An Empirical Unravelling of Lord's Paradox

TL;DR

This paper investigates Lord's Paradox in educational data, showing how baseline imbalances affect effect size estimates and demonstrating that multilevel modelling can reduce these issues, aiding clearer decision-making.

Contribution

It provides empirical evidence on Lord's Paradox using large-scale data and shows how multilevel modelling can mitigate estimation divergences caused by baseline imbalances.

Findings

Impact estimates vary in magnitude and sign due to baseline imbalance.

Multilevel modelling reduces divergence in effect estimates.

Baseline imbalance significantly influences effect size estimation.

Abstract

Lord's Paradox occurs when a continuous covariate is statistically controlled for and the relationship between a continuous outcome and group status indicator changes in both magnitude and direction. This phenomenon poses a challenge to the notion of evidence-based policy, where data are supposed to be self-evident. We examined 50 effect size estimates from 34 large-scale educational interventions, and found that impact estimates are affected in magnitude, with or without reversal in sign, when there is substantial baseline imbalance. We also demonstrated that multilevel modelling can ameliorate the divergence in sign and/or magnitude of effect estimation, which, together with project specific knowledge, promises to help those who are presented with conflicting or confusing evidence in decision making.