Analysis and Design of Certain Quantitative Multiresponse Experiments (eBook)

International Series of Monographs in Applied Statistics and Biometry

R. Gnanadesikan, S. N. Roy, J. N. Srivastava (Autoren)

eBook Download: PDF

2014 | 1. Auflage
314 Seiten
Elsevier Science (Verlag)
978-1-4831-5789-4 (ISBN)

Infos

Analysis and Design of Certain Quantitative Multiresponse Experiments highlights (i) the need for multivariate analysis of variance (MANOVA); (ii) the need for multivariate design for multiresponse experiments; and (iii) the actual procedures and interpretation that have been used for this purpose by the authors. The development in this monograph is such that the theory and methods of uniresponse analysis and design stay very close to classical ANOVA. The book first discusses the multivariate aspect of linear models for location type of parameters, but under a univariate design, i.e. one in which each experimental unit is measured or studied with respect to all the responses. Separate chapters cover point estimation of location parameters; testing of linear hypotheses; properties of test procedures; and confidence bounds on a set of parametric functions. Subsequent chapters discuss a graphical internal comparison method for analyzing certain kinds of multiresponse experimental data; two classes of multiresponse designs, i.e. designated hierarchical and p-block designs; and the construction of various kinds of multiresponse designs.

Inhalt

Front Cover 1
Analysis and Design of Certain Quantitativ Emultiresponse Experiments 4
Copyright Page 5
Table of Contents 6
PREFACE 10
NOTATION 11
CHAPTER I. INTRODUCTION 12
1. Some general remarks on multifactor multiresponse experiments 12
2. The restricted scope of this monograph 14
3. One continuous response and one relevant unstructured factor: fixed-effects model andrandom-effects model of ANOVA 15
4. One continuous response and two or more unstructured factors in cross classification: thetwo models of ANOVA 16
5. One continuous response and one or more structured factors 17
6. Multiresponse experiments and the need for a multivariate development 18
7. Formal versus informal approach 20
8. A brief chapter-wise description of the scope of the present monograph Literature 22
Literature 24
CHAPTER II. LINEAR MODELS 25
1. Some further remarks on structured-unstructured categorization for factors and responses 25
2. Linear models 26
3. Remarks on the multivariate extension 28
Literature 29
CHAPTER III . POINT ESTIMATION OF LOCATION PARAMETERS 30
1. Introduction 30
2.a. Single linear estimation for the uniresponse case 30
2.b. Formulae for estimation of treatment effects under block designs —some examples 32
2.C. Comparison between two different designs in terms of single linear estimation 34
3.a. Simultaneous linear estimation for the uniresponse case 34
3.b. Interpretations of the criteria and their use in comparison of designs 35
4.a. Single linear estimation for the multiresponse case 38
4.b. The same problem under a somewhat more general model 39
5. Some examples of single linear estimation for the multiresponse case 40
6. Simultaneous linear estimation for the multiresponse case 41
7. Summary 42
Literature 42
CHAPTER IV . TESTING OF LINEAR HYPOTHESES 43
1. The fixed-effects model of M ANOVA 43
2. Linear hypotheses under the fixed-effects model of MANOVA 44
3 . Three current test procedures 45
4. The union-intersection principle and its impact on MANOVA and design of experiments 47
5. Some supplementary mathematical and statistical remarks 57
6. Applications of the model (4.2) to some growth curve problems 59
7. Some numerical examples 61
Literature 77
CHAPTER V. PROPERTIES OF THE TEST PROCEDURES 79
1. Introductory remarks 79
2. Intrinsic properties of group I procedures 80
3. Some remarks on the admissibility of the different procedures 83
4. Some results from a Monte Carlo study 84
Literature 89
CHAPTER VI. CONFIDENCE BOUNDS 90
1. General principles 90
2. Bounds connected with a linear hypothesis against a linear alternative under the normalmultivariate linear model I 93
3.a. Exact expressions for bounds associated with the doubly infinite bilinear decomposition 94
3.b. Three examples of bounds associated with the response-wise infinite and contrast-wise finitedecomposition 98
3.C Bounds associated with the response-wise finite and contrast-wise infinite decomposition 99
3.d. Bounds associated with the doubly finite bilinear decomposition 99
4 . Supplementary mathematical and statistical remarks 100
5. Some examples of the total and partial distance functions: block-treatment designs 101
6. Numerical examples 103
Literature 107
CHAPTER VII . GRAPHICAL METHODS AND INTERNAL COMPARISONS 109
1. Internal comparisons: general philosophy 109
2. A multiresponse graphical internal comparisons procedure 110
3. Outline of the procedure 114
4 . Discussion of certain features of the method 115
5. Extensions based on an analogue of the ANOVA identity 116
6. Numerical examples 118
Literature 124
CHAPTER VIII . HIERARCHICAL AND /?-BLOCK MULTIRESPONSE DESÎGNS AND THEIR ANALYSIS 125
1. Introductory remarks on multiresponse designs in general 125
2. General description of hierarchical designs and some formal problems under that class 126
3 . A sketch of the mathematical justification of the procedure proposed in Section 2 130
4 . Multiresponse designs with /?-block systems 132
5. Testability conditions of hierarchical designs with /7-block systems 132
6. Nature of the multivariate designs for an important special case 137
Literature 137
CHAPTER IX . INCOMPLETE MULTIRESPONSE DESIGNS 139
1. Introduction 139
2. A simple example of an IM design 139
3. Procedure for analysis of general multiresponse design 148
4. Concluding remarks 150
Literature 150
CHAPTER X . CONSTRUCTION OF MULTIRESPONSE DESIGNS 151
1. Introduction 151
2. Multiresponse designs arising in factorial experiments 151
3. Multiresponse designs of the block-treatment type 156
BIBLIOGRAPHY 158
APPENDIX A . SOME SPECIFIC MATRIX RESULTS 163
1. Conditional or generalized inverses of certain patterned matrices 163
2. Some transformations and representations of matrices 166
3. Some properties of direct products of matrices Literature 168
APPENDIX B . TABLES AND/OR CHARTS ASSOCIATED WITH THE PROCEDURES 169
APPENDIX C 228
I. Computer programs for multivariate analysis of variance 228
II. Computer program for internal comparisons Literature 291
AUTHOR INDEX 313
SUBJECT INDEX 315

Produkt-Details

• Erscheint lt. Verlag: 15.5.2014
• Sprache: englisch
• Themenwelt: Sachbuch/Ratgeber ► Freizeit / Hobby ► Spielen / Raten
• Themenwelt: Schulbuch / Wörterbuch ► Lexikon / Chroniken
• Themenwelt: Mathematik / Informatik ► Mathematik
• Themenwelt: Technik
• ISBN-10: 1-4831-5789-X / 148315789X
• ISBN-13: 978-1-4831-5789-4 / 9781483157894