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CONTENTS CHAPTER 1 Introduction to experimental design 1.1. The experimental process 1.2 Computers and experimental design 1.3 Overview of experimental design and interpretation. CHAPTER 2 Comparison of mean values 2.1 Introduction 2.2 Comparison of means when the variance of the whole population is known 2.3 Comparison of two means when the variance of the whole population is not known 2.3.1 Treatment of outlying data points 2.4 Comparison of means among more than two groups of data 2.4.1 Analysis of variance 2.4.2 The least significant difference 2.4.3 Two-way analysis of variance CHAPTER 3 Non-parametric methods 3.1 Introduction 3.2 Non-parametric tests for paired data 3.2.1 The sign test 3.2.2 The Wilcoxon signed rank test 3.3 Non-parametric tests for unpaired data 3.3.1 The Wilcoxon two-sample test Chapter 4 Regression and correlation 4.1 Introduction 4.2 Linear regression 4.2.1 The number of degrees of freedom (Cell B11 in Table 4.4) 4.2.2 The coefficient of determination (r2) (Cell A10 in Table 4.4). 4.2.3 The standard errors of the coefficients (Cells A9 and B9 in Table 4.4) 4.2.4 The F value or variance ratio (Cell A11 in Table 4.4). 4.2 5 The two regression lines 4.3 Curve fitting of non-linear relationships 4.3.1 The power series 4.3.2 Quadratic relationships 4.3.3 Cubic equations 4.3.4 Transformations 4.4 Multiple regression analysis 4.4.1 Correlation coefficients 4.4.2 Standard error of the coefficients and the intercept 4.4.3 F value 4.5 Interaction between independent variables 4.6 Stepwise regression 4.7. Rank correlation 4.8. Comments on the correlation coefficient Chapter 5 Multivariate methods 5.1 Introduction 5.2 Multivariate distances 5.2.1 Distance matrices 5.3 Covariance matrices 5.4 Correlation matrices 5.5 Cluster analysis 5.5.1 Cartesian plots 5.5.2 Dendrograms 5.6 Discrimination analysis 5.7 Principal components analysis 5.8 Factor analysis CHAPTER 6 Factorial design of experiments 6.1 Introduction 6.2 Two factor, two level factorial designs 6.2.1 Two factor, two level factorial designs with interaction between the factors 6.3 Notation in factorially designed experiments 6.4 Factorial designs with three factors and two levels 6.5 Factorial design and analysis of variance 6.5.1 Yates's treatment 6.5.2 Factorial design and linear regression 6.6 Replication in factorial designs 6.7 The sequence of experiments 6.8 Factorial designs with three levels 6.9. Three factor, three level factorial designs 6.9.1 Mixed or asymmetric designs 6.10 Blocked factorial designs 6.11 Fractional factorial designs 6.12 Plackett-Burman designs 6.13 Central composite designs 6.14 Box-Behnken designs 6.15 Doehlert designs 6.16 The efficiency of experimental designs CHAPTER 7 Response surface methodology 7.1 Introduction 7.2 Constraints, boundaries and the experimental domain 7.3 Response surfaces generated from first order models 7.4 Response surfaces generated by models of a higher order 7.5 Response surface methodology with three or more factors Chapter 8 Model-dependent optimisation 8.1 Introduction 8.2 Model-dependent optimisation 8.2.1 Extension of the design space 8.3 Optimisation by combining contour plots 8.4. Location of the optimum of multiple responses by the desirability function 8.5 Optimisation using Pareto-optimality CHAPTER 9 Sequential methods and model-independent optimisation 9.1 Introduction 9.2. Sequential analysis 9.2.1. Wald diagrams 9.3. Model-independent optimisation 9.3.1. Optimisation by simplex search 9.4. Comparison of model-independent and model-dependent methods. CHAPTER 10 Experimental designs for mixtures. 10.1 Introduction 10.2 Three component systems and ternary diagrams 10.3 Mixtures with more than three components 10.4 Response surface methodology in experiments with mixtures 10.4.1 Rectilinear relationships between composition and response 10.4.2 Derivation of contour plots from rectilinear models 10.4.3 Higher order relationships between composition and response 10.4.4 Contour plots derived from higher order equations 10.5 The optimisation of mixtures 10.6 Pareto-optimality and mixtures 10 7 Process variables in mixture experiments Chapter 11 Artificial neural networks and experimental design 11.1. Introduction 11.2 Pharmaceutical applications of artificial neural networks Appendices Appendix 1 Statistical tables Appendix 1.1 The cumulative normal distribution (Gaussian distribution) Appendix 1.2 Student's t distribution Appendix 1.3 Analysis of variance Appendix 2 Matrices A2.1 Introduction A2.2 Addition and subtraction of matrices A2.3 Multiplication of matrices A2.3.1 Multiplying a matrix by a constant A2.3.2 Multiplication of one matrix by another A2.3.3 Multiplication by a unit matrix A2.3.4 Multiplication by a null matrix A2.3.5 Transposition of matrices A2.3.6 Inversion of matrices A2.4 Determinants
Library of Congress Subject Headings for this publication:
Drugs -- Research -- Methodology.
Data Interpretation, Statistical.