Statistical Analysis of Designed Experiments, Third Edition (Springer

624 Pages·2009·3.69 MB·English

by  Helge Toutenburg, Shalabh

Springer Texts in Statistics
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Series Editors:
G. Casella
S. Fienberg
I. Olkin
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Helge Toutenburg
Shalabh
Statistical Analysis
of Designed Experiments
Third Edition
Helge Toutenburg Shalabh
Institut für Statistik Department of Mathematics & Statistics
Ludwig-Maximilians-Universität Indian Institute of Technology
Akademiestraße 1 Kanpur-208016
80799 München India
Germany [email protected]
[email protected]
STS Editorial Board
George Casella Stephen Fienberg
Department of Statistics Department of Statistics
University of Florida Carnegie Mellon University
Gainesville, FL 32611-8545 Pittsburg, PA 15213-3890
USA USA
Ingram Olkin
Department of Statistics
Stanford University
Stanford, CA 94305
USA
ISSN1431-875X
ISBN978-1-4419-1147-6 e-ISBN978-1-4419-1148-3
DOI10.1007/978-1-4419-1148-3
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Preface to the Third Edition
This book is the third revised and updated English edition of the German
textbook “Versuchsplanung und Modellwahl” by Helge Toutenburg which
was based on more than 15 years experience of lectures on the course “De-
signofExperiments”attheUniversityofMunichandinteractionswiththe
statisticians from industries and other areas of applied sciences and engi-
neering.Thisisatypeofresource/referencebookwhichcontainsstatistical
methodsusedbyresearchersinappliedareas.Becauseofthediverseexam-
ples combined with software demonstrations it is also useful as a textbook
in more advanced courses,
The applications of design of experiments have seen a significant growth
in the last few decades in different areas like industries, pharmaceutical
sciences, medical sciences, engineering sciences etc. The second edition
of this book received appreciation from academicians, teachers, students
and applied statisticians. As a consequence, Springer-Verlag invited Helge
Toutenburg to revise it and he invited Shalabh for the third edition of the
book.
In our experience with students, statisticians from industries and re-
searchers from other fields of experimental sciences, we realized the
importance of several topics in the design of experiments which will in-
crease the utility of this book. Moreover we experienced that these topics
aremostlyexplainedonlytheoreticallyinmostoftheavailablebooks.Stu-
dents and applied statisticians generally loose their interest and patience
inreadingtoomuchtheorybeforetheycanunderstandthetopicanduseit
in the applications. So we decided to write and include these topics in the
third edition of the book. We have attempted to go into theory only up to
vi Preface to the Third Edition
a necessary level. At several places, we have tried to explain the concepts,
methodologies and utility of the topics with particular cases of designs of
experimentsinsteadofstartingdirectlywithatheoreticalsetup.Wewould
liketoremarkthatthistextmaynotdirectlyappealtoareaderinterested
only in theory. Some good references are provided which can be followed
latertogetatheoreticalgraspafterunderstandingthetextfromthisbook.
We have added a new Chapter 6 on incomplete block designs. This
chapter starts with an introduction to the general theory of incomplete
block designs which is necessary to understand the analysis of balanced
incomplete block design and partially balanced incomplete block design
introduced afterwards. More emphasis is given in explaining the setup,
concept, methodology and various other aspects of these designs. For the
analysis part, the results from the general theory of incomplete block
designs are carried over and used directly.
The Chapter on ”Multifactor Experiments” is extended and topics on
confounding, partial confounding and fractional replications in factorial
experiments are introduced. These topics do not start directly with the
theoretical setup. We have rather considered particular cases of factorial
designs to explain the intricacies of related concepts and have developed
the necessary tools stepwise. Once a reader understands these steps and
gets familiar with the concepts and terminologies, then all the details can
be extended to a general setup.
ThederivationsofthetheoreticalresultsagainareputintoanAppendix
sothatareaderinterestedintheapplicationsisnotburdenedunnecessarily.
