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Fractional Factorial Designs

In: Linear Models and Design

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  • Jay H. Beder

    (University of Wisconsin–Milwaukee)

Abstract

This chapter asks how much of the decompositions of a full factorial design can be recovered when we observe only a subset of all treatment combinations, and what we can do to control the aliasing of effects that automatically results. As in the previous chapter, we study this both in the general setting (arbitrary fractions of arbitrary factorials) and in the special setting of regular fractions in classical symmetric factorials. In the general case we see that the strength of the fraction controls its aliasing and its resolution, leading to a Fundamental Theorem of Aliasing. We discuss a competing approach to aliasing and resolution based on estimability and bias, and we conclude with introductions to relative aberration and to the theory of projections.

Suggested Citation

  • Jay H. Beder, 2022. "Fractional Factorial Designs," Springer Books, in: Linear Models and Design, chapter 0, pages 219-289, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-08176-7_6
    DOI: 10.1007/978-3-031-08176-7_6
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