Analysis and design of certain quantitative multiresponse experiments: with an appendix on computer algorithms and programs
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford [u.a.]
Pergamon Press
1971
|
| Ausgabe: | 1. ed. |
| Schriftenreihe: | International series of monographs in applied statistics and biometry
2 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 304 S. Illustrationen |
| ISBN: | 0080069177 |
Internformat
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| 100 | 1 | |a Roy, Samarendra Nath |d 1906-1964 |e Verfasser |0 (DE-588)172349524 |4 aut | |
| 245 | 1 | 0 | |a Analysis and design of certain quantitative multiresponse experiments |b with an appendix on computer algorithms and programs |c by S. N. Roy, R. Gnanadesikan and J. N. Srivastava |
| 250 | |a 1. ed. | ||
| 264 | 1 | |a Oxford [u.a.] |b Pergamon Press |c 1971 | |
| 300 | |a X, 304 S. |b Illustrationen | ||
| 336 | |b txt |2 rdacontent | ||
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| 650 | 4 | |a Variance - Analyse | |
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| 650 | 7 | |a classification hiérarchique |2 inriac | |
| 650 | 7 | |a test hypothèse |2 inriac | |
| 650 | 4 | |a Étude expérimentale | |
| 650 | 4 | |a Analysis of variance | |
| 650 | 4 | |a Experimental design | |
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Datensatz im Suchindex
| _version_ | 1804116579243261952 |
|---|---|
| adam_text | CONTENTS
Preface ix
Notation x
Chapter I. Introduction 1
1. Some general remarks on multifactor multiresponse experiments 1
2. The restricted scope of this monograph 3
3. One continuous response and one relevant unstructured factor: fixed effects model and
random effects model of ANOVA 4
4. One continuous response and two or more unstructured factors in cross classification: the
two models of ANOVA 5
5. One continuous response and one or more structured factors 6
6. Multiresponse experiments and the need for a multivariate development 7
7. Formal versus informal approach 9
8. A brief chapter wise description of the scope of the present monograph 11
Literature 13
Chapter II. Linear Models 14
1. Some further remarks on structured unstructured categorization for factors and responses 14
2. Linear models 15
2.a. Some general remarks 15
2.b. Some special models 16
3. Remarks on the multivariate extension 17
Literature 18
Chapter III. Point Estimation of Location Parameters 19
1. Introduction 19
2.a. Single linear estimation for the uniresponse case 19
2.b. Formulae for estimation of treatment effects under block designs—some examples 21
2.c. Comparison between two different designs in terms of single linear estimation 23
3.a. Simultaneous linear estimation for the uniresponse case 23
3.b. Interpretations of the criteria and their use in comparison of designs 24
4.a. Single linear estimation for the multiresponse case 27
4.b. The same problem under a somewhat more general model 28
5. Some examples of single linear estimation for the multiresponse case 29
6. Simultaneous linear estimation for the multiresponse case 30
7. Summary 31
Literature 31
Chapter IV. Testing of Linear Hypotheses 32
1. The fixed effects model of MANOVA 32
2. Linear hypotheses under the fixed effects model of MANOVA 33
3. Three current test procedures 34
V
vi CONTENTS
4. The union intersection principle and its impact on MANOVA and design of experiments 36
4.a. Bilinear decomposition of the Ha of MANOVA and some general considerations 36
4.b. Some examples of response wise infinite and contrast wise finite decomposition 39
4.c. An example of response wise finite and contrast wise infinite decomposition: the step
down procedure 41
4.d. Some examples of response wise finite and contrast wise finite decomposition 43
4.e. The main motivation behind the decomposition and the union intersection procedures 45
5. Some supplementary mathematical and statistical remarks 46
5.a. On availability of tables for the use of the various test procedures 46
5.b. A remark on the distribution of the F( s of the step down procedure 47
6. Applications of the model (4.2) to some growth curve problems 48
7. Some numerical examples 50
7.a. The doubly infinite decomposition 50
7.b. Response wise infinite and contrast wise finite decomposition 61
7.c. Response wise finite and contrast wise infinite decomposition 63
Literature 65
