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Repeated Measurements and Cross-Over Designs
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Repeated Measurements and Cross-Over Designs
by Damaraju Raghavarao, Lakshmi Padgett
Repeated Measurements and Cross-Over Designs
Cover
Title page
Copyright page
Dedication
Preface
Chapter 1: Introduction
1.1 Introduction
1.2 One-Sample RMD
1.3 k-Sample RMD
1.4 Split-Plot Designs
1.5 Growth Curves
1.6 Cross-Over Designs
1.7 TWO-PERIOD CROSS-OVER DESIGNS
1.8 Modifications in Cross-Over Designs
1.9 NONPARAMETRIC METHODS
References
Chapter 2: One-Sample Repeated Measurement Designs
2.1 INTRODUCTION
2.2 Testing for Sphericity Condition
2.3 Univariate ANOVA for One-Sample RMD
2.4 Multivariate Methods for One-Sample RMD
2.5 UNIVARIATE ANOVA UNDER NONSPHERICITY CONDITION
2.6 Numerical Example
2.7 Concordance Correlation Coefficient
2.8 Multiresponse Concordance Correlation Coefficient
2.9 Repeated Measurements with Binary Response
References
Chapter 3: k-Sample Repeated Measurements Design
3.1 INTRODUCTION
3.2 Test for the Equality of Dispersion Matrices and Sphericity Condition Of k-Dispersion Matrices
3.3 Univariate ANOVA for k-Sample RMD
3.4 Multivariate Methods for k-Sample RMD
3.5 Numerical Example
3.6 Multivariate Methods with Unequal Dispersion Matrices
3.7 Analysis with Ordered Categorical Response
References
Chapter 4: Growth Curve Models
4.1 INTRODUCTION
4.2 Sigmoidal Curves
4.3 Analysis of Mixed Models
4.4 Simple Linear Growth Curve Model
4.5 Nonlinear Growth Curve Model
4.6 Numerical Example
4.7 Joint Action Models
References
Chapter 5: Cross-Over Designs without Residual Effects
5.1 INTRODUCTION
5.2 Fixed Effects Analysis of CODWOR
5.3 Connectedness in CODWOR
5.4 Orthogonality in CODWOR
5.5 Latin Square Designs
5.6 Youden Square Design and Generalization
5.7 F-Squares
5.8 Lattice Square Designs
5.9 Analysis of CODWOR when the Units Effects are Random
5.10 Numerical Example
5.11 Orthogonal Latin Squares
References
Chapter 6: Cross-Over Designs with Residual Effects
6.1 INTRODUCTION
6.2 Analysis of CODWR
6.3 Bred
6.4 PBCOD (m)
6.5 Numerical Example
6.6 Analysis With Unit (or Subject) Effects Random
6.7 Concluding Remarks
References
Chapter 7: Two-Period Cross-Over Designs with Residual Effects
7.1 INTRODUCTION
7.2 Two-Period, Two-Treatment CODWR Analysis: Parametric Methods
7.3 Two-Period, Two-Treatment CODWR Analysis: NonParametric Methods
7.4 Two-Period t Treatment Cross-Over Design
7.5 Numerical Examples
References
Chapter 8: Other Cross-Over Designs with Residual Effects
8.1 INTRODUCTION
8.2 Extra-Period Designs
8.3 Residual Effects Proportional To direct Effects
8.4 Undiminished Residual Effects Designs
8.5 Treatment Balanced Residual Effects Designs
8.6 A General Linear Model for CODWR
8.7 Nested Design
8.8 Split-Plot Type CODWR
8.9 CODWR in Circular Arrangement
8.10 Numerical Examples
References
Chapter 9: Some Constructions of Cross-Over Designs
9.1 INTRODUCTION
9.2 GALOIS FIELDS
9.3 Generalized Youden Designs
9.4 Williams’ Balanced Residual Effects Designs
9.5 Other Balanced Residual Effects Designs
9.6 Combinatorially Overall Balanced Residual Effects Designs
9.7 Construction of Treatment Balanced Residual Effects Designs
9.8 Some Construction of PBCOD (m)
9.9 Construction of Complete Set of Mols and Patterson’s Bred
9.10 Balanced Circular Arrangements
9.11 CONCLUDING REMARKS
References
Further Reading
Index
Eula
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Title page
CONTENTS
Cover
Title page
Copyright page
Dedication
Preface
Chapter 1: Introduction
1.1 Introduction
1.2 One-Sample RMD
1.3 k-Sample RMD
1.4 Split-Plot Designs
1.5 Growth Curves
1.6 Cross-Over Designs
1.7 TWO-PERIOD CROSS-OVER DESIGNS
1.8 Modifications in Cross-Over Designs
1.9 NONPARAMETRIC METHODS
References
Chapter 2: One-Sample Repeated Measurement Designs
2.1 INTRODUCTION
2.2 Testing for Sphericity Condition
2.3 Univariate ANOVA for One-Sample RMD
2.4 Multivariate Methods for One-Sample RMD
2.5 UNIVARIATE ANOVA UNDER NONSPHERICITY CONDITION
2.6 Numerical Example
2.7 Concordance Correlation Coefficient
2.8 Multiresponse Concordance Correlation Coefficient
2.9 Repeated Measurements with Binary Response
References
Chapter 3: k-Sample Repeated Measurements Design
3.1 INTRODUCTION
3.2 Test for the Equality of Dispersion Matrices and Sphericity Condition Of k-Dispersion Matrices
3.3 Univariate ANOVA for k-Sample RMD
3.4 Multivariate Methods for k-Sample RMD
3.5 Numerical Example
3.6 Multivariate Methods with Unequal Dispersion Matrices
3.7 Analysis with Ordered Categorical Response
References
Chapter 4: Growth Curve Models
