Committee:
Dr. Joseph McKean, Chair
Dr. Joshua Naranjo
Dr. Bradley Huitema
Dr. Jeff Terpstra

Date: Thursday, May 19, 2011 3:30 p.m. to 5:30 p.m.
6625 Everett Tower

Abstract:
Regression to the mean is a statistical phenomenon that often confounds treatment effects in experiments. Consider an experiment involving a treatment, in which a response is measured (baseline) on a subject then a treatment is applied and a second measurement is taken. Then under many bivariate models for the pair of responses (including the bivariate normal), the predicted response of the second measurement will regress to the mean. In experiments where the second response is only taken for a select sample, for example, above a cutoff value, then this regression to the mean effect may mistakenly be thought of as a treatment effect.
This investigation considers a model of the treatment effect that also takes into account this regression to the mean effect. In particular, the researcher considers the multiplicative model of Naranjo and McKean (2001). Naranjo and McKean developed a bootstrap test for treatment effect based on least squares methods for bivariate normal distributions. The study develops robust procedures to assess treatment effects for this multiplicative model. The procedures are based on rank-based methods, for general score functions. The preliminary Monte Carlo investigations show that these procedures are robust. This robust and traditional development extends to models other than the bivariate normal, including multivariate t distributions. The research investigates the finite sample properties of these methods and compares their empirical behavior over a variety of models and situations.

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