Textbook

# Comparing Groups: Randomization and Bootstrap Methods Using R

A hands-on guide to using R to carry out key statistical practices in educational and behavioral sciences research

Computing has become an essential part of the day-to-day practice of statistical work, broadening the types of questions that can now be addressed by research scientists applying newly derived data analytic techniques. Comparing Groups: Randomization and Bootstrap Methods Using R emphasizes the direct link between scientific research questions and data analysis. Rather than relying on mathematical calculations, this book focus on conceptual explanations and the use of statistical computing in an effort to guide readers through the integration of design, statistical methodology, and computation to answer specific research questions regarding group differences.

Utilizing the widely-used, freely accessible R software, the authors introduce a modern approach to promote methods that provide a more complete understanding of statistical concepts. Following an introduction to R, each chapter is driven by a research question, and empirical data analysis is used to provide answers to that question. These examples are data-driven inquiries that promote interaction between statistical methods and ideas and computer application. Computer code and output are interwoven in the book to illustrate exactly how each analysis is carried out and how output is interpreted. Additional topical coverage includes:

• Data exploration of one variable and multivariate data
• Comparing two groups and many groups
• Permutation tests, randomization tests, and the independent samples t-Test
• Bootstrap tests and bootstrap intervals
• Interval estimates and effect sizes

Throughout the book, the authors incorporate data from real-world research studies as well aschapter problems that provide a platform to perform data analyses. A related Web site features a complete collection of the book's datasets along with the accompanying codebooks and the R script files and commands, allowing readers to reproduce the presented output and plots.

Comparing Groups: Randomization and Bootstrap Methods Using R is an excellent book for upper-undergraduate and graduate level courses on statistical methods, particularlyin the educational and behavioral sciences. The book also serves as a valuable resource for researchers who need a practical guide to modern data analytic and computational methods.

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List of Figures.

List of Tables.

Foreword.

Preface.

Acknowledgments.

1. An Introduction to R.

1.1 Getting Started.

1.2 Arithmetic: R as a Calculator.

1.3 Computations in R: Functions.

1.4 Connecting Computations.

1.5 Data Structures: Vectors.

1.6 Getting Help.

1.7 Alternative Ways to Run R.

1.8 Extension: Matrices and Matrix Operations.

Problems.

2. Data Representation and Preparation.

2.1 Tabular Data.

2.2 Data Entry.

2.3 Reading Delimited Data into R.

2.4 Data Structure: Data Frames.

2.5 Recording Syntax using Script Files.

2.6 Simple Graphing in R.

2.7 Extension: Logical Expressions and Graphs for Categorical Variables.

Problems.

3. Data Exploration: One Variable.

3.2 Non-Parametric Density Estimation.

3.3 Summarizing the Findings.

3.4 Extension: Variability Bands for Kernel Densities.

Problems.

4. Exploration of Multivariate Data: Comparing Two Groups.

4.1 Graphically Summarizing the Marginal Distribution.

4.2 Graphically Summarizing Conditional Distributions.

4.4 Numerical Summaries of Data: Estimates of the Population Parameters.

4.4 Summarizing the Findings.

4.5 Extension: Robust Estimation.

Problems.

5. Exploration of Multivariate Data: Comparing Many Groups.

5.1 Graphing Many Conditional Distributions.

5.2 Numerically Summarizing the Data.

5.3 Summarizing the Findings.

5.4 Examining Distributions Conditional on Multiple Variables.

5.5 Extension: Conditioning on Continuous Variables.

Problems.

6. Randomization & Permutation Tests.

6.1 Randomized Experimental Research.

6.2 An Introduction to the Randomization Test.

6.3 Randomization Tests with Large Samples: Monte Carlo Simulation.

6.4 Validity of the Inferences and Conclusions Drawn from a Randomization Test.

6.5 Generalization from the Randomization Results.

6.6 Summarizing the Results for Publication.

6.7 Extension: Test of the Variance.

Problems.

