Data Analysis for Experimental Design

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.

• 1. The Nature of Research1.1 Introduction1.2 Observations and Variables1.3 Behavioral Variables1.4 Stimulus Variables1.5 Individual Difference Variables1.6 Discrete and Continuous Variables1.7 Levels of Measurement1.8 Summarizing Observations in Research1.9 Questions and Problems2. Principles of Experimental Design2.1 The Farmer from Whidbey Island2.2 The Experiment2.3 The Question of Interest2.4 Sample Space and Probability2.5 Simulation of the Experiment2.6 Permutations2.7 Combinations2.8 Probabilities of Possible Outcomes2.9 A Sample Space for the Experiment2.10 Testing a Null Hypothesis2.11 Type I and Type II Errors2.12 Experimental Controls2.13 The Importance of Randomization2.14 A Variation in Design2.15 Summary2.16 Questions and Problems3. The Standard Normal Distribution: An Amazing Approximation3.1 Introduction3.2 Binomial Populations and Binomial Variables3.3 Mean of a Population3.4 Variance and Standard Deviation of a Population3.5 The Average of a Sum and the Variance of a Sum3.6 The Average and Variance of Repeated Samples3.7 The Second Experiment with the Farmer: µT and sT3.8 Representing Probabilities by Areas3.9 The Standard Normal Distribution3.10 The Second Experiment with the Farmer: A Normal Distribution Test3.11 The First Experiment with the Farmer: A Normal Distribution Test3.12 Examples of Binomial Models3.13 Populations That Have Several Possible Values3.14 The Distribution of the Sum from a Uniform Distribution3.15 The Distribution of the Sum T from a U-Shaped Population3.16 The Distribution of the Sum T from a Skewed Population3.17 Summary and Sermon3.18 Questions and Problems4. Tests for Means from Random Samples4.1 Transforming a Sample Mean into a Standard Normal Variable4.2 The Variance and Standard Error of the Mean When the Population Variance s2 Is Known4.3 The Variance and Standard Error of the Mean When Population s2 Is Unknown 4.4 The t Distribution and the One-Sample t Test4.5 Confidence Interval for a Mean4.6 Standard Error of the Difference between Two Means4.7 Confidence Interval for a Difference between Two Means4.8 Test of Significance for a Difference between Two Means: The Two-Sample t Test4.9 Using a Computer Program4.10 Returning to the Farmer Example in Chapter 24.11 Effect Size for a Difference between Two Independent Means4.12 The Null Hypothesis and Alternatives4.13 The Power of the t Test against a Specified Alternative4.14 Estimating the Number of Observations Needed in Comparing Two Treatment Means4.15 Random Assignments of Participants 4.16 Attrition in Behavioral Science Experiments4.17 Summary4.18 Questions and Problems5. Homogeneity and Normality Assumptions5.1 Introduction5.2 Testing Two Variances: The F Distribution5.3 An Example of Testing the Homogeneity of Two Variances5.4 Caveats5.5 Boxplots5.6 A t Test for Two Independent Means When the Population Variances Are Not Equal5.7 Nonrandom Assignment of Subjects5.8 Treatments That Operate Differentially on Individual Difference Variables5.9 Nonadditivity of a Treatment Effect5.10 Transformations of Raw Data5.11 Normality5.12 Summary5.13 Questions and Problems6. The Analysis of Variance: One Between-Subjects Factor6.1 Introduction6.2 Notation for a One-Way Between-Subjects Design6.3 Sums of Squares for the One-Way Between-Subjects Design6.4 One-Way Between-Subjects Design: An Example6.5 Test of Significance for a One-Way Between-Subjects Design6.6 Weighted Means Analysis with Unequal n's6.7 Summary6.8 Questions and Problems7. Pairwise Comparisons7.1 Introduction7.2 A One-Way Between-Subjects Experiment with 4 Treatments7.3 Protection Levels and the Bonferroni Significant Difference (BSD) Test7.4 Fisher's Significant Difference (FSD) Test7.5 The Tukey Significant Difference (TSD) Test7.6 Scheffé's Significant Difference (SSD) Test7.7 The Four Methods: General Considerations7.8 Questions and Problems8. Orthogonal, Planned and Unplanned Comparisons8.1 Introduction8.2 Comparisons on Treatment Means8.3 Standard Error of a Comparison8.4 The t Test of Significance for a Comparison8.5 Orthogonal Comparisons8.6 Choosing a Set of Orthogonal Comparisons8.7 Protection Levels with Orthogonal Comparisons8.8 Treatments as Values of an Ordered Variable8.9 Coefficients for Orthogonal Polynomials8.10 Tests of Significance for Trend Comparisons8.11 The Relation between a Set of Orthogonal Comparisons and the Treatment Sum of Squares8.12 Tests of Significance for Planned Comparisons8.13 Effect Size for Comparisons8.14 The Equality of Variance Assumption8.15 Unequal

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 UniversityThe 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- It is a foundational book that all researchers (or future researchers) should have in their library. --Doody's Review Service, 9/6/2008