INSEAD Library

Includes bibliographical references and index

Digitized

Experimental Design: Procedures for the Behavioral Sciences Contents 1 INTRODUCTION TO BASIC CONCEPTS IN EXPERIMENTAL DESIGN 1.1 Introduction 1.2 Formulation of Plans for Collection and Analysis of Data 1.3 Overview of Types of Experimental Designs 1.4 Threats to Valid Inference-Making 1.5 Ethical Treatment of Research Subjects 1.6 Review of Statistical Inference 1.7 Review Exercises 1 3 8 20 24 25 44 2 FUNDAMENTAL ASSUMPTIONS IN ANALYSIS OF VARIANCE 2.1 Basic Sampling Distributions in Analysis of Variance 2.2 Partition of Total Sum of Squares 2.3 Expectation of Mean Squares 2.4 The F Ratio in Analysis of Variance 2.5 Effects of Failure to Meet Assumptions in Analysis of Variance 2.6 Transformations 2.7 Review Exercises 49 57 64 73 74 79 85 3 MULTIPLE COMPARISON TESTS 3.1 Introduction to Multiple Comparison Tests 3.2 A Priori Orthogonal Contrasts 3.3 Conceptual Unit for Error Rate 3.4 A Priori Nonorthogonal Contrasts 3.5 A Posteriori Nonorthogonal Contrasts 3.6 Comparison of Multiple Comparison Procedures 3.7 Review Exercises 90 95 101 106 114 127 127 4 COMPLETELY RANDOMIZED DESIGN 4.1 Description of Design 4.2 Exploratory Data Analysis 4.3 Computational Example for a Type CR-p Design 4.4 Procedures for Testing Differences Among Means 4.5 Tests for Trends in the Data 4.6 Measures of Association 4.7 Random-Effects Model 4.8 Advantages and Disadvantages of Type CR-p Design 4.9 Review Exercises 134 135 139 146 149 161 163 165 165 5 GENERAL LINEAR MODEL APPROACH TO ANOVA 5.1 Introduction to the General Linear Model 5.2 Estimating Parameters in the General Linear Regression Model 5.3 Regression Model Approach to ANOVA 5.4 ANOVA Via the Regression Model Approach With Dummy Coding 5.5 Alternative Conception of the Test of ß1, = ß2 = . . . ß 5.6 Testing Differences Among Means Using the Regression Model Approach 5.7 ANOVA Via the Regression Model Approach With Effect and Orthogonal Coding 5.8 Experimental Design Model Approach to ANOVA 5.9 ANOVA Via the Less Than Full Rank Experimental Design Model Approach 5.10 ANOVA Via the Full Rank Experimental Design Model Approach 5.11 Summary 5.12 Review Exercises 171 178 184 187 192 195 199 208 211 225 229 230 6 RANDOMIZED BLOCK DESIGNS 6.1 Description of the Randomized Block Design 6.2 Computational Example for a Type RB-p Design 6.3 Alternative Models for a Type RB-p Design 6.4 Some Assumptions Underlying a Type RB-p Design 6.5 Procedures for Testing Differences Among Means 6.6 Tests for Trends in the Data 6.7 Estimating Missing Observations 6.8 Relative Efficiency of Randomized Block Design 6.9 General Linear Model Approach to Type RB-p Design 6.10 Generalized Randomized Block Design 6.11 Advantages and Disadvantages of Type RB-p and GRB-p Designs 6.12 Review Exercises 237 243 247 253 263 266 268 271 273 293 297 298 7 LATIN SQUARE AND RELATED DESIGNS 7.1 Description of Latin Square Design 7.2 Construction and Randomization of Latin Squares 7.3 Computational Example for Type LS-p Design 7.4 Computational Procedures for n = 1 7.5 Experimental Design Model for a Type LS-p Design 7.6 Procedures for Testing Differences Among Means 7.7 Estimating Missing Observations 7.8 Relative Efficiency of Latin Square Design with n = 1 7.9 General Linear Model Approach to Type LS-p Design 7.10 Graeco-Latin Square Design 7.11 Hyper-Graeco-Latin Square Designs 7.12 Advantages and Disadvantages of Type LS-p Design 7.13 Review Exercises 308 309 312 318 319 322 323 326 329 339 341 342 342 8 COMPLETELY RANDOMIZED FACTORIAL DESIGN WITH TWO TREATMENTS 8.1 8.2 8.3 8.4 8.5 Introduction to Factorial Experiments Description of Completely Randomized Factorial Design Computational Example for Type CRF-pq Design Experimental Design Model for a Type CRF-pq Design Procedures for Testing Differences Among Means 350 351 353 359 364 8.6 More on the Interpretation of Interactions 8.7 Test for Trends in the Data 8.8 Estimating Strength of Association in a Type CRF-pq Design 8.9 Rules for Deriving Expected Values of Mean Squares 8.10 Quasi F Ratios 8.11 Preliminary Tests on the Model and Pooling Procedures 8.12 The Analysis of Completely Randomized Factorial Designs With n = 1 8.13 Analysis of Completely Randomized Factorial Designs With Unequal Cell n's 8.14 Advantages and Disadvantages of Factorial Designs 8.15 Review Exercises 365 379 387 389 394 396 399 401 422 423 9 COMPLETELY RANDOMIZED FACTORIAL DESIGN WITH THREE OR MORE TREATMENTS AND RANDOMIZED BLOCK FACTORIAL DESIGN 9.1 Introduction to Type CRF-pqr Design 9.2 Computational Example for Type CRF-pqr Design 9.3 Patterns Underlying Computational Formulas for Type CRF Designs 9.4 Introduction to Randomized Block Factorial Design 9.5 Computational Example for a Type RBF-pq Design 9.6 Expected Value of Mean Squares and the Circularity Assumption 9.7 Analysis of Randomized