Designs with Factors at Three Levels

Paul D. Berger, Robert E. Maurer and Giovana B. Celli
Additional contact information
Paul D. Berger: Bentley University
Robert E. Maurer: Boston University, Questrom School of Business
Giovana B. Celli: Cornell University

Chapter Chapter 12 in Experimental Design, 2018, pp 423-448 from Springer

Abstract: 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.

Keywords: Quadratic Effect; ANOVA Analysis Of Variance (ANOVA); Sign Table; Megastore; interactionInteraction (search for similar items in EconPapers)
Date: 2018
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-64583-4_12

Ordering information: This item can be ordered from
http://www.springer.com/9783319645834

DOI: 10.1007/978-3-319-64583-4_12

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().