Data Analysis by Resampling

C.E. Lunneborg is Professor Emeritus of Psychology and Statistics at the University of Washington. During a career spanning 40 years he has published over 100 technical articles and three university-level texts. His current research interests are in resampling, experimental design, and web-based instruction.

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