Unbiased Confidence Intervals in 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, but unfortunately, both approaches can lead to biased estimates. The traditional approach (CI: observed score ± z · standard error of measurement) fails to take into account the phenomenon that, with imperfect measurement, true scores will be closer to the population average than observed scores will be (regression to the mean). On the other hand, the regression approach (CI: regression-based true score estimate ± z · standard error of the estimate) takes regression to the mean into account. However, this approach 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. It is thus incorrect, for example, to interpret true scores as falling on a standard scale (like T-scores) even when the observed scores were measured on such a scale. Here, I suggest a scale correction for the regression-based true score estimate to preserve the scaling, and thus to ensure both the accuracy and interpretability of the confidence intervals. 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.