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Data Analysis for Experimental Design



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ISBN 9781606230176
Published October 31, 2008 by Guilford Press
439 Pages

 
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Book Description

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.

Useful pedagogical features include:

*Discussions of the assumptions that underlie each statistical test

*Sequential, step-by-step presentations of statistical procedures

*End-of-chapter questions and exercises

*Accessible writing style with scenarios and examples

*A companion Web page (www.umich.edu/~gonzo/daed) offering data and syntax files in R and SPSS for the research examples used in the book, a short guide to SPSS syntax, and detailed course notes on each of the book's topics.

Table of Contents

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1. The Nature of Research

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1.1 Introduction

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1.2 Observations and Variables

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1.3 Behavioral Variables

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1.4 Stimulus Variables

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1.5 Individual Difference Variables

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1.6 Discrete and Continuous Variables

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1.7 Levels of Measurement

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1.8 Summarizing Observations in Research

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1.9 Questions and Problems

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2. Principles of Experimental Design

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2.1 The Farmer from Whidbey Island

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2.2 The Experiment

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2.3 The Question of Interest

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2.4 Sample Space and Probability

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2.5 Simulation of the Experiment

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2.6 Permutations

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2.7 Combinations

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2.8 Probabilities of Possible Outcomes

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2.9 A Sample Space for the Experiment

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2.10 Testing a Null Hypothesis

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2.11 Type I and Type II Errors

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2.12 Experimental Controls

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2.13 The Importance of Randomization

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2.14 A Variation in Design

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2.15 Summary

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2.16 Questions and Problems

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3. The Standard Normal Distribution: An Amazing Approximation

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3.1 Introduction

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3.2 Binomial Populations and Binomial Variables

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3.3 Mean of a Population

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3.4 Variance and Standard Deviation of a Population

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

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3.6 The Average and Variance of Repeated Samples

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3.7 The Second Experiment with the Farmer: µT and sT

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3.8 Representing Probabilities by Areas

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3.9 The Standard Normal Distribution

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

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

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3.12 Examples of Binomial Models

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3.13 Populations That Have Several Possible Values

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3.14 The Distribution of the Sum from a Uniform Distribution

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

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3.16 The Distribution of the Sum T from a Skewed Population

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3.17 Summary and Sermon

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3.18 Questions and Problems

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4. Tests for Means from Random Samples

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4.1 Transforming a Sample Mean into a Standard Normal Variable

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

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

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4.4 The t Distribution and the One-Sample t Test

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4.5 Confidence Interval for a Mean

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4.6 Standard Error of the Difference between Two Means

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4.7 Confidence Interval for a Difference between Two Means

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

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4.9 Using a Computer Program

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4.10 Returning to the Farmer Example in Chapter 2

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4.11 Effect Size for a Difference between Two Independent Means

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4.12 The Null Hypothesis and Alternatives

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4.13 The Power of the t Test against a Specified Alternative

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

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4.15 Random Assignments of Participants

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4.16 Attrition in Behavioral Science Experiments

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4.17 Summary

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4.18 Questions and Problems

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5. Homogeneity and Normality Assumptions

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5.1 Introduction

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5.2 Testing Two Variances: The F Distribution

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5.3 An Example of Testing the Homogeneity of Two Variances

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5.4 Caveats

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5.5 Boxplots

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

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5.7 Nonrandom Assignment of Subjects

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5.8 Treatments That Operate Differentially on Individual Difference Variables

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5.9 Nonadditivity of a Treatment Effect

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5.10 Transformations of Raw Data

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5.11 Normality

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5.12 Summary

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5.13 Questions and Problems

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

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6.1 Introduction

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6.2 Notation for a One-Way Between-Subjects Design

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

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6.4 One-Way Between-Subjects Design: An Example

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

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6.6 Weighted Means Analysis with Unequal n's

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6.7 Summary

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6.8 Questions and Problems

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7. Pairwise Comparisons

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7.1 Introduction

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

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

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7.4 Fisher's Significant Difference (FSD) Test

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7.5 The Tukey Significant Difference (TSD) Test

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7.6 Scheffé's Significant Difference (SSD) Test

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7.7 The Four Methods: General Considerations

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7.8 Questions and Problems

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8. Orthogonal, Planned and Unplanned Comparisons

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8.1 Introduction

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8.2 Comparisons on Treatment Means

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8.3 Standard Error of a Comparison

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8.4 The t Test of Significance for a Comparison

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8.5 Orthogonal Comparisons

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8.6 Choosing a Set of Orthogonal Comparisons

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8.7 Protection Levels with Orthogonal Comparisons

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8.8 Treatments as Values of an Ordered Variable

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8.9 Coefficients for Orthogonal Polynomials

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8.10 Tests of Significance for Trend Comparisons

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

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8.12 Tests of Significance for Planned Comparisons

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8.13 Effect Size for Comparisons

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8.14 The Equality of Variance Assumption

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8.15 Unequal

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Author(s)

Biography

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.

Reviews

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