is related to prediction error (1 - R^2) whereas the SEM is related to unreliability (1 - Reliability) in measurement.
@Imran Anwar and @Christian Geiser, Thank you, now have a clearer picture.
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