PREFACE: DATA ANALYSIS BY RESAMPLING

PART I: RESAMPLING CONCEPTS

INTRODUCTION

CONCEPTS 1: TERMS AND NOTATION

Case, Attributes, Scores, and Treatments / Experimental and Observational Studies / Data Sets, Samples, and Populations / Parameters, Statistics, and Distributions / Distribution Functions

APPLICATIONS 1: CASES, ATTRIBUTES, AND DISTRIBUTIONS

Attributes, Scores, Groups, and Treatments / Distributions of Scores and Statistics / Exercises

CONCEPTS 2: POPULATIONS AND RANDOM SAMPLES

Varieties of Populations / Random Samples

APPLICATIONS 2: RANDOM SAMPLING

Simple Random Samples / Exercises

CONCEPTS 3: STATISTICS AND SAMPLING DISTRIBUTIONS

Statistics and Estimators / Accuracy of Estimation / The Sampling Distribution / Bias of an Estimator / Standard Error of a Statistic / RMS Error of an Estimator / Confidence Interval

APPLICATIONS 3: SAMPLING DISTRIBUTION COMPUTATIONS

Exercises

CONCEPTS 4: TESTING POPULATION HYPOTHESES

Population Statistical Hypotheses / Population Hypothesis Testing

APPLICATIONS 4: NULL SAMPLING DISTRIBUTION P-VALUES

The p-value of a Directional Test / The p-value of a Nondirectional Test / Exercises

CONCEPTS 5: PARAMETRICS, PIVOTALS, AND ASYMPTOTICS

The Unrealizable Sampling Distribution / Sampling Distribution of a Sample Mean / Parametric Population Distributions / Pivotal Form Statistics / Asymptotic Sampling Distributions / Limitations of the Mathematical Approach

APPLICATIONS 5: CIs FOR NORMAL POPULATION MEAN AND VARIANCE

CI for a Normal Population Mean / CI for a Normal Population Variance / Nonparametric CI Estimation / Exercises

CONCEPTS 6: LIMITATIONS OF PARAMETRIC INFERENCE

Range and Precision of Scores / Size of Population / Size of Sample / Roughness of Population Distribution / Parameters and Statistics of Interests / Scarcity of Random Samples / Resampling Inference

APPLICATIONS 6: RESAMPLING APPROACHES TO INFERENCE

Exercises

CONCEPTS 7: THE REAL AND BOOTSTRAP WORLDS

The Real World of Population Inference / The Bootstrap World of Population Inference / Real World Population Distribution Estimates / Nonparametric Population Estimates / Sample Size and Distribution Estimates

APPLICATIONS 7: BOOTSTRAP POPULATION DISTRIBUTIONS

Nonparametric Population Estimates / Exercises

CONCEPTS 8: THE BOOTSTRAP SAMPLING DISTRIBUTION

The Bootstrap Conjecture / Complete Bootstrap Sampling Distributions / Monte Carlo Bootstrap Estimate of Standard Error / The Bootstrap Estimate of Bias / Simple Bootstrap CI Estimates

APPLICATIONS 8: BOOTSTRAP SE, BIAS, AND CI ESTIMATES

Example / Exercises

CONCEPTS 9: BETTER BOOTSTRAP CIs: THE BOOTSTRAP-T

Pivotal Form Statistics / The Bootstrap-t Pivotal Transformation / Forming Bootstrap-t CIs / Estimating the Standard Error of an Estimate / Range of Applications of the Bootstrap-t / Iterated Bootstrap CIs

APPLICATIONS 9: SE AND CIs FOR TRIMMED MEANS

Definition of the Trimmed Mean / Importance of the Trimmed Mean / A Note on Outliers / Determining the Trimming Fraction / Sampling Distribution of the Trimmed Mean / Applications / Exercises

CONCEPTS 10: BETTER BOOTSTRAP CIs: BCA INTERVALS

Bias Corrected and Accelerated CI Estimates / Applications of BCA CI / Better Confidence Interval Estimates

APPLICATIONS 10: USING CI CORRECTION FACTORS

Requirements for a BCA CI / Implementations of the BCA Algorithm / Exercise

CONCEPTS 11: BOOTSTRAP HYPOTHESIS TESTING

CIs, Null Hypothesis Tests, and p-values / Bootstrap-t Hypothesis Testing / Bootstrap Hypothesis Testing Alternatives / CI Hypothesis Testing / Confidence Intervals or p-values?