Chapter V. Properties of the Test Procedures 67
1. Introductory remarks 67
2. Intrinsic properties of group I procedures 68
,, 2.a. Monotonicity property for the /1 criterion 70
: ¦ 2.b. Monotonicity property for the trace criterion 70
2.c. Monotonicity property for the largest root test 71
3. Some remarks on the admissibility of the different procedures 71
4. Some results from a Monte Carlo study 72
4.a. Specifics of the Monte Carlo study 72
4.b. Summary of findings 75
Literature 77
Chapter VI. Confidence Bounds 78
1. General principles 78
l.a. Distinction between general confidence regions and simultaneous confidence intervals 78
l.b. Intervals based on (Ho, H) 78
1 .c. Bounds on the partials 79
1 .d. The nature of the interval estimation in terms of the percentage points of the dis¬
tribution function used 80
1 .e. An additional requirement beyond what is suggested by the pair (Ho, H) 80
l.f. Intervals not prima facie based on any (Ha, H) 80
2. Bounds connected with a linear hypothesis against a linear alternative under the normal
multivariate linear model I 81
2.a. General features 81
2.b. Nature of bounds associated with a bilinear decomposition 81
3.a. Exact expressions for bounds associated with the doubly infinite bilinear decomposition 82
3.a.l. The case u = 1 84
3.a.2. The problem of two mean vectors: two sample case 85
3.a.3. The problem of two mean vectors: single sample case 86
3.b. Three examples of bounds associated with the response wise infinite and contrast wise finite
decomposition 86
3.c. Bounds associated with the response wise finite and contrast wise infinite decomposition 87 i
3.d. Bounds associated with the doubly finite bilinear decomposition 87
CONTENTS vii
4. Supplementary mathematical and statistical remarks 88
4. a. On the derivation of the bounds 88
4.b. On the lengths of the confidence intervals 88
5. Some examples of the total and partial distance functions: block treatment designs 89
6. Numerical examples 91
Literature 95
Chapter VII. Graphical Methods and Internal Comparisons 97
1. Internal comparisons: general philosophy 97
2. A multiresponse graphical internal comparisons procedure 98
3. Outline of the procedure 102
4. Discussion of certain features of the method 103
5. Extensions based on an analogue of the ANOVA identity 104
6. Numerical examples 106
Literature 112
Chapter VIII. Hierarchical and p Block Multiresponse Designs and Their Analysis 113
1. Introductory remarks on multiresponse designs in general 113
2. General description of hierarchical designs and some formal problems under that class 114
3. A sketch of the mathematical justification of the procedure proposed in Section 2 118
4. Multiresponse designs with p block systems 120
5. Testability conditions of hierarchical designs with p block systems 120
6. Nature of the multivariate designs for an important special case 125
Literature 125
Chapter IX. Incomplete Multiresponse Designs 127
1. Introduction 127
2. A simple example of an IM design 127
3. Procedure for analysis of general multiresponse design 136
4. Concluding remarks 138
Literature 138
Chapter X. Construction of Multiresponse Designs 139
1. Introduction 139
2. Multiresponse designs arising in factorial experiments 139
2.a. Not each response is sensitive to every factor 139
2.b. Different sets of effects are important for different factors 143
3. Multiresponse designs of the block treatment type 144
3.a. Hierarchical designs 144
3.b. Regular incomplete multiresponse designs 145
Literature 145
Bibliography 146
Appendix A. Some Specific Matrix Results 151
1. Conditional or generalized inverses of certain patterned matrices 151
2. Some transformations and representations of matrices 154
3. Some properties of direct products of matrices 156
Literature 156
Appendix B. Tables and/or Charts Associated with the Procedures 157
Appendix C. by E. B. Fowlkes and Mrs. E. T. Lee 216
Viii CONTENTS
I. Computer programs for multivariate analysis of variance 216
A. The eight operators 216
B. The main program 226
C. The second program 227
D. FORTRAN IV routines for the MANOVA operators 228
E. Example 232
F. FORTRAN listings for the MANOVA operators 237
G. Programs to be supplied by the user 279
H. Composing FORTRAN IV programs to use the MANOVA operators 279
II. Computer program for internal comparisons 279
Literature 299
Author Index 301
Subject Index 303
|
