Hierarchical Dependencies in Classroom Settings Influence Algorithmic Bias Metrics

Measuring algorithmic bias in machine learning has historically focused on statistical inequalities pertaining to specific groups. However, the most common metrics (i.e., those focused on individual- or group-conditioned error rates) are not currently well-suited to educational settings because they assume that each individual observation is independent from the others. This is not statistically appropriate when studying certain common educational outcomes, because such metrics cannot account for the relationship between students in classrooms or multiple observations per student across an academic year. In this paper, we present novel adaptations of algorithmic bias measurements for regression for both independent and nested data structures. Using hierarchical linear models, we rigorously measure algorithmic bias in a machine learning model of the relationship between student engagement in an intelligent tutoring system and year-end standardized test scores. We conclude that classroom-level influences had a small but significant effect on models. Examining significance with hierarchical linear models helps determine which inequalities in educational settings might be explained by small sample sizes rather than systematic differences.