We thank Dr. John Kimmel of Springer-Verlag for his help in the third
edition of the book.
We invite the readers to send their comments and suggestions on the
contents and treatment of the topics in the book for possible improvement
in future editions.
Mu¨nchen, Germany Helge Toutenburg
Kanpur, India Shalabh
July 7, 2009
Preface
This book is the second English edition of my German textbook that
was originally written parallel to my lecture “Design of Experiments”
which was held at the University of Munich. It is thought to be a type
of resource/reference book which contains statistical methods used by re-
searchersinappliedareas.Becauseofthediverseexamplesitcouldalsobe
used in more advanced undergraduate courses, as a textbook.
It is often called to our attention, by statisticians in the pharmaceu-
tical industry, that there is a need for a summarizing and standardized
representation of the design and analysis of experiments that includes the
differentaspectsofclassicaltheoryforcontinuousresponse,andofmodern
procedures for a categorical and, especially, correlated response, as well as
more complex designs as, for example, cross–over and repeated measures.
Therefore the book is useful for non statisticians who may appreciate the
versatility of methods and examples, and for statisticians who will also
find theoretical basics and extensions. Therefore the book tries to bridge
the gap between the application and theory within methods dealing with
designed experiments.
In order to illustrate the examples we decided to use the software pack-
agesSAS,SPLUS,andSPSS.Eachofthesehasadvantagesovertheothers
andwehopeto haveusedthem inanacceptable way.Concerningthe data
sets we give references where possible.
viii Preface
Staff and graduate students played an essential part in the preparation
ofthemanuscript.Theywrotethetextinwell–triedprecision,worked–out
examples(ThomasNittner),andpreparedseveralsectionsinthebook(Ul-
rike Feldmeier, Andreas Fieger, Christian Heumann, Sabina Illi, Christian
Kastner,OliverLoch,ThomasNittner,ElkeOrtmann,AndreaSch¨opp,and
Irmgard Strehler).
Especially I would like to thank Thomas Nittner who has done a great
deal of work on this second edition. We are very appreciative of the efforts
of those who assisted in the preparation of the English version. In partic-
ular, we would like to thank Sabina Illi and Oliver Loch, as well as V.K.
Srivastava (1943–2001), for their careful reading of the English version.
Thisbookisconstitutedasfollows.AfterashortIntroduction,withsome
examples,wewanttogiveacompactsurveyofthecomparisonoftwosam-
ples (Chapter 2). The well–known linear regression model is discussed in
Chapter 3 with many details, of a theoretical nature, and with emphasis
on sensitivity analysis at the end. Chapter 4 contains single–factor exper-
iments with different kinds of factors, an overview of multiple regressions,
and some special cases, such as regression analysis of variance or models
with random effects. More restrictive designs, like the randomized block
design or Latin squares, are introduced in Chapter 5. Experiments with
morethanonefactoraredescribedinChapter7,withsomebasicssuchas,
e.g., effect coding. As categorical response variables are present in Chap-
ters9and10wehaveputthemodelsforcategoricalresponse,thoughthey
are more theoretical, in Chapter 8. Chapter 9 contains repeated measure
models, with their whole versatility and complexity of designs and testing
procedures. A more difficult design, the cross–over, can be found in Chap-
ter 10. Chapter 11 treats the problem of incomplete data. Apart from the
basicsofmatrixalgebra(AppendixA),thereaderwillfindsomeproofsfor
Chapters 3 and 4 in Appendix B. Last but not least, Appendix C contains
the distributions and tables necessary for a better understanding of the
examples.
Of course, not all aspects can be taken into account, specially as devel-
opmentinthefieldofgeneralizedlinearmodelsissodynamic,itishardto
include all current tendencies. In order to keep up with this development,
the book contains more recent methods for the analysis of clusters.
To some extent, concerning linear models and designed experiments, we
want to recommend the books by McCulloch and Searle (2000), Wu and
Hamada (2000), and Dean and Voss (1998) for supplying revised material.
Preface ix
Finally,wewouldliketothankJohnKimmel,TimothyTaylor,andBrian
HoweofSpringer–VerlagNewYorkfortheircooperationandconfidencein
this book.
Universit¨at Mu¨nchen Helge Toutenburg
March 25, 2002 Thomas Nittner