Permutation Tests for Complex Data

Fortunato Pesarin, Department of Statistics, University of Padova, ItalyProfessor 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, ItalyWithin 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 PrefaceNotation and Abbreviations1 Introduction1.1 On Permutation Analysis1.2 The Permutation Testing Principle1.3 Permutation Approaches1.4 When and Why Conditioning Is Appropriate1.5 Randomization and Permutation1.6 Computational Aspects1.7 Basic Notation1.8 A Problem with Paired Observations1.9 The Permutation Solution1.10 A Two-Sample Problem1.11 One-Way ANOVA2 Theory of One-Dimensional Permutation Tests2.1 Introduction2.2 Definition of Permutation Tests2.3 Some Useful Test Statistics2.4 Equivalence of Permutation Statistics2.5 Arguments for Selecting Permutation Tests2.6 Examples of One-Sample Problems2.7 Examples of Multi-sample Problems2.8 Analysis of Ordered Categorical Variables2.9 Problems and Exercises3 Further Properties of Permutation Tests3.1 Unbiasedness of Two-sample Tests3.2 Power Functions of Permutation Tests3.3 Consistency of Permutation Tests3.4 Permutation Confidence Interval for δ3.5 Extending Inference from Conditional to Unconditional3.6 Optimal Properties3.7 Some Asymptotic Properties3.8 Permutation Central Limit Theorems3.9 Problems and Exercises4 The Nonparametric Combination Methodology4.1 Introduction4.2 The Nonparametric Combination Methodology4.3 Consistency, Unbiasedness and Power of Combined Tests4.4 Some Further Asymptotic Properties4.5 Finite-Sample Consistency4.6 Some Examples of Nonparametric Combination4.7 Comments on the Nonparametric Combination5 Multiple Testing Problems and Multiplicity Adjustment5.1 Defining Raw and Adjusted p-Values5.2 Controlling for Multiplicity5.3 Multiple Testing5.4 The Closed Testing Approach  5.5 Mult Data Example5.6 Washing Test Data5.7 Weighted Methods for Controlling FWE and FDR5.8 Adjusting Stepwise p-Values6 Analysis of Multivariate Categorical Variables6.1 Introduction6.2 The Multivariate McNemar Test6.3 Multivariate Goodness-of-Fit Testing for Ordered Variables6.4 MANOVA with Nominal Categorical Data6.5 Stochastic Ordering6.6 Multifocus Analysis6.7 Isotonic Inference6.8 Test on Moments for Ordered Variables6.9 Heterogeneity Comparisons6.10 Application to PhD Programme Evaluation Using SAS7 Permutation Testing for Repeated Measurements7.1 Introduction7.2 Carry-Over Effects in Repeated Measures Designs7.3 Modelling Repeated Measurements7.4 Testing Solutions7.5 Testing for Repeated Measurements with Missing Data7.6 General Aspects of Permutation Testing with Missing Data7.7 On Missing Data Processes7.8 The Permutation Approach7.9 The Structure of Testing Problems7.10 Permutation Analysis of Missing Values7.11 Germina Data: An Example of an MNAR Model7.12 Multivariate Paired Observations7.13 Repeated Measures and Missing Data7.14 Botulinum Data7.15 Waterfalls Data8 Some Stochastic Ordering Problems8.1 Multivariate Ordered Alternatives8.2 Testing for Umbrella Alternatives8.3 Analysis of Experimental Tumour Growth Curves8.4 Analysis of PERC Data9 NPC Tests for Survival Analysis9.1 Introduction and Main Notation9.2 Comparison of Survival Curves9.3 An Overview of the Literature9.4 Two NPC Tests9.5 An Application to a Biomedical Study10 NPC Tests in Shape Analysis10.1 Introduction10.2 A Brief Overview of Statistical Shape Analysis10.3 Inference with Shape Data10.4 NPC Approach to Shape Analysis10.5 NPC Analysis with Correlated Landmarks10.6 An Application to Mediterranean Monk Seal Skulls11 Multivariate Correlation Analysis and Two-Way ANOVA11.1 Autofluorescence Case Study11.2 Confocal Case Study11.3 Two-Way (M)ANOVA12 Some Case Studies Using NPC Test R. 10 and SAS Macros12.1 An Integrated Approach to Survival Analysis in Observational Studies12.2 Integrating Propensity Score and NPC Testing12.3 Further Applications with NPC Test R. 10 and SAS Macros12.4 A Comparison of Three Survival Curves12.5 Survival Analysis Using NPC Test and SAS12.6 Logistic Regression and NPC Test for Multivariate AnalysisReferencesIndex