Aggregate-Level Test-Scale Linking: A New Solution for an Old Problem?

The Reardon, Kalogrides, and Ho article on validation methods for aggregate-level test scale linking is an attempt to validate a district-level scale aligning procedure that appears to be a new solution to an old problem. Their aligning procedure uses the National Assessment of Educational Progress (NAEP) scale to piece together a patchwork of data structures from different tests of different constructs obtained under different administration conditions and used in different ways by different states. In this article, we critique their linking and validation efforts. Our critique has three components. First, we review the recommendations for linking state assessments to NAEP from several studies and commentaries to provide background from which to interpret Reardon et al.’s validation attempts. Second, we provide a replication of the Reardon et al. empirical validations of its proposed linking procedure to demonstrate that correlations between district means on two test scores can be high even when (1) the constructs being measured by the tests are different and (2) the district-level means estimated using the Reardon et al. linking approach can differ substantially from actual district-level means. Then, we suggest additional checks for construct similarity and subpopulation invariance from other concordance studies that could be used to assess whether the inferences made by Reardon et al. are warranted. Finally, until such checks are made, we urge cautious use of the results of the Reardon et al. results.