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# Permutation Tests for Complex Data: Theory, Applications and Software

ISBN: 978-0-470-51641-6 March 2010 448 Pages

## Description

Complex multivariate testing problems are frequently encountered in many scientific disciplines, such as engineering, medicine and the social sciences. As a result, modern statistics needs permutation testing for complex data with low sample size and many variables, especially in observational studies.

The Authors give a general overview on permutation tests with a focus on recent theoretical advances within univariate and multivariate complex permutation testing problems, this book brings the reader completely up to date with today’s current thinking.

Key Features:

• Examines the most up-to-date methodologies of univariate and multivariate permutation testing.
• Includes extensive software codes in MATLAB, R and SAS, featuring worked examples, and uses real case studies from both experimental and observational studies.
• Includes a standalone free software NPC Test Release 10 with a graphical interface which allows practitioners from every scientific field to easily implement almost all complex testing procedures included in the book.
• Presents and discusses solutions to the most important and frequently encountered real problems in multivariate analyses.
• A supplementary website containing all of the data sets examined in the book along with ready to use software codes.

Together with a wide set of application cases, the Authors present a thorough theory of permutation testing both with formal description and proofs, and analysing real case studies. Practitioners and researchers, working in different scientific fields such as engineering, biostatistics, psychology or medicine will benefit from this book.

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

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

 Permutation Tests for Complex Data (companion website)  Visit the companion website to learn more about the concepts discussed in this book.