A study of nonadditivity in factorial experiments with no replication

Date
1986
Authors
Farmer, Charles
Journal Title
Journal ISSN
Volume Title
Publisher
Altmetrics
Authors
Research Projects
Organizational Units
Statistics
Organizational Unit
Journal Issue
Series
Abstract

Suppose that d experimental treatments, each at a number of levels, are applied to a group of subjects in such a way that each treatment combination is assigned to one, and only one, subject. This is the makeup of a factorial experiment. If the assignment of treatment combinations to subjects is random, standard techniques have long been available for examining the effects of differing levels within a treatment. In this thesis we seek a technique for examining the effects of differing combinations of levels between treatments;For the simplest case, that of two treatments (or factors), we describe a number of techniques; some based on mathematical models, and some based on the rank of a matrix. We extend these techniques to the case where not all levels of one of the treatments are used, but only a random sample of levels. We also supply a procedure for choosing the appropriate technique;When more than one response variable is measured on each subject, the problem becomes a bit more complicated, since these variables may well be correlated. However, we are still able to provide a partial solution to the above problem;The case of three treatments, which, when solved, should suggest a general technique, is also examined here. Although by no means a complete solution, the techniques described present a solid basis for further study.

Description
Keywords
Statistics
Citation
Source