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The standard error of measurement (SEM) is the standard deviation of errors of measurement that are associated with test scores from a particular group of examinees. When used to calculate confidence bands around obtained test scores, it can be helpful in expressing the unreliability of individual test scores in an understandable way. Score bands can also be used to interpret intraindividual and interindividual score differences. Interpreters should be wary of over‐interpretation when using approximations for correctly calculated score bands. It is recommended that SEMs at various score levels be used in calculating score bands rather than a single SEM value.
Leo M. Harvill (Sat,) studied this question.
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