Data Analysis for Experimental Design

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**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 s_{T}. 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 s^{2} Is Known. The
Variance and Standard Error of the Mean When Population
s^{2} 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
2 ^{k} Between-Subjects Factorial Experiment.**
Introduction. An Example of a 2

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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