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Designs with Factors at Three Levels

In: Experimental Design

Author

Listed:
  • Paul D. Berger

    (Bentley University)

  • Robert E. Maurer

    (Boston University, Questrom School of Business)

  • Giovana B. Celli

    (Cornell University)

Abstract

Sometimes, we wish to examine the impact of a factor at three levels rather than at two levels as discussed in previous chapters. For example, to determine the differences in quality among three suppliers, one would consider the factor “supplier” at three levels. However, for factors whose levels are measured on a numerical scale, there is a major and conceptually-different reason to use three levels: to be able to study not only the linear impact of the factor on the response (which is all that can be done when studying a factor that has only two levels), but also the nonlinear impact. The basic analysis-of-variance technique treats the levels of a factor as categorical, whether they actually are or not. One (although not the only) logical and useful way to orthogonally break down the sum of squares associated with a numerical factor is to decompose it into a linear effect and a quadratic effect (for a factor with three numerical levels), a linear effect, a quadratic effect, and a cubic effect (for a factor with four numerical levels), and so forth.

Suggested Citation

  • Paul D. Berger & Robert E. Maurer & Giovana B. Celli, 2018. "Designs with Factors at Three Levels," Springer Books, in: Experimental Design, edition 2, chapter 0, pages 423-448, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-64583-4_12
    DOI: 10.1007/978-3-319-64583-4_12
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