  Randomized A/B tests within online learning platforms represent an exciting
direction in learning sciences. With minimal assumptions, they allow causal
effect estimation without confounding bias and exact statistical inference even
in small samples. However, often experimental samples and/or treatment effects
are small, A/B tests are underpowered, and effect estimates are overly
imprecise. Recent methodological advances have shown that power and statistical
precision can be substantially boosted by coupling design-based causal
estimation to machine-learning models of rich log data from historical users
who were not in the experiment. Estimates using these techniques remain
unbiased and inference remains exact without any additional assumptions. This
paper reviews those methods and applies them to a new dataset including over
250 randomized A/B comparisons conducted within ASSISTments, an online learning
platform. We compare results across experiments using four novel deep-learning
models of auxiliary data and show that incorporating auxiliary data into causal
estimates is roughly equivalent to increasing the sample size by 20\% on
average, or as much as 50-80\% in some cases, relative to t-tests, and by about
10\% on average, or as much as 30-50\%, compared to cutting-edge machine
learning unbiased estimates that use only data from the experiments. We show
that the gains can be even larger for estimating subgroup effects, hold even
when the remnant is unrepresentative of the A/B test sample, and extend to
post-stratification population effects estimators.
