Statistical Analysis of Designed Experiments

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Edition: 2nd
Format: Hardcover
Pub. Date: 2002-10-01
Publisher(s): Springer Verlag
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Summary

This textbook presents the design and analysis of experiments that comprises the aspects of classical theory for continuous response and of modern procedures for categorical response, and especially for correlated categorical response. For any design (independent response and matched pair response) the parametric and nonparametric tests depending on the data level are given. Complex designs, as for example, crossover and repeated measures, are included at an introductory and advanced level. The problem of missing data is discussed and the author proposes procedures for approaching this problem. This volume will be an important reference book for graduate students, university teachers, and for statistical researchers in the pharmaceutical industry and clinical research in medicine and dentistry, as well as in many other applied areas. This second edition contains more examples and graphical illustrations. Chapter 3, ¿The Linear Regression Model,¿ now contains several diagnostic tools and more examples. Chapter 7, "Categorical Response Variables," was completely rewritten. The proofs of the more theoretical Chapters 3 and 4 were moved to an appendix. More emphasis has been placed on explaining and justifying some approaches. Helge Toutenburg is Professor of Statistics at the University of Munich. He has written seventeen books on linear models, statistical methods in quality engineering, and the analysis of designed experiments. He works on applications of statistics to the fields of medicine and engineering.

Author Biography

Helge Toutenburg is a professor of statistics at the University of Munich.

