STATISTICS COLLOQUIUM

Princeton University

Friday, April 18,1997

3:30 pm - refreshments

4:00 pm - talk

Room 327, Yost Hall

Abstract

The terms "picking at random" and "irregular arrangement" are ambiguous. Despite numerous scientific-context-specific definitions of 'too regular' or 'sufficiently irregular', the vast literature on design of experiments - systematized over more than 75 years - remains silent on quantifying degrees of irregularity of experimental arrangements. A precise formulation of these notions is combinatorial, rather than probability-theoretic in nature, and can be based on a family of approximate entropy measures. Our objectives are: (i) to define vector versions of approximate entropy and can be used to grade the irregularity of planar arrangements (including Latin Squares, Nearest-Neighbor Designs, and general block designs); (ii) to associate sets of allowable arrangements with finite maximally-irregular sequences and specified selection rules, thereby making precise the diverse notions of 'valid randomization'; and (iii) to identify conflicts and tradeoffs between the objectives of valid randomization and high degree of irregularity of experimental arrangements.