  The goal of a well-controlled study is to remove unwanted variation when
estimating the causal effect of the intervention of interest. Experiments
conducted in the basic sciences frequently achieve this goal using experimental
controls, such as "negative" and "positive" controls, which are measurements
designed to detect systematic sources of unwanted variation. Here, we introduce
clear, mathematically precise definitions of experimental controls using
potential outcomes. Our definitions provide a unifying statistical framework
for fundamental concepts of experimental design from the biological and other
basic sciences. These controls are defined in terms of whether assumptions are
being made about a specific treatment level, outcome, or contrast between
outcomes. We discuss experimental controls as tools for researchers to wield in
designing experiments and detecting potential design flaws, including using
controls to diagnose unintended factors that influence the outcome of interest,
assess measurement error, and identify important subpopulations. We believe
that experimental controls are powerful tools for reproducible research that
are possibly underutilized by statisticians, epidemiologists, and social
science researchers.