7. Bootstrap Tests.

7.1 Educational Achievement of Latino Immigrants.

7.2 Probability Models: An Interlude.

7.3 Theoretical Probability Models in R.

7.4 Parametric Bootstrap Tests.

7.5 The Parametric Bootstrap.

7.6 Implementing the Parametric Bootstrap in R.

7.7 Summarizing the Results of the Parametric Bootstrap Test.

7.8 Nonparametric  Bootstrap Tests.

7.9 Summarizing the Results for the Nonparametric Bootstrap Test.

7.10 Bootstrapping Using a Pivot Statistic.

7.11 Independence Assumption for the Bootstrap Methods.

7.12 Extension: Testing Functions.

Problems.

8. Philosophical Considerations.

8.1 The Randomization Test vs. the Bootstrap Test.

8.2 Philosophical Frameworks of Classical Inference.

9. Bootstrap Intervals and Effect Sizes.

9.1 Educational Achievement Among Latino Immigrants: Example Revisited.

9.2 Plausible Models to Reproduce the Observed Result.

9.3 Bootstrapping Using an Alternative Model.

9.4 Interpretation of the Interval Estimate.

9.6 Standardized Effect Size: Quantifying the Group Differences in a Common Metric.

9.7 Summarizing the Results.

9.8 Extension: Bootstrapping the Confidence Envelope for a Q-Q Plot.

9.9 Confidence Envelopes.

Problems.

10. Dependent Samples.

10.1 Matching: Reducing the Likelihood of Non-Equivalent Groups.

10.2 Mathematics Achievement Study Design.

10.3 Randomization/Permutation Test for Dependent Samples.

10.4 Effect Size.

10.5 Summarizing the Results of a Dependent Samples Test for Publication.

10.6 To Match or Not to Match: That is the Question.

10.7 Extension: Block Bootstrap.

Problems.

11. Planned Contrasts.

11.1 Planned Comparisons.

11.2 Examination of Weight Loss Conditioned on Diet.

11.3 From Research Questions to Hypotheses.

11.4 Statistical Contrasts.

11.5 Computing the Estimated Contrasts Using the Observed Data.

11.6 Testing Contrasts: Randomization Test.

11.7 Strength of Association: A Measure of Effect.

11.8 Contrast Sum of Squares.

11.9 Eta-Squared for Contrasts.

11.10 Bootstrap Interval for Eta-Squared.

11.11 Summarizing the Results of a Planned Contrast Test Analysis.

11.12 Extension: Orthogonal Contrasts.

Problems.

12. Unplanned Contrasts.

12.1 Unplanned Comparisons.

12.2 Examination of Weight Loss Conditioned on Diet.

12.3 Omnibus Test.

12.4 Group Comparisons After the Omnibus Test.

12.6 Strengths and Limitations of the Four Approaches.

12.7 Summarizing the Results of Unplanned Contrast Tests for Publication.

12.8 Extension: Plots of the Unplanned Contrasts.

Problems.

References.

Author Information
Andrew S. Zieffler, PhD, is Lecturer in the Department of Educational Psychology at the University of Minnesota. Dr. Zieffler has published numerous articles in his areas of research interest, which include the measurement and assessment in statistics education research and statistical computing.

Jeffrey R. Harring, PhD, is Assistant Professor in the Department of Measurement, Statistics, and Evaluation at the University of Maryland. Dr. Harring currently focuses his research on statistical models for repeated measures data and nonlinear structural equation models.

Jeffrey D. Long, PhD, is Professor of Psychiatry in the Carver College of Medicine at The University of Iowa and Head Statistician for Neurobiological Predictors of Huntington's Disease (PREDICT-HD), a longitudinal NIH-funded study of early detection of Huntington's disease. His interests include the analysis of longitudinal and time-to-event data and ordinal data.

Reviews

“The three authors of this book have a deep understanding of research methods and statistics and provide great value in this book for students of this subject and readers interested in it.”  (Biz India, 8 May 2012)

## Available Versions

Comparing Groups: Randomization and Bootstrap Methods Using R
by Andrew S. Zieffler, Jeffrey R. Harring, Jeffrey D. Long
ISBN 978-0-470-62169-1