### Standard error of measurement

Definitions:-
1- “In test theory, the standard error of measurement is the standard deviation of observed test scores for a given true score.”
2- “The standard error of measurement (SEM) is a statistical phenomenon and is unrelated to the accuracy of scoring.”
3- “The standard error (SE) is the standard deviation of the sampling distribution of a statistic.”
4- “An estimate of how often a researcher can expect errors of a given size on an instrument.”
Explanation:-
¢  It is usually estimated with the following formula in which ‘s’ is the standard deviation of the test scores and ‘r’ is the reliability of the test.
¢  S measurement = S √ 1_r.
¢  All test results, including scores on tests and quizzes designed by classroom teachers, are subject to the standard error of measurement.
¢  The term may also be used to refer to an estimate of that standard deviation, derived from a particular sample used to compute the estimate.
¢  For example, the sample mean is the usual estimator of a population mean.
¢  The SEM is in standard deviation units and can be related to the normal curve.
¢  SEM is a related to reliability.
¢  As the reliability increases, the SEM decreases.