Lecture Notes in Statistics

A Calculus for Factorial Arrangements

Authors: Gupta, Sudhir, Mukerjee, Rahul

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About this book

Factorial designs were introduced and popularized by Fisher (1935). Among the early authors, Yates (1937) considered both symmetric and asymmetric factorial designs. Bose and Kishen (1940) and Bose (1947) developed a mathematical theory for symmetric priIi't&-powered factorials while Nair and Roo (1941, 1942, 1948) introduced and explored balanced confounded designs for the asymmetric case. Since then, over the last four decades, there has been a rapid growth of research in factorial designs and a considerable interest is still continuing. Kurkjian and Zelen (1962, 1963) introduced a tensor calculus for factorial arrangements which, as pointed out by Federer (1980), represents a powerful statistical analytic tool in the context of factorial designs. Kurkjian and Zelen (1963) gave the analysis of block designs using the calculus and Zelen and Federer (1964) applied it to the analysis of designs with two-way elimination of heterogeneity. Zelen and Federer (1965) used the calculus for the analysis of designs having several classifications with unequal replications, no empty cells and with all the interactions present. Federer and Zelen (1966) considered applications of the calculus for factorial experiments when the treatments are not all equally replicated, and Paik and Federer (1974) provided extensions to when some of the treatment combinations are not included in the experiment. The calculus, which involves the use of Kronecker products of matrices, is extremely helpful in deriving characterizations, in a compact form, for various important features like balance and orthogonality in a general multifactor setting.

Table of contents (8 chapters)

  • Introduction

    Gupta, Sudhir (et al.)

    Pages 1-2

  • A Calculus for Factorial Arrangements

    Gupta, Sudhir (et al.)

    Pages 3-10

  • Characterizations for Balance with Orthogonal Factorial Structure

    Gupta, Sudhir (et al.)

    Pages 11-23

  • Characterizations for Orthogonal Factorial Structure

    Gupta, Sudhir (et al.)

    Pages 24-47

  • Constructions I: Factorial Experiments in Cyclic and Generalized Cyclic Designs

    Gupta, Sudhir (et al.)

    Pages 48-71

Buy this book

eBook $74.99
price for USA (gross)
  • ISBN 978-1-4419-8730-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $99.00
price for USA
  • ISBN 978-0-387-97172-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
A Calculus for Factorial Arrangements
Authors
Series Title
Lecture Notes in Statistics
Series Volume
59
Copyright
1989
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-1-4419-8730-3
DOI
10.1007/978-1-4419-8730-3
Softcover ISBN
978-0-387-97172-8
Series ISSN
0930-0325
Edition Number
1
Number of Pages
VI, 126
Topics