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| author | Roy, Samarendra Nath 1906-1964 Gnanadesikan, Ramanathan 1932- Srivastava, Jagdish Narain 1933- |
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| discipline | Allgemeines Psychologie Mathematik Wirtschaftswissenschaften |
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| isbn | 0080069177 |
| language | English |
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| series | International series of monographs in applied statistics and biometry |
| series2 | International series of monographs in applied statistics and biometry |
| spelling | Roy, Samarendra Nath 1906-1964 Verfasser (DE-588)172349524 aut Analysis and design of certain quantitative multiresponse experiments with an appendix on computer algorithms and programs by S. N. Roy, R. Gnanadesikan and J. N. Srivastava 1. ed. Oxford [u.a.] Pergamon Press 1971 X, 304 S. Illustrationen txt rdacontent n rdamedia nc rdacarrier International series of monographs in applied statistics and biometry 2 Mathematical Statistics cabt Analyse de variance ram CLASSIFICATION CROISEE inriac Plan d'expérience ram Variance - Analyse analyse variance inriac classification hiérarchique inriac test hypothèse inriac Étude expérimentale Analysis of variance Experimental design Statistik (DE-588)4056995-0 gnd rswk-swf Statistik (DE-588)4056995-0 s DE-604 Gnanadesikan, Ramanathan 1932- Verfasser (DE-588)1089233159 aut Srivastava, Jagdish Narain 1933- Verfasser (DE-588)131854879 aut International series of monographs in applied statistics and biometry 2 (DE-604)BV001889692 2 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001393844&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Roy, Samarendra Nath 1906-1964 Gnanadesikan, Ramanathan 1932- Srivastava, Jagdish Narain 1933- Analysis and design of certain quantitative multiresponse experiments with an appendix on computer algorithms and programs International series of monographs in applied statistics and biometry Mathematical Statistics cabt Analyse de variance ram CLASSIFICATION CROISEE inriac Plan d'expérience ram Variance - Analyse analyse variance inriac classification hiérarchique inriac test hypothèse inriac Étude expérimentale Analysis of variance Experimental design Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4056995-0 |
| title | Analysis and design of certain quantitative multiresponse experiments with an appendix on computer algorithms and programs |
| title_auth | Analysis and design of certain quantitative multiresponse experiments with an appendix on computer algorithms and programs |
| title_exact_search | Analysis and design of certain quantitative multiresponse experiments with an appendix on computer algorithms and programs |
| title_full | Analysis and design of certain quantitative multiresponse experiments with an appendix on computer algorithms and programs by S. N. Roy, R. Gnanadesikan and J. N. Srivastava |
| title_fullStr | Analysis and design of certain quantitative multiresponse experiments with an appendix on computer algorithms and programs by S. N. Roy, R. Gnanadesikan and J. N. Srivastava |
| title_full_unstemmed | Analysis and design of certain quantitative multiresponse experiments with an appendix on computer algorithms and programs by S. N. Roy, R. Gnanadesikan and J. N. Srivastava |
| title_short | Analysis and design of certain quantitative multiresponse experiments |
| title_sort | analysis and design of certain quantitative multiresponse experiments with an appendix on computer algorithms and programs |
| title_sub | with an appendix on computer algorithms and programs |
| topic | Mathematical Statistics cabt Analyse de variance ram CLASSIFICATION CROISEE inriac Plan d'expérience ram Variance - Analyse analyse variance inriac classification hiérarchique inriac test hypothèse inriac Étude expérimentale Analysis of variance Experimental design Statistik (DE-588)4056995-0 gnd |
| topic_facet | Mathematical Statistics Analyse de variance CLASSIFICATION CROISEE Plan d'expérience Variance - Analyse analyse variance classification hiérarchique test hypothèse Étude expérimentale Analysis of variance Experimental design Statistik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001393844&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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