What is Standard error of measurement?
Also called SEM
The standard error of measurement is the expected spread of a person's observed scores around their true score if they could be tested repeatedly. It converts a reliability coefficient into the units of the actual scale, which is what turns an abstract number into a usable statement about one individual candidate.
The formula, and why it is the most useful line in a technical manual
The standard error of measurement equals the standard deviation of the scores multiplied by the square root of one minus the reliability. Every quantity in it is normally published, and the result is expressed in score points rather than as a correlation.
That matters because reliability is a property of a group and the standard error of measurement is what you can say about a person. A reliability of 0.85 tells a candidate nothing. 'Your score is 71, and a repeat sitting would land within about 8 points either side, nineteen times out of twenty' tells them what the instrument can and cannot support.
What to do with it at a decision boundary
Compare it to the distance between the candidate and the cut score. If the gap is smaller than the standard error, the instrument is not distinguishing them from the threshold and the decision is being made by noise.
The standard responses are a review band around the cut, a second independent source of evidence for anyone inside it, or a re-sit. Ranking a shortlist by point score without asking this question is the most common way an organisation manufactures precision it does not have.
From reliability to a usable interval
- Scale standard deviation = 10; reported reliability = 0.85
- SEM = 10 × √(1 − 0.85) = 10 × √0.15 = 10 × 0.387 = 3.87 points
- 95% interval ≈ ±1.96 × 3.87 = ±7.6 points
- So an observed 71 is consistent with a true score anywhere from about 63 to 79.
Now raise reliability to 0.95: SEM falls to 2.24 and the interval to ±4.4. That is what a reliability figure is worth in the only units a candidate can use.
Not the same as standard deviation
The standard deviation describes how spread out a group of people is. The standard error of measurement describes how much one person's score would move on a repeat sitting. Confusing them makes a test look far more precise than it is.
Related terms
More terms beginning with S
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