Measuring Up: What Educational Testing Really Tells Us

by Daniel Koretz

The dashed lines represent a distance of one standard error of measurement above or below the average. The range in this particular case is 66 points, 33 in each direction from the mean, which is similar to the standard error of measurement on the SAT. Roughly two-thirds of the simulated observations lie within that range. This is true in general: an examinee with any given true score, taking a test once, has a probability of about two-thirds of getting a score within the range from one SEM below that score to one SEM above, and a probability of one in three of obtaining a score more than one SEM away from the true score. Extending the range to two standard errors above and below the mean—in this case, from 484 to 616—would encompass about 95 percent of the scores our indefatigable examinee would obtain.