What is the Standard Error of an Assessment?

Any student’s score on an assessment (“observed score”) is comprised of the student’s “true score” combined with measurement error.  The standard error of measurement (SEM) is the square root of the error variance of an assessment.  SEM is used to define the amount of error or “noise” around a score on the assessment.   This is closely related to the reliability of an assessment.  As reliability increases, the standard error of measurement decreases.  The lower the standard error of measurement, the closer the student’s observed score is to their true score on that assessment.