Smoothed Analysis of Variance

Jim Hodges
Division of Biostatistics/School of Dentistry
University of Minnesota

Wednesday, September 21st
3:30pm
Moos 2-690
Minneapolis Campus

Abstract:

This talk presents an approach to smoothing balanced, single-error-term analysis of variance (ANOVA) that emphasizes smoothing interactions, the premise being that for a dependent variable on the right scale, interactions are often absent or small. The approach addresses three other problems: unreplicated designs; masking of large contrasts in effects with many degrees of freedom; and subgroup analysis, where treatment-by-subgroup interactions capture subgroup treatment effects (Dixon & Simon 1991). These issues are examined using an unreplicated 2x4x8 study of denture-lining materials. Our approach is Bayesian but can be viewed as a way to generate smoothing procedures, in which a prior distribution specifies a procedure. We briefly present results from a simulation experiment comparing four priors, unsmoothed ANOVA, and a strategy of dropping non-significant interactions. Three smooth priors have performance advantages over non-smoothed ANOVA if some interactions are actually zero. Our approach is a descendant of Smith (1973) nourished by modern Bayesian computing, and easily extends to allow spatial, temporal, or spatiotemporal smoothing.

A social tea will be held at 3:00 P.M. in A434 Mayo. All are Welcome.
For more details contact 612-624-4655 or see http://www.biostat.umn.edu/seminar_academic.html