Abstract: When studying two-level factorial designs, factorial effects are usually defined as a set of orthogonal treatment contrasts, which we refer to as the orthogonal parameterization (OP). While most design results and analysis strategies have been developed and understood within the scope of the OP, a more appropriate alternative in some situations is the baseline parameterization (BP). In this study, we examine the relationship between the OP and the BP, which allows us to better understand the relatively unexplored BP. In addition to being insightful, this relationship is useful in design construction. The design properties considered here are estimability, optimality, and robustness. We find that a general class of Rechtschaffner designs exhibit robust properties under the BP.

Key words and phrases: Effect hierarchy, efficiency criterion, minimum aberration, orthogonal array, Rechtschaffner design, robust design.