Which expression correctly represents the standard error of measurement?

Which expression correctly represents the standard error of measurement?

• A. the square root of 1 minus the reliability coefficient
• B. The reliability coefficient
• C. The square of the reliability coefficient
• D. 1 minus the reliability coefficient

Answer: (A)

The standard error of measurement reflects how much an observed score is expected to differ from the true score because the test isn’t perfectly reliable. The classic relationship is SEM = SD × sqrt(1 − r), where r is the reliability coefficient. If scores are standardized so the standard deviation is 1, this becomes SEM = sqrt(1 − r). So the expression that matches is the square root of 1 minus the reliability coefficient. The reliability coefficient alone isn’t SEM, the square of the reliability isn’t SEM, and 1 minus the reliability coefficient represents unreliability but not the standard error unless you’re already factoring in the standard deviation.

The standard error of measurement reflects how much an observed score is expected to differ from the true score because the test isn’t perfectly reliable. The classic relationship is SEM = SD × sqrt(1 − r), where r is the reliability coefficient. If scores are standardized so the standard deviation is 1, this becomes SEM = sqrt(1 − r). So the expression that matches is the square root of 1 minus the reliability coefficient. The reliability coefficient alone isn’t SEM, the square of the reliability isn’t SEM, and 1 minus the reliability coefficient represents unreliability but not the standard error unless you’re already factoring in the standard deviation.