In classical test theory, the standard error of measurement is the standard deviation of the random error 
in the model
 |
where 
is an observed score, 
is its unobserved true score, and 
has expectation value
zero. If the observed scores have standard deviation 
,
the true scores and errors are uncorrelated, and
the reliability coefficient is 
, then
 |
The standard error of measurement concerns uncertainty in an individual observed score and is not the same as the standard error of a sample statistic.