APPLICATIONS 11: BOOTSTRAP P-VALUES

Computing a Bootstrap-t p-value / Fixed-alpha CIs and Hypothesis Testing / Computing a BCI CI p-Value / Exercise

CONCEPTS 12: RANDOMIZED TREATMENT ASSIGNMENT

Two Functions of Randomization / Randomization of Sampled Cases / Randomization of Two Available Cases / Statistical Basis for Local Casual Inference / Population Hypothesis Revisited

APPLICATIONS 12: MONTE CARLO REFERENCE DISTRIBUTIONS

Serum Albumen in Diabetic Mice / Resampling Stats Analysis / SC Analysis / S-Plus Analysis / Exercises

CONCEPTS 13: STRATEGIES FOR RANDOMIZING CASES

Independent Randomization of Cases / Completely Randomized Designs / Randomized Blocks Designs / Restricted Randomization / Constraints on Rerandomization

APPLICATIONS 13: IMPLEMENTING CASE RERANDOMIZATION

Completely Randomized Designs / Randomized Blocks Designs / Independent Randomization of Cases / Restricted Randomization / Exercises

CONCEPTS 14: RANDOM TREATMENT SEQUENCES

Between- and Within-Cases Designs / Randomizing the Sequence of Treatments / Casual Inference for Within-Cases Designs / Sequence of Randomization Strategies

APPLICATIONS 14: RERANDOMIZING TREATMENT SEQUENCES

Analysis of the AB-BA Design / Sequences of k > 2 Treatments / Exercises

CONCEPTS 15: BETWEEN- AND WITHIN-CASE DECISIONS

Between/Within Designs / Between/Within Resampling Strategies / Doubly Randomized Available Cases

APPLICATIONS 15: INTERACTIONS AND SIMPLE EFFECTS

Simple and Main Effects / Exercises

CONCEPTS 16: SUBSAMPLES: STABILITY OF DESCRIPTION

Nonrandom Studies and Data Sets / Local Descriptive Inference / Descriptive Stability and Case Homogeneity / Subsample Descriptions / Employing Subsample Descriptions / Subsamples and Randomized Studies

APPLICATIONS 16: STRUCTURED & UNSTRUCTURED DATA

Half-Samples of Unstructured Data / Subsamples of Source-Structured Cases / Exercises

PART II: RESAMPLING APPLICATIONS

INTRODUCTION

APPLICATIONS 17: A SINGLE GROUP OF CASES

Random Sample or Set of Available Cases / Typical Size of Score Distribution / Variability of Attribute Scores / Association Between Two Attributes / Exercises

APPLICATIONS 18: TWO INDEPENDENT GROUPS OF CASES

Constitution of Independent Groups / Location Comparisons for Samples / Magnitude Differences, CR and RB Designs / Magnitude Differences, Nonrandom Designs / Study Size / Exercises

APPLICATIONS 19: MULTIPLE INDEPENDENT GROUPS

Multiple Group Parametric Comparisons / Nonparametric K-group Comparison / Comparisons among Randomized Groups / Comparisons among Nonrandom Groups / Adjustment for Multiple Comparisons / Exercises

APPLICATIONS 20: MULTIPLE FACTORS AND COVARIATES

Two Treatment Factors / Treatment and Blocking Factors / Covariate Adjustment of Treatment Scores / Exercises

APPLICATIONS 21: WITHIN-CASES TREATMENT COMPARISONS

Normal Models, Univariate and Multivariate / Bootstrap Treatment Comparisons / Randomized Sequence of Treatments / Nonrandom Repeated Measures / Exercises

APPLICATIONS 22: LINEAR MODELS: MEASURED RESPONSE

The Parametric Linear Model / Nonparametric Linear Models / Prediction Accuracy / Linear Models for Randomized Cases / Linear Models for Nonrandom Studies / Exercises

APPLICATIONS 23: CATEGORICAL RESPONSE ATTRIBUTES

Cross-Classification of Cases / The 2 × 2 Table / Logistic Regression / Exercises

POSTSCRIPT: GENERALITY, CAUSALITY & STABILITY

Study Design and Resampling / Resampling Tools / REFERENCES / INDEX