Unbiased Confidence Intervals for Psychological Testing: The Regression-Based True Score Approach With Scale Correction

Two different approaches for calculating confidence intervals (CIs) for individual scores in psychological testing practice have been discussed in the literature within the framework of classical test theory. The traditional approach (CI: observed score ± <i>z</i> · standard error of measurement) has been criticized because it does not consider the phenomenon that, with imperfect measurement, true scores will be closer to the population average than the observed scores (regression to the mean). The regression approach (CI: regression-based true score estimate ± <i>z</i> · standard error of the estimate) takes this effect into account, but has the disadvantage that it leads to confidence intervals that are on a different scale than the observed scores. The different scaling occurs because true scores have a smaller standard deviation than observed scores, and the extent of this shrinkage depends on the reliability of the test. Here, I suggest a scale correction for the regression-based true score estimate to preserve the original scaling. Simulations indicate that this approach has the desired properties and outperforms the two existing approaches. The regression approach with scale correction is therefore recommended for calculating confidence intervals for individual scores in psychological testing practice.