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Effects in a Factorial Experiment

In: Linear Models and Design

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  • Jay H. Beder

    (University of Wisconsin–Milwaukee)

Abstract

Building on the ideas developed in Chap. 1 , we describe the main hypotheses for a factorial (ANOVA) experiment having three or fewer factors, and the lattices formed by these hypotheses (see Fig. 2.1) and by their corresponding subspaces. The goal is to clarify the statistical meaning of the hypotheses in terms of the cell means of the experiment. We contrast this with the factor-effects approach, and spend some time showing its relationship with the cell means model, which is the one we will use almost exclusively throughout the book. The main exception is the modeling of random effects, where the standard approach starts with the factor-effects model, as we discuss in Sect. 2.5.

Suggested Citation

  • Jay H. Beder, 2022. "Effects in a Factorial Experiment," Springer Books, in: Linear Models and Design, chapter 0, pages 27-60, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-08176-7_2
    DOI: 10.1007/978-3-031-08176-7_2
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