In paired experiments, participants are grouped into pairs with similar characteristics, and one observation from each pair is randomly assigned to treatment. The resulting treatment and control groups should be well-balanced; however, there may still be small chance imbalances. Building on work for completely randomized experiments, we propose a…

Causal effects are commonly defined as comparisons of the potential outcomes under treatment and control, but this definition is threatened by the possibility that either the treatment or the control condition is not well defined, existing instead in more than one version. This is often a real possibility in nonexperimental or observational…