Permutation Tests for Complex Data

Fortunato Pesarin, Department of Statistics, University of Padova, Italy Professor Pesarin has been actively involved in the areas of multidimensional testing and permutation for almost 40 years, and is the author of dozens of publications in numerous international journals. Luigi Salmaso, Department of Management and Engineering, University of Padova, Italy Within the last 10 years, Dr Salmaso has amassed a large number of published articles, in a variety of journals, and has taught a number of courses in statsistics and nonparametric methods.

Contents Preface

Notation and Abbreviations

1 Introduction

1.1 On Permutation Analysis

1.2 The Permutation Testing Principle

1.3 Permutation Approaches

1.4 When and Why Conditioning Is Appropriate

1.5 Randomization and Permutation

1.6 Computational Aspects

1.7 Basic Notation

1.8 A Problem with Paired Observations

1.9 The Permutation Solution

1.10 A Two-Sample Problem

1.11 One-Way ANOVA

2 Theory of One-Dimensional Permutation Tests

2.1 Introduction

2.2 Definition of Permutation Tests

2.3 Some Useful Test Statistics

2.4 Equivalence of Permutation Statistics

2.5 Arguments for Selecting Permutation Tests

2.6 Examples of One-Sample Problems

2.7 Examples of Multi-sample Problems

2.8 Analysis of Ordered Categorical Variables

2.9 Problems and Exercises

3 Further Properties of Permutation Tests

3.1 Unbiasedness of Two-sample Tests

3.2 Power Functions of Permutation Tests

3.3 Consistency of Permutation Tests

3.4 Permutation Confidence Interval for δ

3.5 Extending Inference from Conditional to Unconditional

3.6 Optimal Properties

3.7 Some Asymptotic Properties

3.8 Permutation Central Limit Theorems

3.9 Problems and Exercises

4 The Nonparametric Combination Methodology

4.1 Introduction

4.2 The Nonparametric Combination Methodology

4.3 Consistency, Unbiasedness and Power of Combined Tests

4.4 Some Further Asymptotic Properties

4.5 Finite-Sample Consistency

4.6 Some Examples of Nonparametric Combination

4.7 Comments on the Nonparametric Combination

5 Multiple Testing Problems and Multiplicity Adjustment

5.1 Defining Raw and Adjusted p-Values

5.2 Controlling for Multiplicity

5.3 Multiple Testing

5.4 The Closed Testing Approach  

5.5 Mult Data Example

5.6 Washing Test Data

5.7 Weighted Methods for Controlling FWE and FDR

5.8 Adjusting Stepwise p-Values

6 Analysis of Multivariate Categorical Variables

6.1 Introduction

6.2 The Multivariate McNemar Test

6.3 Multivariate Goodness-of-Fit Testing for Ordered Variables

6.4 MANOVA with Nominal Categorical Data

6.5 Stochastic Ordering

6.6 Multifocus Analysis

6.7 Isotonic Inference

6.8 Test on Moments for Ordered Variables

6.9 Heterogeneity Comparisons

6.10 Application to PhD Programme Evaluation Using SAS

7 Permutation Testing for Repeated Measurements

7.1 Introduction

7.2 Carry-Over Effects in Repeated Measures Designs

7.3 Modelling Repeated Measurements

7.4 Testing Solutions

7.5 Testing for Repeated Measurements with Missing Data

7.6 General Aspects of Permutation Testing with Missing Data

7.7 On Missing Data Processes

7.8 The Permutation Approach

7.9 The Structure of Testing Problems

7.10 Permutation Analysis of Missing Values

7.11 Germina Data: An Example of an MNAR Model

7.12 Multivariate Paired Observations

7.13 Repeated Measures and Missing Data

7.14 Botulinum Data

7.15 Waterfalls Data

8 Some Stochastic Ordering Problems

8.1 Multivariate Ordered Alternatives

8.2 Testing for Umbrella Alternatives

8.3 Analysis of Experimental Tumour Growth Curves

8.4 Analysis of PERC Data

9 NPC Tests for Survival Analysis

9.1 Introduction and Main Notation

9.2 Comparison of Survival Curves

9.3 An Overview of the Literature

9.4 Two NPC Tests

9.5 An Application to a Biomedical Study

10 NPC Tests in Shape Analysis

10.1 Introduction

10.2 A Brief Overview of Statistical Shape Analysis

10.3 Inference with Shape Data

10.4 NPC Approach to Shape Analysis

10.5 NPC Analysis with Correlated Landmarks

10.6 An Application to Mediterranean Monk Seal Skulls

11 Multivariate Correlation Analysis and Two-Way ANOVA

11.1 Autofluorescence Case Study

11.2 Confocal Case Study

11.3 Two-Way (M)ANOVA

12 Some Case Studies Using NPC Test R. 10 and SAS Macros

12.1 An Integrated Approach to Survival Analysis in Observational Studies

12.2 Integrating Propensity Score and NPC Testing

12.3 Further Applications with NPC Test R. 10 and SAS Macros

12.4 A Comparison of Three Survival Curves

12.5 Survival Analysis Using NPC Test and SAS

12.6 Logistic Regression and NPC Test for Multivariate Analysis

References

Index