Explain what the standard error of measurement is and how to use it to construct a confidence interval around an observed score.
What will be an ideal response?
• The SEM is an estimate of how much the individual’s observed test score (X) might differ from the individual’s true test score (T).
• It is an index of the amount of inconsistency or error expected in an individual’s observed test score.
• As the reliability of a test increases, the SEM decreases because high reliability indicates a low level of random error. Low random error means that the observed score will be a good estimate of the true score.
• A confidence interval is a range of observed scores that we feel confident will include the test taker’s true score.
• The formula for calculating the 95% confidence interval is X ± 1.96 (SEM) where X is the observed test score.
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