--- title: "Standard error of measurement" description: "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." canonical: https://www.assessall.com/guides/glossary/s/standard-error-of-measurement updated: 2026-09-23 source: AssessAll --- # Standard error of measurement _Also known as: 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. ## Comparing two people needs a different statistic, and it is wider The standard error of measurement puts an interval around one person's score. Comparing two people is a different question, because both scores carry error and the gap between them therefore carries both. The statistic for that is the [standard error of the difference](https://www.assessall.com/guides/glossary/s/standard-error-of-the-difference), and the relation is fixed: SED = √2 × SEM, about 1.41 times wider. Maury Buster's paper on applied statistical banding for the International Personnel Assessment Council (2005) states the split exactly — use the standard error of measurement for the "interval of likely/possible true scores around a given individual's score", and the standard error of the difference to "test the significance between two individuals' scores". Running the individual interval on a two-candidate comparison is the most common misuse of the number on this page. On the worked example below, the individual 95% interval is ±7.6 points, but two candidates must be more than 10.7 points apart before the instrument has distinguished them. [How to decide between two final candidates](https://www.assessall.com/guides/how-to-decide-between-two-final-candidates) works that through, including why checking whether the two individual intervals overlap is the wrong test and errs by roughly 40%. ## It is not one number across the scale The formula above yields a single figure used for every candidate, which is a convenience rather than a fact about the instrument. Huebner and Skar put it plainly in Practical Assessment, Research & Evaluation 26(14), 2021: "the standard error of measurement is not a score-invariant property", and a general SEM is "a fixed value used for all candidates… the confidence interval is equal in size across students and across different levels of competence." The conditional standard error of measurement is the version computed at each point on the scale, and it is not flat. In their writing-assessment data "the SEMs were lower for students scoring around the mean", with a non-linear relationship between scaled score and error — so precision is best in the middle and worse towards the extremes. That has a direct consequence for anyone setting a [cut score](https://www.assessall.com/guides/glossary/c/cut-score) high or low on the scale: a cut placed away from the centre sits in a region where the true error is larger than the headline SEM in the manual, so the review band around it should be wider, not the same. Ask a vendor whether the SEM they quote is general or conditional, and if conditional, what it is at your cut. --- Source: https://www.assessall.com/guides/glossary/s/standard-error-of-measurement