__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.

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