Experimental Design/ procedures for the behavioral sciences Kirk,Roger E.

CHAPTER I Research Strategies and the Control
of Nuisance Variables
1.1 Introcliiclion I
1.2 Formulation of Plans for the C'olleetion and Analysis of Data 2
1.3 Research Strategies 6
1.4 Other Research Strategies 9
1.5 Threats to Valid inference Making 16
1.6 Other Threats to Valid Inference Making 19
1.7 Controlling Nuisance Variables and Minimizing
Threats to Valid Inference Making 21
1.8 Ethical Treatment of Subjects 24 '
1.9 Review Exercises 26
CHAPTER 2 Experimental Designs: An Overview
2.1 introduction 30
2.2 Overv iew of Some liasie Experimental Designs 30
2.3 Classiilcation of Analysis of Variance Designs 45
2.4 Selecting an Appropriate Design 4S
2.5 Rev iew of Statistical Inference 49
2.6 Review Exercises 70
CHAPTER 3 Fundamental Assumptions
in Analysis of Variance
3.1 Sampling Distributions in Analysis of Variance 77
3.2 Partition of the Total Sum of Squares S6
3.3 l-.xpectation of the Mean Squares 92
3.4 4 he/■ Statistic in Analvsis of Variance 95
3.5 Effects of Failure to Meet Assumptions in Analysis of Variance 96
3.6 Transformations 103
3.7 Other Procedures for Dealing With Nonnormality,
Unequal Variances, and Outliers 108
3.8 Supplement for Section 3.3 111
3.9 Review Exercises 117
CHAPTER 4 Completely Randomized Design
4.1 Description of the Design 125
4.2 Exploratory Data Analysis 127
4.3 Computational Example for CR-4 Design 131
4.4 Measures of Strength of Association and Effect Size 134
4.5 Power and the Determination of Sample Size 138
4.6 Random-Effects Model 145
4.7 Advantages and Disadvantages of CR-p Design 146
4.8 Review Exercises 146
CHAPTERS Multiple Comparison Tests
5.1 Introduction to Multiple Comparison Tests 154
5.2 Procedures for Testing p - 1 a Priori Orthogonal Contrasts 170
5.3 Procedures for Testing p - 1 Contrasts Involving a Control Group Mean 176
5.4 Procedures for Testing C a Priori Nonorthogonal Contrasts 179
5.5 Procedures for Testing All Pairwise Contrasts 187
5.6 Testing All Contrasts Suggested by an Inspection of the Data 198
5.7 Other Multiple Comparison Procedures 200
5.8 Comparison of Multiple Comparison Procedures 201
5.9 Review Exercises 201
CHAPTER 6 Trend Analysis
6.1 Introduction to Tests for Trends 209
6.2 Test for the Linear Trend Contrast 211
6.3 Tests for Higher-Order Trend Contrasts 218
6.4 Linear and Curvilinear Con-elation 225
6.5 Variance Accounted for by Mean Contrasts 225
6.6 Review Exercises 227
CHAPTER 7 General Linear Model Approach to ANOVA
7.1 Comparison of Analysis of Variance and Multiple Regression
7.2 Operations With Vectors and Matrices 234
7.3 General Linear Model 244
7.4 Estimating the Parameters in a Regression Model 247
7.5 Regression Model Approach to ANOVA 253
7.6 Alternative Conception ofthe Tost or[3, - [3. = p;, _ j = 0 262
7.7 Cell Means Model Approach to ANOVA 266
7.8 Summary 272
7.9 Re\ ie\v lixcrcises 272
CHAPTER 8 Randomized Block Designs
8.1 Description of Randomized Block Design 280
8.2 Computational Example tor RB-p Design 288
8.3 Alternative Models for RB-/; Design 296
8.4 Some Assumptions Underlying RB-p Design 303
8.5 Procedures for Testing DilTercnces Among Means 314
8.6 Tests for Trends 319
8.7 Relative Efilcicncy of Randomized Block Design 321
8.8 Cell Mean Model Approach to the RB-p Design 322
