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A Calculus for Factorial Arrangements

  • Book
  • © 1989

Overview

Authors:
  1. Sudhir Gupta

    1. Division of Statistics, Department of Mathematical Sciences, Northern Illinois University, DeKalb, USA

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  2. Rahul Mukerjee

    1. Stat-Math Division, Indian Statistical Institute, Calcutta, India

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    You can also search for this author in PubMed   Google Scholar

Part of the book series: Lecture Notes in Statistics (LNS, volume 59)

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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.

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Table of contents (8 chapters)

  1. Front Matter

    Pages I-VI
    Download chapter PDF

  2. Introduction

    • Sudhir Gupta, Rahul Mukerjee
    Pages 1-2

  3. A Calculus for Factorial Arrangements

    • Sudhir Gupta, Rahul Mukerjee
    Pages 3-10

  4. Characterizations for Balance with Orthogonal Factorial Structure

    • Sudhir Gupta, Rahul Mukerjee
    Pages 11-23

  5. Characterizations for Orthogonal Factorial Structure

    • Sudhir Gupta, Rahul Mukerjee
    Pages 24-47

  6. Constructions I: Factorial Experiments in Cyclic and Generalized Cyclic Designs

    • Sudhir Gupta, Rahul Mukerjee
    Pages 48-71

  7. Constructions II: Designs Based on Kronecker Type Products

    • Sudhir Gupta, Rahul Mukerjee
    Pages 72-87

  8. More on Single Replicate Factorial Designs

    • Sudhir Gupta, Rahul Mukerjee
    Pages 88-97

  9. Further Developments

    • Sudhir Gupta, Rahul Mukerjee
    Pages 98-112

  10. Back Matter

    Pages 113-126
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Authors and Affiliations

  • Division of Statistics, Department of Mathematical Sciences, Northern Illinois University, DeKalb, USA

    Sudhir Gupta

  • Stat-Math Division, Indian Statistical Institute, Calcutta, India

    Rahul Mukerjee

Bibliographic Information

  • Book Title: A Calculus for Factorial Arrangements

  • Authors: Sudhir Gupta, Rahul Mukerjee

  • Series Title: Lecture Notes in Statistics

  • DOI: https://doi.org/10.1007/978-1-4419-8730-3

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1989

  • Softcover ISBN: 978-0-387-97172-8Published: 22 November 1989

  • eBook ISBN: 978-1-4419-8730-3Published: 10 September 2012

  • Series ISSN: 0930-0325

  • Series E-ISSN: 2197-7186

  • Edition Number: 1

  • Number of Pages: VI, 126

  • Topics: Applications of Mathematics

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