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 under-powered, 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 the gains can be even larger for estimating subgroup effects, that they hold even when the remnant is unrepresentative of the A/B test sample, and extend to post-stratification population effects estimators.
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Power and sample size calculations for rerandomization
Power analyses are an important aspect of experimental design, because they help determine how experiments are implemented in practice. It is common to specify a desired level of power and compute the sample size necessary to obtain that power. Such calculations are well known for completely randomized experiments, but there can be many benefits to using other experimental designs. For example, it has recently been established that rerandomization, where subjects are randomized until covariate balance is obtained, increases the precision of causal effect estimators. This work establishes the power of rerandomized treatment-control experiments, thereby allowing for sample size calculators. We find the surprising result that, while power is often greater under rerandomization than complete randomization, the opposite can occur for very small treatment effects. The reason is that inference under rerandomization can be relatively more conservative, in the sense that it can have a lower Type-I error at the same nominal significance level, and this additional conservativeness adversely affects power. This surprising result is due to treatment effect heterogeneity, a quantity often ignored in power analyses. We find that heterogeneity increases power for large effect sizes, but decreases power for small effect sizes.
more » « less- Award ID(s):
- 1945136
- NSF-PAR ID:
- 10490479
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Biometrika
- Volume:
- 111
- Issue:
- 1
- ISSN:
- 0006-3444
- Format(s):
- Medium: X Size: p. 355-363
- Size(s):
- p. 355-363
- Sponsoring Org:
- National Science Foundation
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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.more » « less
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