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.

Commentary on “Validation Methods for Aggregate-Level Test Scale Linking: A Case Study Mapping School District Test Score Distributions to a Common Scale”

In this commentary, I share my perspective on the goals of assessments in general, on linking assessments that were developed according to different specifications and for different purposes, and I propose several considerations for the authors and the readers. This brief commentary is structured around three perspectives (1) the context of this research, (2) the methodology proposed here, and (3) the consequences for applied research.

Commentary on “Validation Methods for Aggregate-Level Test Scale Linking: A Case Study Mapping School District Test Score Distributions to a Common Scale”

This paper begins by setting the linking methods of Reardon, Kalogrides, and Ho in the broader literature on linking. Trends in the validity data suggest that there may be a conditional bias in the estimates of district means, but the data in the article are not conclusive on this point. Further, the data used in their case study might support the validity of the methods only over a limited range of the ability continuum. Applications of the method are then discussed. Contrary to the title, the application of the linking results is not limited to aggregate-level data. Because the potential application is so broad, further research is needed on issues such as the possibility of conditional bias and the validity of estimates over the full range of possible values. Validity is not a dichotomous concept where validity exists or it does not. The evidence reported by Reardon et al. provides substantial, but incomplete, support for the validity of the linked measures in this case study.

Commentary on Reardon, Kalogrides, and Ho’s “Validation Methods for Aggregate-Level Test Scale Linking: A Case Study Mapping School District Test Score Distributions to a Common Scale”

The studies presented by Reardon, Kalogrides, and Ho provide preliminary support for a National Assessment of Educational Progress–based aggregate linking of state assessments when used for research purposes. In this commentary, I suggest future efforts to explore possible sources of district-level bias, evaluation of predictive accuracy at the state level, and a better understanding of the performance of the linking when applied to the inevitable nonrepresentative district samples that will be encountered in research studies.