  This article considers causal inference for treatment contrasts from a
randomized experiment using potential outcomes in a finite population setting.
Adopting a Neymanian repeated sampling approach that integrates such causal
inference with finite population survey sampling, an inferential framework is
developed for general mechanisms of assigning experimental units to multiple
treatments. This framework extends classical methods by allowing the
possibility of randomization restrictions and unequal replications. Novel
conditions that are "milder" than strict additivity of treatment effects, yet
permit unbiased estimation of the finite population sampling variance of any
treatment contrast estimator, are derived. The consequences of departures from
such conditions are also studied under the criterion of minimax bias, and a new
justification for using the Neymanian conservative sampling variance estimator
in experiments is provided. The proposed approach can readily be extended to
the case of treatments with a general factorial structure.
