Data Analysis for Experimental Design

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This engaging text shows how statistics and methods work together, demonstrating a variety of techniques for evaluating statistical results against the specifics of the methodological design. Richard Gonzalez elucidates the fundamental concepts involved in analysis of variance (ANOVA), focusing on single degree-of-freedom tests, or comparisons, wherever possible. Potential threats to making a causal inference from an experimental design are highlighted. With an emphasis on basic between-subjects and within-subjects designs, Gonzalez resists presenting the countless "exceptions to the rule" that make many statistics textbooks so unwieldy and confusing for students and beginning researchers. Ideal for graduate courses in experimental design or data analysis, the text may also be used by advanced undergraduates preparing to do senior theses.

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Editorial Reviews

Doody's Review Service
Reviewer: Gary B Kaniuk, Psy.D.(Cermak Health Services)
Description: This book details various statistical analyses, particularly focusing on ANOVA (analysis of variance), and discusses methodological designs (between subjects and within subjects) and how to best describe their results using different statistical tests.
Purpose: The author's goal is to "highlight the relatively simple concepts that drive analysis of variance, rather than to write a comprehensive handbook of every detail related to the analysis of experimental design." He adds, "My other goal in writing this book was to show readers how methods and statistics work together."
Audience: The book is intended for graduate courses in experimental design or data analysis, but also can be used by advanced undergraduates preparing to do senior theses. The author, a professor of psychology at the University of Michigan and associate editor of American Psychologist, conducts research in judgment and decision making.
Features: An introduction to research and experimental design begins the book, followed by a discussion of basic statistics involved in describing normal distributions. The remainder of the book focuses on determining differences between means, understanding analysis of variance, pairwise comparisons, and factorial experiments. The chapters are broken down into various topics in the table of contents, making it easy for readers to find what they need. Each chapter has a summary and questions and problems at the end for self-testing. However, the answers are not provided so readers are left in the dark on the mathematical computations. Examples allow readers to see how statistics are used and what they mean. The author discusses the principles that underlie the various statistical tests and two appendixes detail the method of least squares and various statistical tables. The book begins on a fairly simple level but becomes rather complex by the fifth chapter, although numerous tables and figures add clarity.
Assessment: This is a comprehensive look at how to analyze experimental data and readers will not be disappointed, if they have a good background in basic statistics. It is a foundational book that all researchers (or future researchers) should have in their library.
From the Publisher

"This book is up to date, clearly written, and has a well-crafted array of study questions and exercises at the end of each chapter that will benefit both instructors and students. The strong links to modern statistical software will be appreciated, as will the patient explanations regarding what one is really doing when analyzing data--and why."--John R. Nesselroade, PhD, Hugh Scott Hamilton Professor of Psychology, University of Virginia

"Data Analysis for Experimental Design goes beyond the standard factual presentation to offer insights on strategy and interpretation. Detailed and engaging, the book builds logically from a small set of principles involving design, sampling, distributions, and inference to offer a thorough treatment of tests of hypotheses involving means. The author uses clever and incisive examples to illustrate fundamental aspects of research design and strategy. Relatively little prior training in statistical methods is assumed, making this an excellent text for a first course in applied statistical methods for graduate students."--Rick H. Hoyle, PhD, Department of Psychology and Neuroscience, Duke University

"The book provides graduate students and behavioral science researchers with a thorough introduction to experimental design, with an emphasis on developing a simple and intuitive understanding of the basic concepts of analysis of variance. The strength of this book lies in the clear exposition of complex statistical ideas and the comprehensive coverage of the subject area. The book is also noteworthy for its special attention to proper interpretations of hypothesis-testing results, confidence interval, and effect size, as well as for its explicit treatment of technical assumptions underlying statistical tests. This excellent text is highly recommended."--Jay Myung, PhD, Department of Psychology, Ohio State University

"The discussion of simple ANOVA concepts leads delightfully into more elaborate or general models. One of the very real strengths of this text is its treatment of multiple-comparison methods. There is a wonderful discussion of planned and unplanned contrasts and their use with or without preceding omnibus significance tests. The discussion of orthogonal contrasts and orthogonal polynomials is another strength."--Warren E. Lacefield, PhD, Department of Educational Leadership, Research, and Technology, Western Michigan University

"The arrangement of topics, flow of discussion, conversational language, and general coverage make this a highly readable and informative textbook. Students and instructors will especially appreciate the author's 'storytelling' approach, which is interesting and relevant as well as conceptually rigorous."--Warren E. Lacefield, PhD, Department of Educational Leadership, Research, and Technology, Western Michigan University

"I could see using this book in an upper-level experimental methods course for undergraduates, or in a first course for graduate students in psychology, assuming they have all had introductory statistics."--Michael Milburn, PhD, Department of Psychology, University of Massachusetts-Boston

