Mark S. Handcock

"Comparison (Relative) Distributions Approaches to Factorial Data"

Presented to the American Statistical Association Workshop 2005 "Nonparametric Statistics: Frontier"

January 15 2005, Texas A&M University

Parzen (1977) considered using the relative ranks of data from two distributions for the purposes of comparison of the distributions. He further developed these ideas under the title 'comparison change analysis' (Parzen 1992). Separately, Cwik and Mielniczuk (1989, 1990, 1993) consider non-parametric density estimation for the relative ranks that accounted for the two-sample nature of the data. These ideas have been further developed in the sociological context in the 90's. Morris, Bernhardt and Handcock (1994) study changes in yearly earnings by race and gender from 1967 to 1987. A book length treatment building on Parzen's philosophy is given by Handcock and Morris (1999). In this work we extend these ideas to the analysis of factorial data. We consider graphical estimates of nonparametric factorial effects and interactions. These are appropriate for both experimental and observational data and provide a comparative distributional perspective on the work of Akritas and Arnold (1994).