Design and Analysis: A Researcher's Handbook

Description

The fourth edition of Design and Analysis continues to offer a readily accessible introduction to the designed experiment in research and the statistical analysis of the data from such experiments. Unique because it emphasizes the use of analytical procedures, this book is appropriate for all as it requires knowledge of only the most fundamental mathematical skills and little or no formal statistical background. Topics include: single- and two-factor designs with independent groups of subjects; corresponding designs with multiple observations; analysis of designs with unequal sample sizes; analysis of covariance; designs with three factors, including all combinations of between-subjects and within-subject factors; random factors and statistical generalization; and nested factors. This book lives up to its name as a handbook, because of its usefulness as a source and guide to researchers who require assistance in both planning a study and analyzing its results. Cover Contents Preface Part I Introduction 1 Experimental Design 1.1 Variables in Experimental Research 1.2 Control in Experimentation 1.3 Populations and Generalizing 1.4 The Basic Experimental Designs Part II Single-Factor Experiments 2 Sources of Variability and Sums of Squares 2.1 The Logic of Hypothesis Testing 2.2 The Component Deviations 2.3 Sums of Squares: Defining Formulas 2.4 Sums of Squares: Computational Formulas Comment Exercises 3 Variance Estimates and the F Ratio 3.1 Completing the Analysis 3.2 Evaluating the F Ratio 3.3 Errors in Hypothesis Testing 3.4 A Complete Numerical Example 3.5 Unequal Sample Sizes Comment Exercises 4 Analytical Comparisons Among Treatment Means 4.1 The Need for Analytical Comparisons 4.2 An Example of Planned Comparisons 4.3 Comparisons Among Treatment Means 4.4 Evaluating Contrasts with a t Test 4.5 Orthogonal Contrasts 4.6 Composite Contrasts Derived from Theory 4.7 Comparing Three or More Means Exercises 5 Analysis of Trend 5.1 Analysis of Linear Trend 5.2 Analysis of Quadratic Trend 5.3 Higher-Order Trend Components 5.4 Theoretical Prediction of Trend Components 5.5 Planning a Trend Analysis 5.6 Monotonic Trend Analysis Exercises 6 Simultaneous Comparisons and the Control of Type I Errors 6.1 Research Questions and Type I Error 6.2 Planned Comparisons 6.3 Restricted Sets of Contrasts 6.4 Pairwise Comparisons 6.5 Post-Hoc Error Correction Exercises 7 The Linear Model and Its Assumptions 7.1 The Statistical Model 7.2 Sampling Bias and the Loss of Subjects 7.3 Violations of Distributional Assumptions 7.4 Dealing with Heterogeneity of Variance 7.5 Contrasts with Heterogeneous Variance Exercises 8 Effect Size, Power, and Sample Size 8.1 Descriptive Measures of Effect Size 8.2 Effect Sizes in the Population 8.3 Power and Sample Size 8.4 Determining Sample Size Comments 8.5 Determining Power Comments Exercises 9 Using Statistical Software 9.1 Using the Programs 9.2 An Example 9.3 Hints, Cautions, and Advice Exercises Part III Two-Way Factorial Experiments 10 Introduction to Factorial Designs 10.1 Basic Information from a Factorial Design 10.2 The Concept of Interaction 10.3 The Definition of an Interaction 10.4 Further Examples of Interaction 10.5 Measurement of the Dependent Variable Exercises 11 The Overall Two-Factor Analysis 11.1 Component Deviations 11.2 Computations in the Two-Way Analysis 11.3 A Numerical Example 11.4 The Statistical Model 11.5 Designs with a Blocking Factor 11.6 Measuring Effect Size 11.7 Sample Size and Power Exercises 12 Detailed Analysis of Main Effects and Simple Effects 12.1 Interpreting a Two-Way Design 12.2 Comparisons for the Marginal Means 12.3 Interpreting the Interaction 12.4 Testing the Simple Effects 12.5 Simple Comparisons 12.6 Effect Sizes and Power for Simple Effects 12.7 