Analysis and Design of Certain Quantitative Multiresponse Experiments

PrefaceNotationChapter 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 LiteratureChapter II. Linear Models 1. Some Further Remarks on Structured-unstructured Categorization for Factors and Responses 2. Linear Models 2.a. Some General Remarks 2.b. Some Special Models 3. Remarks on the Multivariate Extension LiteratureChapter III. Point Estimation of Location Parameters 1. 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 5. Some Examples of Single Linear Estimation for the Multi-response Case 6. Simultaneous Linear Estimation for the Multi-response Case 7. Summary LiteratureChapter IV. Testing of Linear Hypotheses 1. The Fixed-effects Model of MANOVA 2. Linear Hypotheses under the Fixed-effects Model of MANOVA 3 . Three Current Test Procedures 4. 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 5. 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 6. Applications of the Model (4.2) to Some Growth Curve Problems 7. 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 LiteratureChapter V. Properties of the Test Procedures 1. Introductory Remarks 2. 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 3. Some Remarks on the Admissibility of the Different Procedures 4. Some Results from a Monte Carlo Study 4.a. Specifics of the Monte Carlo Study 4.b. Summary of Findings LiteratureChapter VI. Confidence Bounds 1. 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.