The Gains From Vertical Scaling

It is often assumed that a vertical scale is necessary when value-added models depend upon the gain scores of students across two or more points in time. This article examines the conditions under which the scale transformations associated with the vertical scaling process would be expected to have a significant impact on normative interpretations using gain scores. It is shown that this will depend upon the extent to which adopting a particular vertical scaling approach leads to a large degree of scale shrinkage (decreases in score variability over time). Empirical data are used to compare school-level gain scores computed as a function of different vertical scales transformed to represent increasing, decreasing, and constant trends in score variability across grades. A pragmatic approach is also presented to assess the departure of a given vertical scale from a scale with ideal equal-interval properties. Finally, longitudinal data are used to illustrate a case when the availability of a vertical scale will be most important: when questions are being posed about the magnitudes of student-level growth trajectories.