The Impact of Vertical Scaling Decisions on Growth Interpretations

Most growth models implicitly assume that test scores have been vertically scaled. What may not be widely appreciated are the different choices that must be made when creating a vertical score scale. In this paper empirical patterns of growth in student achievement are compared as a function of different approaches to creating a vertical scale. Longitudinal item‐level data from a standardized reading test are analyzed for two cohorts of students between Grades 3 and 6 and Grades 4 and 7 for the entire state of Colorado from 2003 to 2006. Eight different vertical scales were established on the basis of choices made for three key variables: Item Response Theory modeling approach, linking approach, and ability estimation approach. It is shown that interpretations of empirical growth patterns appear to depend upon the extent to which a vertical scale has been effectively “stretched” or “compressed” by the psychometric decisions made to establish it. While all of the vertical scales considered show patterns of decelerating growth across grade levels, there is little evidence of scale shrinkage.