How are reliability and the standard error of measurement related?

• A. The reliability of scores across administrations; the standard error of measurement estimates the expected score range around observed scores.
• B. Reliability is about test length; SEM is about difficulty.
• C. Reliability equals SEM.
• D. Reliability is a property of items only, SEM is of tests.

Answer: (A)

The key idea here is how measurement precision connects with score consistency. Reliability tells you how stable a test score is across repeated administrations: a highly reliable test yields similar results when given again, so scores are consistent. The standard error of measurement (SEM) quantifies how precise a single observed score is by estimating the typical amount of error that accompanies that score. Put together, SEM is derived from reliability and the score’s variability: SEM = SD × sqrt(1 − reliability). This means as reliability goes up, SEM goes down, so observed scores are closer to the true ability.

So the best description is that reliability concerns consistency across administrations, while SEM estimates the expected range of the true score around an observed score (the typical measurement error you’d expect for that score). For example, with a standard deviation of 15 and a reliability of 0.9, SEM is about 4.7, so a score of 85 would typically reflect a true ability in roughly 80 to 90. The other statements miss this relationship: reliability is not about test length or difficulty, SEM is not simply equal to reliability, and reliability isn’t a property of items alone but of the overall test scores.