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Estimation of the Conditional Standard Error of Measurement for Stratified Tests

Livingston, Samuel A.
Publication Year:
Report Number:
ETS Research Report
Document Type:
Page Count:
Subject/Key Words:
Error of Measurement, Mathematical Formulas, Statistical Analysis, Test Reliability


The standard error of measurement (SEM) is a measure of the inconsistency in the scores of a particular group of test takers. It is largest for test takers with scores ranging in the 50 percent correct bracket; with nearly perfect scores, it is smaller. On tests used to make pass/fail decisions, the test takers' scores tend to cluster in the range of 80-90 percent correct, with the passing score in the range of 60-70 correct. In this case, the SEM for the full group of test takers will be much smaller than the SEM for those with scores near the passing score. But, the test takers with scores near the passing score are the ones for whom the reliability of the test is the most important. For them, measurement errors can make the difference between passing and failing. For this reason, the important SEM is not the SEM for the full group of test takers, rather, the SEM at the passing score, which will often be substantially larger. A formula for this, and its derivation, are provided. (AUTHOR/CE). (8pp.)

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