Block Design With Missing Observations 9.8 Minimizing Time and Location Effects by the Use of a Randomized Block Factorial Design 9.9 Review Exercises 429 431 435 441 443 446 449 453 453 10 HIERARCHICAL DESIGNS 10.1 Introduction to Hierarchical Designs 10.2 Computational Example for Type CRH-pq(A) Design 10.3 Experimental Design Model for a Type CRH-pq (A) Design 10.4 Procedures for Testing Differences Among Means 10.5 Estimating Strength of Association in a Type CRH-pq (A) Design 10.6 Description of Other Completely Randomized Hierarchical Designs 10.7 Analyzing Hierarchical Designs Using Computer Programs for Crossed Treatments 10.8 Analysis of Unbalanced Hierarchical Designs 10.9 Advantages and Disadvantages of Hierarchical Designs 10.10 Review Exercises 456 459 464 466 467 468 479 480 483 484 11 SPLIT-PLOT FACTORIAL DESIGN: DESIGN WITH GROUP-TREATMENT CONFOUNDING 11.1 Introduction to Split-Plot Factorial Design 11.2 Computational Example for Type SPF-p · q Design 11.3 Experimental Design Model for a Type SPF-p · q Design 11.4 Some Assumptions Underlying a Type SPF-p · q Design 11.5 Procedures for Testing Hypotheses About Means 11.6 Procedures for Testing Hypotheses About Simple Main Effects and Treatment-Contrast Interactions 11.7 Test for Trends in a Type SPF-p · q Design 11.8 Relative Efficiency of Split-Plot Factorial Design 11.9 Introduction to Type SPF-pr · q Design 11.10 Computational Procedures for Type SPF-prt · q Design 11.11 Computational Procedures for Type SPF-p · qr Design 11.12 Computational Procedures for Type SPF-p · qrt Design 11.13 Computational Procedures for Type SPF-pr · qt Design 11.14 Evaluation of Sequence Effects 11.15 Analysis of a Type SPF-p · q Design Using the Full Rank Model Approach 11.16 Advantages and Disadvantages of Split-Plot Factorial Designs 11.17 Review Exercises 489 492 493 500 505 510 513 519 523 531 535 544 547 549 550 564 564 12 CONFOUNDED FACTORIAL DESIGNS: DESIGNS WITH GROUP-INTERACTION CONFOUNDING 12.1 Introduction to Confounding in Factorial Experiments 12.2 Use of Modular Arithmetric in Constructing Confounded Designs 12.3 Computational Procedures for Type RBCF-22 Design 12.4 Experimental Design Model for a Type RBCF-22 Design 12.5 Layout and Analysis for a Type RBCF-23 Design 12.6 Complete Versus Partial Confounding 12.7 Computational Procedures for Type RBPF-23 Design 12.8 Computational Procedures for Type RBCF-32 and RBPF-32 Designs 601 12.9 Analysis Procedures for Higher-Order Confounded Designs 12.10 Alternative Notation and Computational Systems 12.11 Computational Procedures for Type RBPF-322 Design 12.12 Analysis of Confounded Factorial Designs Using the Full Rank Model Approach 12.13 Group-Interaction Confounding by Means of a Latin Square 12.14 Double Confounding 12.15 Advantages and Disadvantages of Confounding in Factorial Designs 12.16 Review Exercises 570 573 577 579 583 590 591 613 626 627 637 648 656 656 658 13 FRACTIONAL FACTORIAL DESIGNS: DESIGNS WITH TREATMENT-INTERACTION CONFOUNDING 13.1 Introduction to Fractional Factorial Designs 13.2 General Procedures for Constructing Type CRFF-2k Designs 13.3 Computational Procedures for Type CRFF-24 Design 13.4 Computational Procedures for Type CRFF-34 Design 13.5 General Procedures for Constructing Type RBFF-2k Design 13.6 Other Types of CRFF and RBFF Designs 13.7 Introduction to Latin Square Fractional Factorial Design 13.8 Computational Procedures for Type LSFF-p -p2 Design 13.9 Computational Procedures for Type LSFF-p3t Design 13.10 Computational Procedures for Type LSFF-p4u Design 13.11 Computational Procedures for Type GLSFF-p 3 Design 13.12 Analysis of Fractional Factorial Designs Using the Full Rank Model Approach 13.13 Advantages and Disadvantages of Fractional Factorial Designs 13.14 Review Exercises 664 666 669 674 680 681 683 685 687 696 698 699 710 711 14 ANALYSIS OF COVARIANCE 14.1 Introduction to Analysis of Covariance 14.2 Rationale Underlying Covariate Adjustment 14.3 Layout and Computational Procedures for Type CRAC-p Design 14.4 Assumptions of the Model for Type CRAC-p Design 14.5 Procedures for Testing Differences Among Means in Type CRAC-p Design 14.6 Analysis With Two Covariates 14.7 Analysis of Covariance for Randomized Block Design 14.8 Analysis of Covariance for Latin Square Design 14.9 Analysis of Covariance for Factorial Experiments 14.10 Covariance Versus Stratification 715 720 728 731 734 737 740 743 743 750 14.11 General Linear Model Approach to Type CRAC-p Design 14.12 Advantages and Disadvantages of Analysis of Covariance 14.13 Review Exercises Appendix A Rules of Summation 753 755 758 763 768 773 778 806 850 891 905 Appendix B Rules of Expectation, Variance, and Covariance Appendix C Orthogonal Coefficients for Unequal Intervals and Unequal n's Appendix D Matrix Algebra Appendix E Tables Appendix F Answers to Starred Exercises References Index