Controlling Familywise Type I Error Exercises 13 The Analysis of Interaction Components 13.1 Types of Interaction Components 13.2 Analyzing Interaction Contrasts 13.3 Orthogonal Interaction Contrasts 13.4 Testing Contrast-by-Factor Interactions 13.5 Contrasts Outside the Factorial Structure 13.6 Multiple Tests and Type I Error Exercises Part IV The General Linear Model 14 The General Linear Model and Unbalanced Designs 14.1 The General Linear Model 14.2 The Two-Factor Analysis 14.3 Averaging of Groups and Individuals 14.4 Contrasts and Other Analytical Analyses 14.5 Sensitivity to Assumptions Exercises 15 The Analysis of Covariance 15.1 Covariance and Linear Regression 15.2 The Analysis of Covariance 15.3 Adjusted Means 15.4 Extensions of the Design 15.5 Assumptions of the Analysis of Covariance 15.6 Blocking and the Analysis of Covariance 15.7 Preexisting Covariate Differences 15.8 Effect Sizes, Power, and Sample Size Exercises Part V Within-Subject Designs 16 The Single-Factor Within-Subject Design: Basic Calculations 16.1 The Analysis of Variance 16.2 Analytical Comparisons 16.3 Effect Size and Power 16.4 Computer Analysis Exercises 17 The Single-Factor Within Subject Design: Further Topics 17.1 Advantages and Limitations 17.2 The Statistical Model 17.3 The Sphericity Assumption 17.4 Incidental Effects 17.5 Analyzing a Counterbalanced Design 17.6 Missing Data in Within-Subject Designs Comment Exercises 18 The Two-Factor Within-Subject Design 18.1 The Overall Analysis 18.2 Contrasts and Other Analytical Analyses 18.3 Assumptions and the Statistical Model 18.4 Counterbalancing of Nuisance Variables 18.5 Effect Size and Sample Sizes Exercises 19 The Two-Factor Mixed Design: Overall Analysis 19.1 The Overall Analysis of Variance 19.2 Statistical Model and Assumptions 19.3 The Multivariate Alternative 19.4 Missing Data and Unequal Sample Sizes 19.5 Effect Sizes and Sample-Size Calculations Exercises 20 The Two-Factor Mixed Design: Analytical Analyses 20.1 Analysis of the Between-Subjects Factor 20.2 Analysis of the Within-Subject Factor 20.3 Analyses Involving the Interaction Exercises Part VI Higher Factorial Designs and Other Extensions 21 The Three-Factor Design: The Overall Analysis of Variance 21.1 Components of the Three-Way Design 21.2 The Three-Way Interaction 21.3 Computational Procedures 21.4 Effect Size, Sample Size, and Power Exercises 22 The Three-Factor Design: Analytical Analysis 22.1 Overview of the Analytical Analysis 22.2 Analyses Involving the Cell Means 22.3 Effects Based on Marginal Means 22.4 Three-Factor Interaction Components 22.5 Contrast-by-Factor Interactions 22.6 Extension to Higher-Order Designs Exercises 23 Within-Subject and Mixed Designs 23.1 Varieties of Three-Factor Designs 23.2 The Overall Analysis 23.3 Two Examples of Mixed Designs 23.4 Analytical Analyses in the A×B×C×S Design 23.5 Analytical Analysis in Mixed Design Exercises 24 Random Factors and Generalizing Results 24.1 Statistical Generalization over Design Factors 24.2 Random Factors and the F Ratio 24.3 Error Terms in Random-Factor Designs 24.4 Design Considerations with Random Factors Exercises 25 Nested Factors 25.1 Nested Factors 25.2 Analysis of the Nested Designs 25.3 Crossing a Nested Factor with Another Factor 25.4 Planning a Study with Random Factors Exercises 26 Higher-Order Designs 26.1 Multifactor Experiments in the Behavioral Sciences 26.2 Analyzing Higher-Order Designs Exercises A Statistical Tables A.1 Critical Values of the F Distribution A.2 Critical Values of the t Distribution A.3 Coefficients of Orthogonal Polynomials A.4 Critical Values of the Šidák-Bonferroni t Statistic A.5 Critical Values for Dunnett's Test A.6 Critical Values of the Studentized Range Statistic A.7 Power Functions B Abbreviated Answers to the Exercises References Subject Index Author Index