A Potential Outcome View to Analyze 2 Level Factorial Designs

• Activity Number: 474
• Type: Contributed
• Date/Time: Wednesday, August 1, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Valeria Espinosa*+ and Tirthankar Dasgupta and Donald B Rubin
• Companies: Harvard University and Harvard University and Harvard University
• Keywords: Posterior Predictive Checks ; Factorial Designs ; Fisher Randomization Test ; Sequential Assessment

Abstract

Factorial designs (Yates 1937, Fisher 1942) have been widely used in many scientific and industrial settings. These designs are used to assess efficiently the relevance of several factors and their interactions. In this context, the goal is the screening of "active" effects from the large pool of possibly active factorial effects. The traditional ways of analyzing such experiments assume an underlying normal population and restrict the range of effects that can be tested to the means. We explore two methods based on the Rubin Causal Model: a potential outcome version of the Loughin and Noble (1997) randomization proposal and a Posterior Predictive Check approach. This framework was proposed for experiments by Neyman in 1923, and extended to observational studies by Rubin in 1974. The term was coined by Holland (1986). This perspective allows the relaxation of the classical assumptions. Both methods are based on sequential testing with the same starting point: a Fisher randomization test for a sharp null of no treatment effect whatsoever. Simulation results for the classical setting will be presented. Various discrepancy measures and stopping rules are compared.