Test Measurement Error and Inference from Value-Added Models

It is widely known that standardized tests are noisy measures of student learning, but value added models (VAMs) rarely account for test measurement error (TME). We incorporate information about TME directly into VAMs, focusing on TME that derives from the testing instrument itself. Our analysis is divided into two parts – one based on simulated data and the other based on administrative micro data from Missouri. In the simulations we control the data generating process, which ensures that we obtain accurate TME metrics. In the real-data portion of our analysis we use estimates of TME provided by a major test publisher. In both the simulations and real-data analyses, we find that inference from VAMs is improved by making simple TME adjustments to the models. The improvement is larger in the simulations, but even in the real-data analysis the improvement is on the order of what one could expect if teacher-level sample sizes were increased by 11 to 17 percent.