8.9 Generalized Randomized Block Design 336
8.10 Advantages and Disadvantages of RB-/? and GRB-/J Designs 343
8.11 Review Exercises 344
CHAPTER 9 Completely Randomized Factorial
Design With Two Treatments
9.1 Introduction to Factorial Designs 357
9.2 Description of Completely Randomized Factorial Design 357
9.3 Computational Example for CRF-/;(/ Design 360
9.4 Experimental Design Model for CRF-/;f/Design 368
9.5 Procedures for Testing Differences Among Means 372
9.6 More on the Interpretation of Interactions 373
9.7 Tests for Trends 386
9.8 Estimating Strength of Association, Effect Size.
Power, and Sample Size 395
9.9 Rules for Deriving Expected Values of Mean Squares 400
9.10 Quasi F Statistics 404
9.11 Preliminary Tests on the Model and Pooling Procedures 406
9.12 Analysis of Completely Randomized Factorial Designs With n = I 409
9.13 Cell Means Model Approach to
Completely Randomized Factorial Design 41 1
9.14 Analysis of Completely Randomized Factorial Designs
With Missing Observations and Empty Cells 422
9.15 Advantages and Disadvantages of Factorial Designs 431
9.16 Review Exercises 432
CHAPTER 10 Completely Randomized Factorial Design
With Three or More Treatments and
Randomized Block Factorial Design
10.1 Introduction to CRF-pqr Design 439
10.2 Computational Example for CRF-pqr Design 441
10.3 Patterns Underlying Sum-of-Squares Fonnulas 448
10.4 Formulating Coefficient Matrices for the Cell Means Model 451
10.5 Introduction to Randomized Block Factorial Design 458
10.6 Computational Example for RBF-p^ Design 460
10.7 Expected Value of Mean Squares and the Sphericity Conditions 465
10.8 Cell Means Model Approach to Randomized Block Factorial Design 469
10.9 Minimizing Time and Location Effects by Using a Randomized Block
Factorial Design 484
10.10 Review Exercises 485
CHAPTER I I Hierarchical Designs
11.1 Introduction to Hierarchical Designs 489
11.2 Computational Example for CRH-pr/(zI) Design 492
11.3 Experimental Design Model for CRH-p7(/l) Design 496
11.4 Procedures for Testing Differences Among Means 498
11.5 Estimating Strength of Association, Effect Size, Power, and Sample Size 500
11.6 Description of Other Completely Randomized Hierarchical Designs 502
11.7 Cell Means Model for Completely Randomized Hierarchical Design 515
11.8 Cell Means Model for Randomized Block Hierarchical Design 521
11.9 Advantages and Disadvantages of Hierarchical Designs 530
11.10 Review Exercises 531
CHAPTER 12 Split-Plot Factorial Design:
Design With Group-Treatment Confounding
12.1 Description of Split-Plot Factorial Design 541
12.2 Computational Example for SPF-/; (7 Design 544
12.3 Experimental Design Model for SPF-p q Design 550
12.4 Some Assumptions Underlying SPF-p-^ Design 555
12.5 Procedures for Testing Differences Among Means 560
12.6 Procedures for Testing Hypotheses About Simple Main
Effects and Treatment-Contrast Interactions 566
12.7 Relative Efficiency of Split-Plot Factorial Design 569
12.8 Computational Procedures for SPF-/;; -i/ Design 570
12.9 Computational Procedures for SPF-prt-q Design 579
12.10 Computational Procedures for SPF-p <7;-Design 583
12.11 Computational Procedures for SPF-p-^;7 Design 590
12.12 Computational Procedures for SPF-/j7- (7/Design 595
12.13 Evaluation of Sequence EiTccts 595
12.14 Cell Means Model Approach to SPF-/;-t/ Design 597
12.15 Advantages and Disadvantages of Split-Plot Factorial Designs 613
