Not all percentiles are equal: examining non-linear relationships between two, popular teacher evaluation measures

In this study, we estimated the relationship between two popular measures of teacher effectiveness—teachers’ value-added model (VAM) estimates, represented in this study via median growth percentiles (MGPs), and teachers’ observational scores, derived from the TAP System for Teacher and Student Advancement. We examined the relationship between these measures separately for teachers at different values of the MGPs distribution, as opposed to examining a conventional aggregated correlation. Previous research has shown that these aggregated (co)relationships are typically very weak, but in this study, we demonstrate that such correlations vary by the location of the score in the overall score distribution, and that the relationship between teachers’ MGPs and observational scores is non-linear. This suggests that when these two indicators of teacher quality are used together, especially for high-stakes decision-making purposes (e.g., tenure, merit pay, termination), teachers’ positions in the score distribution should be considered in the design of any teacher evaluation system or formulation.