Which statement best describes how the observed score relates to the true score and error?

• A. Observed score equals true score plus error score.
• B. Observed score equals true score minus error score.
• C. Observed score equals the average of true scores.
• D. Observed score is independent of the true score.

Answer: (A)

In measurement, the observed score is formed by adding the true score to the measurement error. The true score reflects the examinee’s actual ability or knowledge, while the error captures all random influences that can shift the result on a particular occasion (guessing, ambiguous questions, momentary distractions, scoring variations, etc.). Because these random factors can push the result up or down, the observed score can be higher or lower than the true score. That’s why the correct description is observed score equals true score plus error.

Why the other ideas don’t fit: subtracting the error would imply the error always reduces the observed score, which isn’t how measurement error works since it can move the score in either direction. Saying the observed score is the average of true scores misrepresents a single administration’s result, which is affected by the specific error on that occasion. And claiming the observed score is independent of the true score ignores the role of error as the deviation from the true score that creates the observed value.