Analysis and Design of Certain Quantitative Multiresponse Experiments

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.

Contenu

Preface
Notation
Chapter I. Introduction

1. Some General Remarks on Multi-factor Multi-response Experiments
2. The Restricted Scope of this Monograph
3. One Continuous Response and One Relevant Unstructured Factor: Fixed-effects Model and Random-effects Model of ANOVA
4. One Continuous Response and Two or More Unstructured Factors in cross Classification: The Two Models of ANOVA
5. One Continuous Response and One or More Structured Factors
6. Multi-response Experiments and the Need for a Multivariate Development
7. Formal versus Informal Approach
8. A Brief Chapter-wise Description of the Scope of the Present Monograph
   Literature
   Chapter II. Linear Models
9. Some Further Remarks on Structured-unstructured Categorization for Factors and Responses
10. Linear Models
    2.a. Some General Remarks
    2.b. Some Special Models
11. Remarks on the Multivariate Extension
    Literature
    Chapter III. Point Estimation of Location Parameters
12. Introduction
    2.a. Single Linear Estimation for the Uni-response Case
    2.b. Formula for Estimation of Treatment Effects under Block Designs - Some Examples
    2.c. Comparison between Two Different Designs in Terms of Single Linear Estimation
    3.a. Simultaneous Linear Estimation for the Uni-response Case
    3.b. Interpretations of the Criteria and their Use in Comparison of Designs
    4.a. Single Linear Estimation for the Multi-response Case
    4.b. The Same Problem under a Somewhat More General Model
13. Some Examples of Single Linear Estimation for the Multi-response Case
14. Simultaneous Linear Estimation for the Multi-response Case
15. Summary
    Literature
    Chapter IV. Testing of Linear Hypotheses
16. The Fixed-effects Model of MANOVA
17. Linear Hypotheses under the Fixed-effects Model of MANOVA
    3 . Three Current Test Procedures
18. The Union-intersection Principle and its Impact on MANOVA and Design of Experiments
    4.a. Bilinear Decomposition of the H0 of MANOVA and Some General Considerations
    4.b. Some Examples of Response-wise Infinite and Contrast-wise Finite Decomposition
    4.c. An Example of Response-wise Finite and Contrast-wise Infinite Decomposition: The Step-down Procedure
    4.d. Some Examples of Response-wise Finite and Contrast-wise Finite Decomposition
    4.e. The Main Motivation behind the Decomposition and the Union-intersection Procedures
19. Some Supplementary Mathematical and Statistical Remarks
    5.a. On Availability of Tables for the Use of the Various Test Procedures
    5.b. A Remark on the Distribution of the Fi's of the Step-down Procedure
20. Applications of the Model (4.2) to Some Growth Curve Problems
21. Some Numerical Examples
    7.a. The Doubly Infinite Decomposition
    7.b. Response-wise Infinite and Contrast-wise Finite Decomposition
    7.c. Response-wise Finite and Contrast-wise Infinite Decomposition
    Literature
    Chapter V. Properties of the Test Procedures
22. Introductory Remarks
23. Intrinsic Properties of Group I Procedures
    2.a. Monotonicity Property for the A-criterion
    2.b. Monotonicity Property for the Trace Criterion
    2.C. Monotonicity Property for the Largest-root Test
24. Some Remarks on the Admissibility of the Different Procedures
25. Some Results from a Monte Carlo Study
    4.a. Specifics of the Monte Carlo Study
    4.b. Summary of Findings
    Literature
    Chapter VI. Confidence Bounds
26. General Principles
    l.a. Distinction between General Confidence Regions and Simultaneous Confidence Intervals
    l.b. Intervals Based on (H0,H)
    1.c. Bounds on the "Partials"
    l.d. The Nature of the Interval Estimation in Terms of the Percentage Points of the Distribution Function Used
    1.e. An Additional Requirement beyond what is Suggested by the Pair (H0,H)
    1.f. Intervals not Prima Facie Based on any (H0,H)
27. Bounds Connected with a Linear Hypothesis against a Linear Alternative under the Normal Multivariate Linear Model I
    2.a. General Features
    2.b. Nature of Bounds Associated with a Bilinear Decomposition
    3.a. Exact Expressions for Bounds Associated with the Doubly Infinite Bilinear Decomposition
    3.a.l. The Case u = 1
    3.a.2. The Problem of Two Mean Vectors: Two-sample Case
    3.a.3. The Problem of Two Mean Vectors: Single-sample Case
    3.b. Three Examples of Bounds Associated with the Response-wise Infinite and Contrast-wise Finite Decomposition
    3.c. Bounds Associated with the Response-wise Finite and Contrast-wise Infinite Decomposition
    3.d. Bounds Associated with the Doubly Finite Bilinear Decomposition
28. Supplementary Mathematical and Statistical Remarks
    4.a. On the Derivation of the Bounds
    4.b. On the Lengths of the Confidence Intervals
29. Some Examples of the Total and Partial Distance Functions: Block-treatment Designs
30. Numerical Examples
    Literature
    Chapter VII. Graphical Methods and Internal Comparisons
31. Internal Comparisons: General Philosophy
32. A Multi-response Graphical Internal Comparisons Procedure
33. Outline of the Procedure
34. Discussion of Certain Features of the Method
35. Extensions Based on an Analog of the ANOVA Identity
36. Numerical Examples
    Literature
    Chapter VIII. Hierarchical and p-Block Multi-response Designs and their Analysis
37. Introductory Remarks on Multi-response Designs in General
38. General Description of Hierarchical Designs and Some Formal Problems under that Class
39. A Sketch of the Mathematical Justification of the Procedure Proposed in Section 2
40. Multi-response Designs with p-Block Systems
41. Testability Conditions of Hierarchical Designs with p-Block Systems
42. Nature of the Multivariate Designs for an Important Special Case
    Literature
    Chapter IX. Incomplete Multi-response Designs
43. Introduction
44. A Simple Example of an IM Design
45. Procedure for Analysis of General Multi-response Design
46. Concluding Remarks
    Literature
    Chapter X. Construction of Multi-response Designs
47. Introduction
48. Multi-response Designs Arising in Factorial Experiments
    2.a. Not Each Response is Sensitive to Every Factor
    2.b. Different Sets of Effects are Important for Different Factors
49. Multi-response Designs of the Lock-treatment Type
    3.a. Hierarchical Designs
    3.b. Regular Incomplete Multi-response Designs
    Literature
    Bibliography
    Appendix A. Some Specific Matrix Results
50. Conditional or Generalized Inverses of Certain Patterned Matrices
51. Some Transformations and Representations of Matrices
52. Some Properties of Direct Products of Matrices
    Literature
    Appendix B. Tables and/or Charts Associated with the Procedures
    Appendix C …