Orthogonality, Orthogonal Decomposition, and Their Role in Modern Experimental Design

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 5 in Experimental Design, 2018, pp 155-179 from Springer

Abstract: Abstract In Chap. 2 , we saw how to investigate whether or not one factor influences some dependent variable. Our approach was to partition the total sum of squares (TSS), the variability in the original data, into two components – the sum of squares between columns (SSBc), attributable to the factor under study, and the sum of squares within a column (SSW), the variability not explained by the factor under study, and instead explained by “everything else.” Finally, these quantities were combined with the appropriate degrees of freedom in order to assess statistical significance. We were able to accept or reject the null hypothesis that all column means are equal (or, correspondingly, reject or accept that the factor under study has an impact on the response). In Chap. 4 , we discussed multiple-comparison techniques for asking more detailed questions about the factor under study; for example, if not all column means are equal, how do they differ? We now present a more sophisticated, flexible, and potent way to analyze (or “decompose”) the impact of a factor on the response, not limited to pairwise comparisons.

Keywords: Column Means; ANOVA Analysis Of Variance (ANOVA); Aspirin Brands; placeboPlacebo; productInner Product (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_5

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

DOI: 10.1007/978-3-319-64583-4_5

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 ().