Orthogonal contrasts for both balanced and unbalanced designs and both ordered and unordered treatments

We consider designs with t treatments, the ith level of which has ni observations. Four cases are examined: treatment levels both ordered and not, and the design balanced, with all ni equal, and not. A general construction is given that takes observations, typically treatment sums or treatment rank...

Full description

Saved in:
Bibliographic Details
Published in:Statistica Neerlandica 2024-02, Vol.78 (1), p.68-78
Main Authors: Rayner, J. C. W., Livingston, G. C.
Format: Article
Language:English
Subjects:
balanced incomplete block designs
completely randomized design
Helmert matrices
Latin square design
Quadratic forms
randomized block design
supplemented balanced design
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We consider designs with t treatments, the ith level of which has ni observations. Four cases are examined: treatment levels both ordered and not, and the design balanced, with all ni equal, and not. A general construction is given that takes observations, typically treatment sums or treatment rank sums, constructs a simple quadratic form and expresses it as a sum of squares of orthogonal contrasts. For the case of ordered treatment levels, the Kruskal–Wallis, Friedman and Durbin tests are recovered by this construction. A dataset where the design is the supplemented balanced, which is an unbalanced design in our terminology, is analyzed. When treatment levels are not ordered the construction also applies. We then focus on Helmert contrasts.
ISSN:0039-0402
1467-9574
DOI:10.1111/stan.12305