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Product Details

  • ISBN-13: 9781606230176
  • Publisher: Guilford Publications, Inc.
  • Publication date: 9/12/2008
  • Edition description: New Edition
  • Pages: 439
  • Product dimensions: 7.00 (w) x 10.10 (h) x 1.10 (d)

Meet the Author

Richard Gonzalez is Professor of Psychology at the University of Michigan. He also holds faculty appointments in the Department of Statistics at the University of Michigan and in the Department of Marketing at the Ross School of Business; is a Research Professor at the Research Center for Group Dynamics, which is housed in the Institute for Social Research, University of Michigan; and has taught statistics courses to social science students at all levels at the University of Washington, the University of Warsaw, the University of Michigan, and Princeton University. Dr. Gonzalez's research is in the area of judgment and decision making. His empirical and theoretical research deals with how people make decisions. Given that behavioral scientists make decisions from their data, his interest in decision processes automatically led Dr. Gonzalez to the study of statistical inference. His research contributions in data analysis include statistical methods for interdependent data, multidimensional scaling, and structural equations modeling. Dr. Gonzalez is currently Associate Editor of American Psychologist, and is on the editorial boards of Psychological Methods, Psychological Review, Psychological Science, and the Journal of Experimental Psychology: Learning, Memory, and Cognition. He is an elected member of the Society of Experimental Social Psychology and of the Society of Multivariate Experimental Psychology.

