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Contents
Preface
vii
Symbols
xi
Chapter 1. Introduction
1
1.1 On combinatorial inference
1
1.2 On Geometric Data Analysis
4
1.3 On Inductive Data Analysis
5
1.4 Compatational Aspects
6
Chapter 2. Cloud of Points in a Geometric Space
9
2.1 Basic Statistics
10
2.2 Covariance Structure of a Cloud
14
2.3 Mahalanobis Distance an Principal Ellipsoids
20
2.4 Partition of a Cloud
25
Chaper 3.Combinatorial Typicality Tests
29
3.1 The Typicality Problem
29
3.2 Combinatorial Typicality Test for Mean Point
32
3.3 One-dimensional Case: Typicality Test for Mean
45
3.4 Combinatorial Typicality Test for Variance
49
3.5 Combinatorial Inference in GDA
51
3.6 Computations with R and Coheris Spad Software
55
Chapter 4. Geometric Typicality Test
65
4.1 Principle of the Test
65
4.2 Geoemtric Tupicality Test for Mean Point
69
4.3 One-dimensional Case: Typicality for Mean
86
4.4 The case of a Design with Two Repeated Measures
90
4.5 Other Methods
92
4.6 Computations with R and Coheris Spad Software
97
Chapter 5. Homogeneity Permutation Tests
107
5.1 The Homogeneity Problem
107
5.2 Principle of Combinatorial Homogeneity Tests
108
5.3 Homogeneity of Independent Groups: General Case
109
5.4 Homogeneity of Two Independent Groups
116
5.4 The Case of a Repeated Measures Design
133
5.5 Other Methods
140
5.6 Computations with R and Coheris Spad Software
141
Chapter 6. Research Case Studies
153
6.1 The Parkinson Study
156
6.2 The Members of French Parliament and Globalisation
170
6.3 The European Central Bankers Study
188
6.4 Cognitive Tests and Education
200
Bibliography
245
Author Index
250
Subject Index
252