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### Conditional Standard Error of Measurement

It is often assumed that classical test theory requires the standard errors of measurement to be constant for all examinees. This is not true. Rather standard errors of measurement can and do vary for examinees with different true scores. A conditional standard error of measurement (CSEM) is a measure of the variation of observed scores for an individual examinee with a particular true score. Measurement is more precise for examinees with small CSEMs.

In 1955, Frederic Lord developed the best known CSEM for number-correct scores. Its estimator is ${x}_{p}\left(k-{x}_{p}\right)/\left(k-1\right)$, where xp is the number of correct dichotomously scored items for examinee p, and k is the total number of items in a test. Subsequently, in 1984, Leonard Feldt extended Lord’s method to tests in which items ...