How does the SEM relate to observed scores?

How does the SEM relate to observed scores?

• A. It defines the exact true score.
• B. It defines the smallest detectable change.
• C. It defines the population mean.
• D. It defines the expected range of measurement error around an observed score.

Answer: (D)

Standard Error of Measurement shows how precise a single observed score is by capturing the typical amount of error that comes from imperfect reliability. Think of an observed score as true score plus random error. The SEM is the standard deviation of that error, so it defines the expected range of measurement error around an observed score. For example, with an SEM of 3, an observed score of 75 would imply the true score is likely around 75 ± 3, meaning about 72 to 78 for about 68% of cases, and roughly 69 to 81 for about 95% of cases (using two SEMs). The SEM isn’t the exact true score, nor the population mean, and while related to detecting change, the smallest detectable change uses SEM in a separate calculation.

Standard Error of Measurement shows how precise a single observed score is by capturing the typical amount of error that comes from imperfect reliability. Think of an observed score as true score plus random error. The SEM is the standard deviation of that error, so it defines the expected range of measurement error around an observed score.

For example, with an SEM of 3, an observed score of 75 would imply the true score is likely around 75 ± 3, meaning about 72 to 78 for about 68% of cases, and roughly 69 to 81 for about 95% of cases (using two SEMs). The SEM isn’t the exact true score, nor the population mean, and while related to detecting change, the smallest detectable change uses SEM in a separate calculation.