Boosting Precision in Educational A/B Tests Using Auxiliary Information and Design-Based Estimators

Randomized A/B tests within online learning platforms enable us to draw unbiased causal estimators. However, precise estimates of treatment effects can be challenging due to minimal participation, resulting in underpowered A/B tests. Recent advancements indicate that leveraging auxiliary information from detailed logs and employing design-based estimators can yield unbiased and precise statistical inferences with minimal assumptions, even in small sample sizes. Our ongoing research aims to incorporate the Remnant Leave-One-Out Potential outcomes (ReLOOP) estimator and its variants into ASSISTments, an online tutoring platform. In this work, we define \emph{remnant} (auxiliary information for experiments) data and identify the common outcomes of interest for educational trials. We also formulate and train various predictive models using both prior student statistics and prior assignment statistics, evaluating which model performs better in terms of Mean Squared Error (MSE) and Coefficient of Determination ($R^{2}$). In addition, we establish an infrastructure to facilitate combining remnant-based predicted outcomes and ReLOOP estimators in tutoring experiments, used to boost power in educational A/B tests. Our preliminary findings suggest that incorporating auxiliary information into the ReLOOP estimator is roughly equivalent to increase sample size by 44\\% compared to conventional t-tests (difference-in-means estimator, DM) and by 12\\% compared to Leave-One-Out Potential outcomes (LOOP) estimator, which relies solely on experimental data. When applied to A/B tests in online tutoring platforms, improved precision via ReLOOP estimators allows for inferences to be made earlier in the development process and thus will lead to more rapid development of optimized learning systems.