4.1 INTRODUCTION
4.2 Sigmoidal Curves
4.3 Analysis of Mixed Models
4.4 Simple Linear Growth Curve Model
4.5 Nonlinear Growth Curve Model
4.6 Numerical Example
4.7 Joint Action Models
References
Chapter 5: Cross-Over Designs without Residual Effects
5.1 INTRODUCTION
5.2 Fixed Effects Analysis of CODWOR
5.3 Connectedness in CODWOR
5.4 Orthogonality in CODWOR
5.5 Latin Square Designs
5.6 Youden Square Design and Generalization
5.7 F-Squares
5.8 Lattice Square Designs
5.9 Analysis of CODWOR when the Units Effects are Random
5.10 Numerical Example
5.11 Orthogonal Latin Squares
References
Chapter 6: Cross-Over Designs with Residual Effects
6.1 INTRODUCTION
6.2 Analysis of CODWR
6.3 Bred
6.4 PBCOD (m)
6.5 Numerical Example
6.6 Analysis With Unit (or Subject) Effects Random
6.7 Concluding Remarks
References
Chapter 7: Two-Period Cross-Over Designs with Residual Effects
7.1 INTRODUCTION
7.2 Two-Period, Two-Treatment CODWR Analysis: Parametric Methods
7.3 Two-Period, Two-Treatment CODWR Analysis: NonParametric Methods
7.4 Two-Period t Treatment Cross-Over Design
7.5 Numerical Examples
References
Chapter 8: Other Cross-Over Designs with Residual Effects
8.1 INTRODUCTION
8.2 Extra-Period Designs
8.3 Residual Effects Proportional To direct Effects
8.4 Undiminished Residual Effects Designs
8.5 Treatment Balanced Residual Effects Designs
8.6 A General Linear Model for CODWR
8.7 Nested Design
8.8 Split-Plot Type CODWR
8.9 CODWR in Circular Arrangement
8.10 Numerical Examples
References
Chapter 9: Some Constructions of Cross-Over Designs
9.1 INTRODUCTION
9.2 GALOIS FIELDS
9.3 Generalized Youden Designs
9.4 Williams’ Balanced Residual Effects Designs
9.5 Other Balanced Residual Effects Designs
9.6 Combinatorially Overall Balanced Residual Effects Designs
9.7 Construction of Treatment Balanced Residual Effects Designs
9.8 Some Construction of PBCOD (m)
9.9 Construction of Complete Set of Mols and Patterson’s Bred
9.10 Balanced Circular Arrangements
9.11 CONCLUDING REMARKS
References
Further Reading
Index
Eula
List of Tables
Chapter 01
Table 1.4.1 Artificial data for profile analysis
Table 1.6.1 A Latin square design for four treatments
Table 1.6.2 CODWOR for four treatments
Table 1.6.3 F-square design with v = 3 and n = 6
Table 1.6.4 Youden square design with v = 7, k = 3, and λ = 1
Table 1.8.1 GRED for seven treatments
Chapter 02
Table 2.3.1 Univariate ANOVA for one-sample RMD
Table 2.6.1 Artificial data of test scores
Table 2.8.1 Systolic and diastolic BP for three treatments
Table 2.9.1 Performance of students in three tests
Chapter 03
Table 3.3.1 k-Sample RMD ANOVA
Table 3.4.1 ANOVA for testing groups in a k-sample RMD
Table 3.5.1 Artificial data of ABS scores
Table 3.7.1 Data of Table 3.5.1 with ordered categorical response
Table 3.7.2 Marginal estimated probabilities for the data of Table 3.7.1
Chapter 04
Table 4.2.1 Artificial data of exercise time (
X
) and weight loss (
Y
)
Table 4.2.2 Comparison of the parameter for the three models
Table 4.3.1 Average class GPA based on teaching method and instructor
Table 4.6.1 Artificial data on change of A1C
Table 4.6.2 Artificial data on weight loss
Table 4.7.1 Artificial data on the percentage reduction of diastolic BP
Chapter 05
Table 5.1.1 Design for v = b = k = 4
Table 5.1.2 Design for v = b = 7, k = 3
Table 5.2.1 Anova table for CODWOR
Table 5.5.1 Anova table of a Latin square design
Table 5.6.1 Anova table of a Youden square design
Table 5.10.1 Gas mileage on cars with gas additives
Table 5.11.1 Gas mileage with gas additives
Table 5.11.2 Anova table for a pair of orthogonal Latin squares
Chapter 06
Table 6.2.1 ANOVA for GRED-I
Table 6.3.1 ANOVA table for BREDs of Williams
Table 6.5.1 Apples sale data using a three-period BRED
Chapter 07
Table 7.2.1 R for selected S1/S0 and σu2/σ2
Table 7.4.1 ANOVA for Balaam’s design
Table 7.5.1 Artificial data on cholesterol change
Table 7.5.2 Artificial data on coffee brand elevation
Chapter 08
Table 8.3.1 ANOVA table with residual effects proportional to direct effects for Williams’ design
Table 8.8.1 Skeleton ANOVA
Table 8.9.1 ANOVA table for circular residual effects design
Table 8.10.1 Artificial data on exercise time, medication, and run times
Table 8.10.2 Artificial data of a testing experiment
Chapter 09
Table 9.2.1 Addition table with s = 5
Table 9.2.2 Multiplication table with s = 5
Table 9.2.3 Some minimal functions
List of Illustrations
Chapter 01
Figure 1.3.1 Parallel profiles.
Figure 1.3.2 Intersecting nonparallel profiles.
Figure 1.3.3 Nonparallel profiles with different slopes.
Figure 1.4.1 Split-plot layout.
Guide
Cover
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