Simultaneous One-Sided Tests With Application to Education Evaluation Systems

Abstract

There is widespread interest in using various statistical inference tools as a part of the evaluations for individual teachers and schools. Evaluation systems typically involve classifying hundreds or even thousands of teachers or schools according to their estimated performance. Many current evaluations are largely based on individual estimates and hypothesis tests, with little or no consideration of controlling simultaneous error rates and their potential effect on the whole educational evaluation system. In this article, we discuss controlling simultaneous errors in classification of teachers or schools by a decision-theoretic approach. We first develop a β-mixture model to estimate the local false discovery rate (local fdr) by the classic p-values from one-sided tests. We discuss a few decision rules based on standard loss functions. We also construct a controversy loss function to further accommodate the incoherence between effect size and local fdr. We apply the proposed approach to evaluate adequate yearly progress (AYP) in math proficiency of Pennsylvania schools.