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Block Designs: A Randomization Approach

Volume I: Analysis

  • Tadeusz Caliński
  • Sanpei Kageyama

Part of the Lecture Notes in Statistics book series (LNS, volume 150)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Tadeusz Caliński, Sanpei Kageyama
    Pages 1-28
  3. Tadeusz Caliński, Sanpei Kageyama
    Pages 29-48
  4. Tadeusz Caliński, Sanpei Kageyama
    Pages 49-190
  5. Tadeusz Caliński, Sanpei Kageyama
    Pages 191-216
  6. Tadeusz Caliński, Sanpei Kageyama
    Pages 217-284
  7. Back Matter
    Pages 285-316

About this book

Introduction

In most of the literature on block designs, when considering the analysis of experimental results, it is assumed that the expected value of the response of an experimental unit is the sum of three separate components, a general mean parameter, a parameter measuring the effect of the treatment applied and a parameter measuring the effect of the block in which the experimental unit is located. In addition, it is usually assumed that the responses are uncorrelated, with the same variance. Adding to this the assumption of normal distribution of the responses, one obtains the so-called "normal-theory model" on which the usual analysis of variance is based. Referring to it, Scheffe (1959, p. 105) writes that "there is nothing in the 'normal-theory model' of the two-way layout . . . that reflects the increased accuracy possible by good blocking. " Moreover, according to him, such a model "is inappropriate to those randomized-blocks experiments where the 'errors' are caused mainly by differences among the experimental units rather than measurement errors. " In view of this opinion, he has devoted one of the chapters of his book (Chapter 9) to randomization models, being convinced that "an understanding of the nature of the error distribution generated by the physical act of randomization should be part of our knowledge of the basic theory of the analysis of variance.

Keywords

DEX Mathematica Volume block design classification construction design efficiency model tool

Authors and affiliations

  • Tadeusz Caliński
    • 1
  • Sanpei Kageyama
    • 2
  1. 1.Department of Mathematical and Statistical MethodsAgricultural University of PoznańPoznańPoland
  2. 2.Department of Mathematics, Faculty of School EducationHiroshima UniversityHigashi-Hiroshima 739Japan

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-1192-1
  • Copyright Information Springer-Verlag New York, Inc. 2000
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-98578-7
  • Online ISBN 978-1-4612-1192-1
  • Series Print ISSN 0930-0325
  • Buy this book on publisher's site