  Multi-armed bandit algorithms have been argued for decades as useful for
adaptively randomized experiments. In such experiments, an algorithm varies
which arms (e.g. alternative interventions to help students learn) are assigned
to participants, with the goal of assigning higher-reward arms to as many
participants as possible. We applied the bandit algorithm Thompson Sampling
(TS) to run adaptive experiments in three university classes. Instructors saw
great value in trying to rapidly use data to give their students in the
experiments better arms (e.g. better explanations of a concept). Our
deployment, however, illustrated a major barrier for scientists and
practitioners to use such adaptive experiments: a lack of quantifiable insight
into how much statistical analysis of specific real-world experiments is
impacted (Pallmann et al, 2018; FDA, 2019), compared to traditional uniform
random assignment. We therefore use our case study of the ubiquitous two-arm
binary reward setting to empirically investigate the impact of using Thompson
Sampling instead of uniform random assignment. In this setting, using common
statistical hypothesis tests, we show that collecting data with TS can as much
as double the False Positive Rate (FPR; incorrectly reporting differences when
none exist) and the False Negative Rate (FNR; failing to report differences
when they exist)...