Table of Contents

Preface v
Introduction
1(20)
Data, Variables, and Random Processes
1(2)
Basic Principles of Experimental Design
3(2)
Scaling of Variables
5(2)
Measuring and Scaling in Statistical Medicine
7(1)
Experimental Design in Biotechnology
8(1)
Relative Importance of Effects-The Pareto Principle
9(1)
An Alternative Chart
10(5)
A One--Way Factorial Experiment by Example
15(4)
Exercises and Questions
19(2)
Comparison of Two Samples
21(24)
Introduction
21(1)
Paired t-Test and Matched-Pair Design
22(3)
Comparison of Means in Independent Groups
25(4)
Two-Sample t-Test
25(1)
Testing H0 : σ2A = σ2B = σ2
25(1)
Comparison of Means in the Case of Unequal Variances
26(1)
Transformations of Data to Assure Homogeneity of Variances
27(1)
Necessary Sample Size and Power of the Test
27(1)
Comparison of Means without Prior Testing H0 : σ2A = σ2B; Cochran-Cox Test for Independent Groups
27(2)
Wilcoxon's Sign-Rank Test in the Matched-Pair Design
29(4)
Rank Test for Homogeneity of Wilcoxon, Mann and Whitney
33(5)
Comparison of Two Groups with Categorical Response
38(3)
McNemar's Test and Matched-Pair Design
38(1)
Fisher's Exact Test for Two Independent Groups
39(2)
Exercises and Questions
41(4)
The Linear Regression Model
45(66)
Descriptive Linear Regression
45(2)
The Principle of Ordinary Least Squares
47(3)
Geometric Properties of Ordinary Least Squares Estimation
50(1)
Best Linear Unbiased Estimation
51(9)
Linear Estimators
52(1)
Mean Square Error
53(2)
Best Linear Unbiased Estimation
55(2)
Estimation of σ2
57(3)
Multicollinearity
60(7)
Extreme Multicollinearity and Estimability
60(1)
Estimation within Extreme Multicollinearity
61(2)
Weak Multicollinearity
63(4)
Classical Regression under Normal Errors
67(2)
Testing Linear Hypotheses
69(4)
Analysis of Variance and Goodness of Fit
73(10)
Bivariate Regression
73(6)
Multiple Regression
79(4)
The General Linear Regression Model
83(3)
Introduction
83(2)
Misspecification of the Covariance Matrix
85(1)
Diagnostic Tools
86(24)
Introduction
86(1)
Prediction Matrix
86(5)
Effect of a Single Observation on the Estimation of Parameters
91(5)
Diagnostic Plots for Testing the Model Assumptions
96(1)
Measures Based on the Confidence Ellipsoid
97(5)
Partial Regression Plots
102(2)
Regression Diagnostics by Animating Graphics
104(6)
Exercises and Questions
110(1)
Single-Factor Experiments with Fixed and Random Effects
111(46)
Models I and II in the Analysis of Variance
111(1)
One-Way Classification for the Multiple Comparison of Means
112(11)
Representation as a Restrictive Model
115(2)
Decomposition of the Error Sum of Squares
117(3)
Estimation of σ2 by M SError
120(3)
Comparison of Single Means
123(9)
Linear Contrasts
123(3)
Contrasts of the Total Response Values in the Balanced Case
126(6)
Multiple Comparisons
132(10)
Introduction
132(1)
Experimentwise Comparisons
132(3)
Select Pairwise Comparisons
135(7)
Regression Analysis of Variance
142(3)
One-Factorial Models with Random Effects
145(4)
Rank Analysis of Variance in the Completely Randomized Design
149(5)
Kruskal-Wallis Test
149(3)
Multiple Comparisons
152(2)
Exercises and Questions
154(3)
More Restrictive Designs
157(22)
Randomized Block Design
157(8)
Latin Squares
165(7)
Analysis of Variance
167(5)
Rank Variance Analysis in the Randomized Block Design
172(4)
Friedman Test
172(3)
Multiple Comparisons
175(1)
Exercises and Questions
176(3)
Multifactor Experiments
179(52)
Elementary Definitions and Principles
179(4)
Two-Factor Experiments (Fixed Effects)
183(5)
Two-Factor Experiments in Effect Coding
188(8)
Two-Factorial Experiment with Block Effects
196(3)
Two-Factorial Model with Fixed Effects-Confidence Intervals and Elementary Tests
199(4)
Two-Factorial Model with Random or Mixed Effects
203(8)
Model with Random Effects
203(4)
Mixed Model
207(4)
Three-Factorial Designs
211(4)
Split-Plot Design
215(4)
2k Factorial Design
219(6)
The 22 Design
219(3)
The 23 Design
222(3)
Exercises and Questions
225(6)
Models for Categorical Response Variables
231(64)
Generalized Linear Models
231(14)
Extension of the Regression Model
231(2)
Structure of the Generalized Linear Model
233(3)
Score Function and Information Matrix
236(1)
Maximum Likelihood Estimation
237(3)
Testing of Hypotheses and Goodness of Fit
240(1)
Overdispersion
241(2)
Quasi Loglikelihood
243(2)
Contingency Tables
245(9)
Overview
245(1)
Ways of Comparing Proportions
246(3)
Sampling in Two-Way Contingency Tables
249(1)
Likelihood Function and Maximum Likelihood Estimates
