Permutation Tests for Complex Data : Theory, Applications and Software

by Fortunato Pesarin (University of Padova, Italy); Luigi Salmaso (University of Padova)

• ISBN13: 9780470689523
• ISBN10: 0470689528
• Format: eBook
• Copyright: 2010-02-01
• Publisher: Wiley

Summary

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.

Table of Contents

Preface

Notation and Abbreviations

Introduction

On Permutation Analysis

The Permutation Testing Principle

Permutation Approaches

When and Why Conditioning Is Appropriate

Randomization and Permutation

Computational Aspects

Basic Notation

A Problem with Paired Observations

The Permutation Solution

A Two-Sample Problem

One-Way ANOVA

Theory of One-Dimensional Permutation Tests

Introduction

Definition of Permutation Tests

Some Useful Test Statistics

Equivalence of Permutation Statistics

Arguments for Selecting Permutation Tests

Examples of One-Sample Problems

Examples of Multi-sample Problems

Analysis of Ordered Categorical Variables

Problems and Exercises

Further Properties of Permutation Tests

Unbiasedness of Two-sample Tests

Power Functions of Permutation Tests

Consistency of Permutation Tests

Permutation Confidence Interval for ¿

Extending Inference from Conditional to Unconditional

Optimal Properties

Some Asymptotic Properties

Permutation Central Limit Theorems

Problems and Exercises

The Nonparametric Combination Methodology

Introduction

The Nonparametric Combination Methodology

Consistency, Unbiasedness and Power of Combined Tests

Some Further Asymptotic Properties

Finite-Sample Consistency

Some Examples of Nonparametric Combination

Comments on the Nonparametric Combination

Multiple Testing Problems and Multiplicity Adjustment

Defining Raw and Adjusted p -Values

Controlling for Multiplicity

Multiple Testing

The Closed Testing Approach

Mult Data Example

Washing Test Data

Weighted Methods for Controlling FWE and FDR

Adjusting Stepwise p -Values

Analysis of Multivariate Categorical Variables

Introduction

The Multivariate McNemar Test

Multivariate Goodness-of-Fit Testing for Ordered Variables

MANOVA with Nominal Categorical Data

Stochastic Ordering

Multifocus Analysis

Isotonic Inference

Test on Moments for Ordered Variables

Heterogeneity Comparisons

Application to PhD Programme Evaluation Using SAS

Permutation Testing for Repeated Measurements

Introduction

Carry-Over Effects in Repeated Measures Designs

Modelling Repeated Measurements

Testing Solutions

Testing for Repeated Measurements with Missing Data

General Aspects of Permutation Testing with Missing Data

On Missing Data Processes

The Permutation Approach

The Structure of Testing Problems

Permutation Analysis of Missing Values

Germina Data: An Example of an MNAR Model

Multivariate Paired Observations

Repeated Measures and Missing Data

Botulinum Data

Waterfalls Data

Some Stochastic Ordering Problems

Multivariate Ordered Alternatives

Testing for Umbrella Alternatives

Analysis of Experimental Tumour Growth Curves

Analysis of PERC Data

NPC Tests for Survival Analysis

Introduction and Main Notation

Comparison of Survival Curves

An Overview of the Literature

Two NPC Tests

An Application to a Biomedical Study

NPC Tests in Shape Analysis

Introduction

A Brief Overview of Statistical Shape Analysis

Inference with Shape Data

NPC Approach to Shape Analysis

NPC Analysis with Correlated Landmarks

An Application to Mediterranean Monk Seal Skulls

Multivariate Correlation Analysis and Two-Way ANOVA

Autofluorescence Case Study

Confocal Case Study

Two-Way (M)ANOVA

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

An Integrated Approach to Survival Analysis in Observational Studies

Integrating Propensity Score and NPC Testing

Further Applications with NPC Test R. 10 and SAS Macros

A Comparison of Three Survival Curves

Survival Analysis Using NPC Test and SAS

Logistic Regression and NPC Test for Multivariate Analysis

References

Index

Table of Contents provided by Publisher. All Rights Reserved.