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.
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.