250(2)
Testing the Goodness of Fit
252(2)
Generalized Linear Model for Binary Response
254(4)
Logit Models and Logistic Regression
254(3)
Testing the Model
257(1)
Distribution Function as a Link Function
258(1)
Logit Models for Categorical Data
258(2)
Goodness of Fit-Likelihood Ratio Test
260(1)
Loglinear Models for Categorical Variables
261(6)
Two-Way Contingency Tables
261(3)
Three-Way Contingency Tables
264(3)
The Special Case of Binary Response
267(3)
Coding of Categorical Explanatory Variables
270(7)
Dummy and Effect Coding
270(3)
Coding of Response Models
273(1)
Coding of Models for the Hazard Rate
274(3)
Extensions to Dependent Binary Variables
277(17)
Overview
277(2)
Modeling Approaches for Correlated Response
279(1)
Quasi-Likelihood Approach for Correlated Binary Response
280(1)
The Generalized Estimating Equation Method by Liang and Zeger
281(2)
Properties of the Generalized Estimating Equation Estimate βG
283(1)
Efficiency of the Generalized Estimating Equation and Independence Estimating Equation Methods
284(1)
Choice of the Quasi-Correlation Matrix Ri(α)
285(1)
Bivariate Binary Correlated Response Variables
285(1)
The Generalized Estimating Equation Method
286(2)
The Independence Estimating Equation Method
288(1)
An Example from the Field of Dentistry
288(5)
Full Likelihood Approach for Marginal Models
293(1)
Exercises and Questions
294(1)
Repeated Measures Model
295(46)
The Fundamental Model for One Population
295(3)
The Repeated Measures Model for Two Populations
298(3)
Univariate and Multivariate Analysis
301(5)
The Univariate One-Sample Case
301(1)
The Multivariate One-Sample Case
301(5)
The Univariate Two-Sample Case
306(1)
The Multivariate Two-Sample Case
307(1)
Testing of H0 : Σx = Σy
308(1)
Univariate Analysis of Variance in the Repeated Measures Model
309(15)
Testing of Hypotheses in the Case of Compound Symmetry
309(2)
Testing of Hypotheses in the Case of Sphericity
311(4)
The Problem of Nonsphericity
315(1)
Application of Univariate Modified Approaches in the Case of Nonsphericity
316(1)
Multiple Tests
317(1)
Examples
318(6)
Multivariate Rank Tests in the Repeated Measures Model
324(5)
Categorical Regression for the Repeated Binary Response Data
329(10)
Logit Models for the Repeated Binary Response for the Comparison of Therapies
329(1)
First-Order Markov Chain Models
330(2)
Multinomial Sampling and Loglinear Models for a Global Comparison of Therapies
332(7)
Exercises and Questions
339(2)
Cross-Over Design
341(44)
Introduction
341(1)
Linear Model and Notations
342(1)
2 x 2 Cross-Over (Classical Approach)
343(25)
Analysis Using t-Tests
344(4)
Analysis of Variance
348(4)
Residual Analysis and Plotting the Data
352(4)
Alternative Parametrizations in 2 x 2 Cross-Over
356(12)
Cross-Over Analysis Using Rank Tests
368(1)
2 x 2 Cross-Over and Categorical (Binary) Response
368(16)
Introduction
368(4)
Loglinear and Logit Models
372(12)
Exercises and Questions
384(1)
Statistical Analysis of Incomplete Data
385(30)
Introduction
385(5)
Missing Data in the Response
390(3)
Least Squares Analysis for Complete Data
390(1)
Least Squares Analysis for Filled-Up Data
391(1)
Analysis of Covariance-Bartlett's Method
392(1)
Missing Values in the X-Matrix
393(7)
Missing Values and Loss of Efficiency
394(3)
Standard Methods for Incomplete X-Matrices
397(3)
Adjusting for Missing Data in 2 x 2 Cross-Over Designs
400(7)
Notation
400(2)
Maximum Likelihood Estimator (Rao, 1956)
402(1)
Test Procedures
403(4)
Missing Categorical Data
407(5)
Introduction
407(1)
Maximum Likelihood Estimation in the Complete Data Case
408(1)
Ad-Hoc Methods
409(1)
Model-Based Methods
410(2)
Exercises and Questions
412(3)
A Matrix Algebra 415(38)
Introduction
415(3)
Trace of a Matrix
418(1)
Determinant of a Matrix
418(2)
Inverse of a Matrix
420(1)
Orthogonal Matrices
421(1)
Rank of a Matrix
422(1)
Range and Null Space
422(1)
Eigenvalues and Eigenvectors
423(2)
Decomposition of Matrices
425(2)
Definite Matrices and Quadratic Forms
427(6)
Idempotent Matrices
433(1)
Generalized Inverse
434(8)
Projections
442(1)
Functions of Normally Distributed Variables
443(3)
Differentiation of Scalar Functions of Matrices
446(3)
Miscellaneous Results, Stochastic Convergence
449(4)
B Theoretical Proofs 453(26)
The Linear Regression Model
453(22)
Single-Factor Experiments with Fixed and Random Effects
475(4)
C Distributions and Tables 479(8)
References 487(10)
Index 497

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