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Table of Contents

1. The Nature of Research

1.1 Introduction

1.2 Observations and Variables

1.3 Behavioral Variables

1.4 Stimulus Variables

1.5 Individual Difference Variables

1.6 Discrete and Continuous Variables

1.7 Levels of Measurement

1.8 Summarizing Observations in Research

1.9 Questions and Problems

2. Principles of Experimental Design

2.1 The Farmer from Whidbey Island

2.2 The Experiment

2.3 The Question of Interest

2.4 Sample Space and Probability

2.5 Simulation of the Experiment

2.6 Permutations

2.7 Combinations

2.8 Probabilities of Possible Outcomes

2.9 A Sample Space for the Experiment

2.10 Testing a Null Hypothesis

2.11 Type I and Type II Errors

2.12 Experimental Controls

2.13 The Importance of Randomization

2.14 A Variation in Design

2.15 Summary

2.16 Questions and Problems

3. The Standard Normal Distribution: An Amazing Approximation

3.1 Introduction

3.2 Binomial Populations and Binomial Variables

3.3 Mean of a Population

3.4 Variance and Standard Deviation of a Population

3.5 The Average of a Sum and the Variance of a Sum

3.6 The Average and Variance of Repeated Samples

3.7 The Second Experiment with the Farmer: µT and sT

3.8 Representing Probabilities by Areas

3.9 The Standard Normal Distribution

3.10 The Second Experiment with the Farmer: A Normal Distribution Test

3.11 The First Experiment with the Farmer: A Normal Distribution Test

3.12 Examples of Binomial Models

3.13 Populations That Have Several Possible Values

3.14 The Distribution of the Sum from a Uniform Distribution

3.15 The Distribution of the Sum T from a U-Shaped Population

3.16 The Distribution of the Sum T from a Skewed Population

3.17 Summary and Sermon

3.18 Questions and Problems

4. Tests for Means from Random Samples

4.1 Transforming a Sample Mean into a Standard Normal Variable

4.2 The Variance and Standard Error of the Mean When the Population Variance s2 Is Known

4.3 The Variance and Standard Error of the Mean When Population s2 Is Unknown

4.4 The t Distribution and the One-Sample t Test

4.5 Confidence Interval for a Mean

4.6 Standard Error of the Difference between Two Means

4.7 Confidence Interval for a Difference between Two Means

4.8 Test of Significance for a Difference between Two Means: The Two-Sample t Test

4.9 Using a Computer Program

4.10 Returning to the Farmer Example in Chapter 2

4.11 Effect Size for a Difference between Two Independent Means

4.12 The Null Hypothesis and Alternatives

4.13 The Power of the t Test against a Specified Alternative

4.14 Estimating the Number of Observations Needed in Comparing Two Treatment Means

4.15 Random Assignments of Participants

4.16 Attrition in Behavioral Science Experiments

4.17 Summary

4.18 Questions and Problems

5. Homogeneity and Normality Assumptions

5.1 Introduction

5.2 Testing Two Variances: The F Distribution

5.3 An Example of Testing the Homogeneity of Two Variances

5.4 Caveats

5.5 Boxplots

5.6 A t Test for Two Independent Means When the Population Variances Are Not Equal

5.7 Nonrandom Assignment of Subjects

5.8 Treatments That Operate Differentially on Individual Difference Variables

5.9 Nonadditivity of a Treatment Effect

5.10 Transformations of Raw Data

5.11 Normality

5.12 Summary

5.13 Questions and Problems

6. The Analysis of Variance: One Between-Subjects Factor

6.1 Introduction

6.2 Notation for a One-Way Between-Subjects Design

6.3 Sums of Squares for the One-Way Between-Subjects Design

6.4 One-Way Between-Subjects Design: An Example

6.5 Test of Significance for a One-Way Between-Subjects Design

6.6 Weighted Means Analysis with Unequal n's

6.7 Summary

6.8 Questions and Problems

7. Pairwise Comparisons

7.1 Introduction

7.2 A One-Way Between-Subjects Experiment with 4 Treatments

7.3 Protection Levels and the Bonferroni Significant Difference (BSD) Test

7.4 Fisher's Significant Difference (FSD) Test

7.5 The Tukey Significant Difference (TSD) Test

7.6 Scheffé's Significant Difference (SSD) Test

7.7 The Four Methods: General Considerations

7.8 Questions and Problems

8. Orthogonal, Planned and Unplanned Comparisons

8.1 Introduction

8.2 Comparisons on Treatment Means

8.3 Standard Error of a Comparison

8.4 The t Test of Significance for a Comparison

8.5 Orthogonal Comparisons

8.6 Choosing a Set of Orthogonal Comparisons

8.7 Protection Levels with Orthogonal Comparisons

8.8 Treatments as Values of an Ordered Variable

8.9 Coefficients for Orthogonal Polynomials

8.10 Tests of Significance for Trend Comparisons

8.11 The Relation between a Set of Orthogonal Comparisons and the Treatment Sum of Squares

8.12 Tests of Significance for Planned Comparisons

8.13 Effect Size for Comparisons

8.14 The Equality of Variance Assumption

8.15 Unequal Sample Size

8.16 Unplanned Comparisons

8.17 Summary

8.18 Questions and Problems

9. The 2k Between-Subjects Factorial Experiment

9.1 Introduction

9.2 An Example of a 23 Factorial Experiment

9.3 Assumption of Homogeneity of Variance

9.4 Factorial Data as a One-Way Between-Subjects Design

9.5 Partitioning the Treatment Sum of Squares

9.6 Summary of the Analysis of Variance

9.7 Graphs That Depict the Interactions

9.8 Other 2k Factorial Experiments

9.9 Notation and Sums of Squares for a Factorial Experiment

9.10 Summary

9.11 Questions and Problems

10. Between-Subjects Factorial Experiments: Factors with More Than Two Levels

10.1 Introduction

10.2 An Example of a 4 x 3 x 2 Factorial Experiment

10.3 Partitioning the Sum of Squares into Main Effects and Interactions

10.4 Orthogonal Partitioning for Main Effects

10.5 Orthogonal Partitioning for Interactions

10.6 Effect Size for Comparisons in a Factorial Design

10.7 Performing Multiple Tests

10.8 The Structural Model and Nomenclature

10.9 Summary

10.10 Questions and Problems

11. Between-Subjects Factorial Experiments: Further Considerations

11.1 The Scheffé Test for Comparisons

11.2 Pairwise Comparisons in Factorial Designs

11.3 Unequal Sample Sizes in a Factorial Design

11.4 Individual Difference Factors

11.5 Control Variables

11.6 Random-Effect Factors

11.7 Nested Factors

11.8 Homogeneity of Variance

11.9 Summary

11.10 Questions and Problems

12. Within-Subjects Factors: One-Way and 2k Factorial Designs

12.1 Introduction

12.2 Example: One-Way ANOVA with a Within-Subjects Factor

12.3 Trend Analysis on One-Way Within-Subjects Designs

12.4 Assumptions and Effect Size Measures

12.5 2k  Factorial Designs: All Within-Subjects Factors

12.6 Multiple Tests

12.7 Design Considerations with Within-Subjects Designs

12.8 Scheffé Test for Within-Subjects Factors

12.9 SPSS Syntax

12.10 Multilevel Approach to Within-Subjects Designs

12.11 Summary

12.12 Questions and Problems

13. Within-Subjects Factors: General Designs

13.1 Introduction

13.2 General Within-Subjects Factorial Design

13.3 Designs Containing Both Within-Subjects and Between-Subjects Factors

13.4 Omnibus Tests

13.5 Summary

13.6 Questions and Problems

14. Contrasts on Binomial Data: Between-Subjects Designs

14.1 Introduction

14.2 Preliminaries

14.3 Four Examples of Wald Tests

14.4 Other Statistical Tests for Comparisons on Proportions

14.5 Numerical Examples

14.6 How Do These Tests Differ and What Do They Test?

14.7 Summary

14.8 Questions and Problems

15. Debriefing

15.1 Introduction

15.2 Descriptive Statistics and Plotting Data

15.3 Presenting Your Results

15.4 Nonparametric Statistical Tests

15.5 Nonexperimental Controls

15.6 Questions and Problems

Appendix A. The Method of Least Squares

Appendix B. Statistical Tables

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