Causal inference from $2^k$ factorial designs using the potential   outcomes model
  A framework for causal inference from two-level factorial designs is proposed. The framework utilizes the concept of potential outcomes that lies at the center stage of causal inference and extends Neyman's repeated sampling approach for estimation of causal effects and randomization tests based on Fisher's sharp null hypothesis to the case of 2-level factorial experiments. The framework allows for statistical inference from a finite population, permits definition and estimation of estimands other than "average factorial effects" and leads to more flexible inference procedures than those based on ordinary least squares estimation from a linear model. 
Tirthankar Dasgupta, Natesh S. Pillai, Donald B. Rubin
stat.ME math.ST stat.AP stat.TH