12.16 Review Exercises 613
CHAPTER 13 Analysis of Covariance
13.1 Introduction to Analysis of Cox ariance 621
13.2 Rationale Underlying Covariate Adjustment 625
13.3 Layout and Computational Procedures for CRAC-p Design 633
13.4 Some Assumptions Underlying CRAC-/? Design 637
13.5 Procedures for Testing DilTerences Among Means in CRAC-p Design 640
13.6 Analysis With Two Covariales 642
13.7 Analysis of Covariance for Randomized Block Design 646
13.8 Analysis of Covariance for Factorial Designs 648
13.9 Covariance Versus Slratitlcation 654
13.10 Regression Model Approach to Analysis of Covariance 656
13.11 Cell Means Model Approach to Analysis of Covariance 660
13.12 Advantages and Disadvantages of Analysis of Covariance 663
13.13 Review Exercises 664
CHAPTER 14 Latin Square and Related Designs
14.1 Description of Latin Square Design 671
14.2 Construction and Randomization of Latin Squares 672
14.3 Computational Example for Latin Square Design 675
14.4 Computational Procedures for/? =1 681
14.5 Experimental Design Model for Latin Square Design 684
14.6 Procedures for Testing Differences Among Means 687
14.7 Relative Efficiency of Latin Square Design With // = 1 687
14.8 Analysis of Covariance for Latin Square Design 690
14.9 Cell Means Model Approach to Latin Square Design 692
14.10 Graeco-Latin Square Design 700
14.11 Flyper-Graeco-Latin Square Designs 702
14.12 C rossover Design 703
14.13 Advantages and Disadvantages of Designs Based on a Latin Square 710
14.14 Review Exercises 71 1
CHAPTER 15 Confounded Factorial Designs:
Designs With Group-Interaction Confounding
15.1 Group-Interaction Confounding 719
15.2 Use of Modular Arithmetic in Constructing Confounded Designs 722
15.3 Computational Procedures for RBCF-2' Desiun 726
15.4 Experimental Design Model for RBCF-2' Design 729 -
15.5 Layout and Analysis for RBCF-2^ Design 732
15.6 Complete Versus Partial Confounding 739
15.7 Computational Procedures for RBPF-23 Design 740
15.8 Computational Procedures for RBCF-3^ and RBPF-3- Designs 749
15.9 Analysis Procedures for Higher-Order Confounded Designs 760
15.'10 Alternative Notation and Computational Systems 772
15.11 Computational Procedures for RBPF-32- Design 775
15.12 Cell Means Model Approach to RBCF-^" Design 785
15.13 Group-Interaction Confounding by Means of a Latin Square 787
15.14 Advantages and Disadvantages of Confounding in Factorial Designs 793
15.15 Review Exercises 796
CHAPTER 16 Fractional Factorial Designs: Designs With Treatment-
Interaction Confounding
16.1 Introduction to Fractional Factorial Designs 803
16.2 General Procedures for Constructing Completely
Randomized Fractional Factorial Designs 805
16.3 Computational Procedures for CRFF-2''~'Design 810
16.4 Computational Procedures for CRFF-3"^'Design 814,
16.5 Ceil Means Model for CRFF-p^ ' Design 820
16.6 General Procedures for Constructing RBFF-/?^"'" Designs 823
16.7 Other Types of CRFF and RBFF Designs 824
16^ Introduction to Latin Square Fractional Factorial Designs 825
16.9 Computational Procedures for LSFF-/^^^ Design 828
16.10 Computational Procedures for LSFF-pV Design 832
16.11 Computational Procedures for LSFF-p^n Design 838
16.12 Computational Procedures for GLSFF-/5^ Design 840
16.13 Advantages and Disadvantages of Fractional Factorial Designs 841
16.14 Review Exercises 842