ABSTRACT
This chapter introduces the term confounding using the mathematical model of the experiment. It also introduces modular arithmetic and shows how to generate the confounding pattern. The chapter also shows how to compute expected mean squares for fractional designs. It explores how to generate the fraction of all possible combinations that will actually be run. The chapter also explores how to analyze the data, specifically the sums of squares and mean squares values. It deviates from the normal stream of things to show several methods for selecting a fractional design. Even when subject matter knowledge is not available, fractional designs are often run with the intention of running follow-up designs. There are many approaches taken to designing and analyzing fractional experiments. The layout sheet for fractional designs is identical to the layout sheet for full factorial designs except only a fraction of all possible combinations appear.
