The standard error of measurement (SEM) is the standard deviation of observed scores around a true score. Under classical test theory, an observed score is the score a student actually receives and a true score is the score one would receive if no random errors affected the score. The standard error is calculated by subtracting a scale's estimate of internal reliability from 1 and multiplying the square root of that difference by the observed scores' standard deviation—higher internal reliability estimates result in smaller standard errors of measurement. Because observed scores are assumed to be normally distributed around true scores, the standard error of measurement can be used as a standard deviation to compute confidence intervals to estimate a student's true score. For example, by multiplying ...