Adaptive Tests of Significance Using Permutations of Residuals with R and SAS

CONTENTS

Preface

1 Introduction

1.1 Why Use Adaptive Tests?

1.2 A Brief History of Adaptive Tests

1.2.1 Early Tests and Estimators

1.2.2 Rank Tests

1.2.3 The Weighted Least Squares Approach

1.2.4 Recent Rank-Based Tests

1.3 The Adaptive Test of Hogg, Fisher, and Randies

1.3.1 Level of Significance of the HFR Test

1.3.2 Comparison of Power of the HFR Test to the t Test

1.4 Limitations of Rank-Based Tests

1.5 The Adaptive Weighted Least Squares Approach

1.5.1 Level of Significance

1.5.2 Comparison of Power of the Adaptive WLS Test to the t Test and the HFR Test

1.6 Development of the Adaptive WLS Test

2 Smoothing Methods and Normalizing Transformations

2.1 Traditional Estimators of the Median and the Interquartile Range

2.2 Percentile Estimators that Use the Smooth Cumulative Distribution Function

2.2.1 Smoothing the Cumulative Distribution Function

2.2.2 Using the Smoothed c.d.f. to Compute Percentiles

2.2.3 R Code for Smoothing the c.d.f.

2.2.4 R Code for Finding Percentiles

2.3 Estimating the Bandwidth

2.3.1 An Estimator of Variability Based on Traditional Percentiles

2.3.2 R Code for Finding the Bandwidth

2.3.3 An Estimator of Variability Based on Percentiles from the Smoothed Distribution Function

2.4 Normalizing Transformations

2.4.1 Traditional Normalizing Methods

2.4.2 Normalizing Data by Weighting

2.5 The Weighting Algorithm

2.5.1 An Example of the Weighing Procedure

2.5.2 R Code for Weighting the Observations

2.6 Computing the Bandwidth

2.6.1 Error Distributions

2.6.2 Measuring ...