Efficiency Analysis with Educational Data: How to Deal with Plausible Values from International Large-Scale Assessments

Abstract

International large-scale assessments (ILSAs) provide several measures as a representation of educational outcomes, the so-called plausible values, which are frequently interpreted as a representation of the ability range of students. In this paper, we focus on how this information should be incorporated into the estimation of efficiency measures of student or school performance using data envelopment analysis (DEA). Thus far, previous studies that have adopted this approach using data from ILSAs have used only one of the available plausible values or an average of all of them. We propose an approach based on the fuzzy DEA, which allows us to consider the whole distribution of results as a proxy of student abilities. To assess the extent to which our proposal offers similar results to those obtained in previous studies, we provide an empirical example using PISA data from 2015. Our results suggest that the performance measures estimated using the fuzzy DEA approach are strongly correlated with measures calculated using just one plausible value or an average measure. Therefore, we conclude that the studies that decide upon using one of these options do not seem to be making a significant error in their estimates.