Preface Part One: Introduction 1 Introduction Examples Notation 1.1 Review of Objectives and different approaches 1.2 Some general comments 1.3 Review of books on multivariate analysis 1.4 Some matrix algebra revision 1.5 The general linear model Exercises 2 Multivariate distributions 2.1 Multivariate, marginal and conditional distributions 2.2 Means, variances, covariances and correlations 2.

3 The multivariate normal distribution 2.4 The bivariate normal distribution 2.5 Other multivariate distributions 2.5.1 Multivariate discrete distributions 2.5.2 Multivariate continuous distributions Exercises 3. Preliminary data analysis 3.

1 Processing the data 3.1.1 Data editing 3.2 Calculating summary statistics 3.2.1 Interpreting the sample correlation matrix 3.2.2 The rank of R 3.

3 Plotting the data 3.4 The analysis of discrete data Exercises Part Two: Finding New Underlying Variables 4. Principal component analysis 4.1 Introduction 4.2 Derivation of principal components 4.3.1 Principal components from the correlation matrix 4.2.

2 Estimating the principal components 4.3 Further results on PCA 4.3.1 Mean-corrected component scores 4.3.2 The inverse transformation 4.3.3 Zero eigenvalues 4.

3.4 Small eigenvalues 4.3.5 Repeated roots 4.3.6 Orthogonality 4.3.7 Component loadings/component correlations 4.

3.8 Off-diagonal structure 4.3.9 Uncorrelated variables 4.4 The problem of scaling in PCA 4.5 Discussion 4.5.1 The identification of important components 4.

5.2 The use of components in subsequent analyses 4.6 PCA for multivariate normal data 4.7 Summary Exercises 5. Factor analysis 5.1 Introduction 5.2 The factor-analysis model 5.3 Estimating the factor loadings 5.

4 Discussion Part Three: Procedures Based on the Multivariate Normal Distribution 6. The multivariate normal distribution 6.1 Introduction 6.2 Definition of the multivariate normal distribution 6.3 Properties of the multivariate normal distribution 6.4 Linear compounds and linear combinations 6.5 Estimation of the parameters of the distribution 6.6 The Wishart distribution 6.

7 The joint distribution of the sample mean vector and the sample covariance matrix 6.8 The Hotelling T²-distribution Exercises 7. Procedures based on normal distribution theory 7.1 Introduction 7.2 One-sample procedures 7.3 Confidence intervals and further analysis 7.4 Tests of structural relations among the components of the mean 7.5 Two-sample procedures 7.

6 Confidence intervals and further analysis 7.7 Tests of structural relations among the components of the means 7.8 Discriminant analysis Exercises 8. The multivariate analysis of variance 8.1 Introduction 8.2 MANOVA calculations 8.3 Testing hypotheses 8.3.

1 The special case: The univariate procedure 8.3.2 The multivariate model for Example 8.1 8.3.3 Multivariate test procedure 8.3.4 Distributional approximations 8.

3.5 Applications of the methodology 8.4 Further analysis 8.5 The dimensionality of the alternative hypothesis 8.6 Canonical variates analysis 8.7 Linear functional relationships 8.8 Discriminant analysis Exercises 9. The multivariate analysis of covariance and related topics 9.

1 Introduction 9.2 Multivariate regression 9.2.1 The special case: Univariate multiple regression 9.2.2 The general case: Multivariate regression 9.3 Canonical correlation 9.4 The multivariate analysis of covariance 9.

4.1 The special case: Univariate analysis of covariance 9.4.2 The multivariate case: An example 9.4.3 The multivariate case: General results 9.5 The test for additional information 9.6 A test of an assigned subset of linear compounds Exercises Part Four: Multidimensional Scaling and Cluster Analysis 10.

Multidimensional scaling 10.1 Introduction 10.2 Measures of similarity and dissimilarity 10.2.1 Similarity coefficients for binary data 10.3 Classical scaling 10.3.1 The calculation of co-ordinate values from Euclidean distances 10.

3.2 The relationship between classical scaling and principal component analysis 10.3.3 Classical scaling for a dissimilarity matrix 10.3.4 Interpretation of the results 10.3.5 Some related methods 10.

4 Ordinal scaling 10.4.1 The iterative procedure 10.4.2 Interpreting the results 10.5 A comparison 10.6 Concluding remarks Exercises 11 Cluster analysis 11.1 Introduction 11.

1.1 Objectives 11.1.2 Clumping, dissection and clustering variables 11.1.3 Some other preliminary points 11.2 Visual approaches to finding a partition 11.3 Hierarchical trees 11.

4 Single-link clustering 11.5 Some other clustering procedures 11.5.1 Method or algorithm? 11.6 A comparison of procedures 11.6.1 Some desirable conditions for hierarchical clustering methods 11.6.

2 A comparison Exercises References Answers to exercises Name Index Subject Index.