  Randomized control trials (RCTs) have been the gold standard to evaluate the
effectiveness of a program, policy, or treatment on an outcome of interest.
However, many RCTs assume that study participants are willing to share their
(potentially sensitive) data, specifically their response to treatment. This
assumption, while trivial at first, is becoming difficult to satisfy in the
modern era, especially in online settings where there are more regulations to
protect individuals' data. The paper presents a new, simple experimental design
that is differentially private, one of the strongest notions of data privacy.
Also, using works on noncompliance in experimental psychology, we show that our
design is robust against "adversarial" participants who may distrust
investigators with their personal data and provide contaminated responses to
intentionally bias the results of the experiment. Under our new design, we
propose unbiased and asymptotically Normal estimators for the average treatment
effect. We also present a doubly robust, covariate-adjusted estimator that uses
pre-treatment covariates (if available) to improve efficiency. We conclude by
using the proposed experimental design to evaluate the effectiveness of online
statistics courses at the University of Wisconsin-Madison during the Spring
2021 semester, where many classes were online due to COVID-19.
