Adaptive tests of significance using permutations of residuals with R and SAS /
"This book concerns adaptive tests of significance, which are statistical tests that use the data to modify the test procedures. The modification is used to reduce the influence of outliers. These adaptive tests are attractive because they are often more powerful than traditional tests, and the...
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Hoboken, N.J. :
Wiley,
2012.
|
| Subjects: | |
| Online Access: | CONNECT |
Table of Contents:
- 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 Randles; 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 Test1.6 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 Percentiles2.3.2 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 Errors in Adaptive Weighting; 2.6.3 Simulation Studies; 2.7 Examples of Transformed Data.
- Exercises3 A Two-Sample Adaptive Test; 3.1 A Two-Sample Model; 3.2 Computing the Adaptive Weights; 3.2.1 R Code for Computing the Weights; 3.3 The Test Statistics for Adaptive Tests; 3.3.1 R Code to Compute the Test Statistic; 3.4 Permutation Methods for Two-Sample Tests; 3.4.1 Permutation of Observations; 3.4.2 Permutation of Residuals; 3.4.3 R Code for Permutations; 3.5 An Example of a Two-Sample Test; 3.6 R Code for the Two-Sample Test; 3.6.1 R Code for Computing the Test Statistics; 3.6.2 R Code to Compute the Traditional F Test Statistic and p-Value.
- 3.6.3 An R Function that Computes the p-Value for the Adaptive Test3.6.4 R Code to Perform the Adaptive Test; 3.7 Level of Significance of the Adaptive Test; 3.8 Power of the Adaptive Test; 3.9 Sample Size Estimation; 3.10 A SAS Macro for the Adaptive Test; 3.11 Modifications for One-Tailed Tests; 3.12 Justification of the Weighting Method; 3.13 Comments on the Adaptive Two-sample Test; Exercises; 4 Permutation Tests with Linear Models; 4.1 Introduction; 4.2 Notation; 4.3 Permutations with Blocking; 4.4 Linear Models in Matrix Form; 4.5 Permutation Methods; 4.5.1 The Permute-Errors Method.
