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At the heart of CTT is the notion that error is endemic to measurement.

By the beginning of the 20th century, the concept of (p. 462) measurement error was well recognized, and psychometricians focused their efforts on estimating and accounting for error.

In CTT, an observed measure or score (X) consists of two constituent parts—the true score (T) and measurement error (E):

. Measurement error, however, also will account for a certain portion of score variance.

According to CTT, measurement error arises because mental processes are idiosyncratic and in a state of change such that individuals are incapable of performing optimally on a single test or performance task.

random error and systematic error.

(SEM) represents the average of the total random error for all individuals

SEM represents the spread of observed scores for a single individual if that person were tested multiple times.

That score, however, is an imperfect measure of the student’s true ability.

For example, CTT provides in-depth analysis of item characteristics,