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Data Analysis for Experimental Design


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Table of Contents

Part 1. The Nature of Research. Introduction. Observations and Variables. Behavioral Variables. Stimulus Variables. Individual Difference Variables. Discrete and Continuous Variables. Levels of Measurement. Summarizing Observations in Research. Questions and Problems. Part 2. Principles of Experimental Design. The Farmer from Whidbey Island. The Experiment. The Question of Interest. Sample Space and Probability. Simulation of the Experiment. Permutations. Combinations. Probabilities of Possible Outcomes. A Sample Space for the Experiment. Testing a Null Hypothesis. Type I and Type II Errors. Experimental Controls. The Importance of Randomization. A Variation in Design. Summary. Questions and Problems. Part 3. The Standard Normal Distribution: An Amazing Approximation. Introduction. Binomial Populations and Binomial Variables. Mean of a Population. Variance and Standard Deviation of a Population. The Average of a Sum and the Variance of a Sum. The Average and Variance of Repeated Samples. The Second Experiment with the Farmer: T and sT. Representing Probabilities by Areas. The Standard Normal Distribution. The Second Experiment with the Farmer: A Normal Distribution Test. The First Experiment with the Farmer: A Normal Distribution Test. Examples of Binomial Models. Populations That Have Several Possible Values. The Distribution of the Sum from a Uniform Distribution. The Distribution of the Sum T from a U-Shaped Population. The Distribution of the Sum T from a Skewed Population. Summary and Sermon. Questions and Problems. Part 4. Tests for Means from Random Samples. Transforming a Sample Mean into a Standard Normal Variable. The Variance and Standard Error of the Mean When the Population Variance s2 Is Known. The Variance and Standard Error of the Mean When Population s2 Is Unknown. The t Distribution and the One-Sample t Test. Confidence Interval for a Mean. Standard Error of the Difference between Two Means. Confidence Interval for a Difference between Two Means. Test of Significance for a Difference between Two Means: The Two-Sample t Test. Using a Computer Program. Returning to the Farmer Example in Chapter 2. Effect Size for a Difference between Two Independent Means. The Null Hypothesis and Alternatives. The Power of the t Test against a Specified Alternative. Estimating the Number of Observations Needed in Comparing Two Treatment Means. Random Assignments of Participants. Attrition in Behavioral Science Experiments. Summary. Questions and Problems. Part 5. Homogeneity and Normality Assumptions. Introduction. Testing Two Variances: The F Distribution. An Example of Testing the Homogeneity of Two Variances. Caveats. Boxplots. A t Test for Two Independent Means When the Population Variances Are Not Equal. Nonrandom Assignment of Subjects. Treatments That Operate Differentially on Individual Difference Variables. Nonadditivity of a Treatment Effect. Transformations of Raw Data. Normality. Summary. Questions and Problems. Part 6. The Analysis of Variance: One Between-Subjects Factor. Introduction. Notation for a One-Way Between-Subjects Design. Sums of Squares for the One-Way Between-Subjects Design. One-Way Between-Subjects Design: An Example. Test of Significance for a One-Way Between-Subjects Design. Weighted Means Analysis with Unequal n's. Summary. Questions and Problems. Part 7. Pairwise Comparisons. Introduction. A One-Way Between-Subjects Experiment with 4 Treatments. Protection Levels and the Bonferroni Significant Difference (BSD) Test. Fisher's Significant Difference (FSD) Test. The Tukey Significant Difference (TSD) Test. Scheffe's Significant Difference (SSD) Test. The Four Methods: General Considerations. Questions and Problems. Orthogonal, Planned and Unplanned Comparisons. Introduction. Comparisons on Treatment Means. Standard Error of a Comparison. The t Test of Significance for a Comparison. Part 8. Orthogonal Comparisons. Choosing a Set of Orthogonal Comparisons. Protection Levels with Orthogonal Comparisons. Treatments as Values of an Ordered Variable. Coefficients for Orthogonal Polynomials. Tests of Significance for Trend Comparisons. The Relation between a Set of Orthogonal Comparisons and the Treatment Sum of Squares. Tests of Significance for Planned Comparisons. Effect Size for Comparisons. The Equality of Variance Assumption. Unequal Sample Size. Unplanned Comparisons. Summary. Questions and Problems. Part 9. The 2k Between-Subjects Factorial Experiment. Introduction. An Example of a 23 Factorial Experiment. Assumption of Homogeneity of Variance. Factorial Data as a One-Way Between-Subjects Design. Partitioning the Treatment Sum of Squares. Summary of the Analysis of Variance. Graphs That Depict the Interactions. Other 2k Factorial Experiments. Notation and Sums of Squares for a Factorial Experiment. Summary. Questions and Problems. Part 10. Between-Subjects Factorial Experiments: Factors with More Than Two Levels. Introduction. An Example of a 4 x 3 x 2 Factorial Experiment. Partitioning the Sum of Squares into Main Effects and Interactions. Orthogonal Partitioning for Main Effects. Orthogonal Partitioning for Interactions. Effect Size for Comparisons in a Factorial Design. Performing Multiple Tests. The Structural Model and Nomenclature. Summary. Questions and Problems. Part 11. Between-Subjects Factorial Experiments: Further Considerations. The Scheffe Test for Comparisons. Pairwise Comparisons in Factorial Designs. Unequal Sample Sizes in a Factorial Design. Individual Difference Factors. Control Variables. Random-Effect Factors. Nested Factors. Homogeneity of Variance. Summary. Questions and Problems. Part 12. Within-Subjects Factors: One-Way and 2k Factorial Designs. Introduction. Example: One-Way ANOVA with a Within-Subjects Factor. Trend Analysis on One-Way Within-Subjects Designs. Assumptions and Effect Size Measures. 2k Factorial Designs: All Within-Subjects Factors. Multiple Tests. Design Considerations with Within-Subjects Designs. Scheffe Test for Within-Subjects Factors. SPSS Syntax. Multilevel Approach to Within-Subjects Designs. Summary. Questions and Problems. Part 13. Within-Subjects Factors: General Designs. Introduction. General Within-Subjects Factorial Design. Designs Containing Both Within-Subjects and Between-Subjects Factors. Omnibus Tests. Summary. Questions and Problems. Part 14. Contrasts on Binomial Data: Between-Subjects Designs. Introduction. Preliminaries. Four Examples of Wald Tests. Other Statistical Tests for Comparisons on Proportions. Numerical Examples. How Do These Tests Differ and What Do They Test? Summary. Questions and Problems. Part 15. Debriefing. Introduction. Descriptive Statistics and Plotting Data. Presenting Your Results. Nonparametric Statistical Tests. Nonexperimental Controls. Questions and Problems. Appendix A. The Method of Least Squares. Appendix B. Statistical Tables.

About 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.


"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, Department of Psychology, University of Massachusetts, Boston "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, Department of Educational Leadership, Research, and Technology, Western Michigan University "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, 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, 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 intervals, and effect size, as well as for its explicit treatment of technical assumptions underlying statistical tests. This excellent text is highly recommended." - Jay Myung, Department of Psychology, Ohio State University

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