Experimental Design : Procedures for the Behavioral Sciences

by Roger E. Kirk

• ISBN13: 9781412974455
• ISBN10: 1412974453
• Edition: 4th
• Format: Hardcover
• Copyright: 2012-06-13
• Publisher: SAGE Publications, Inc

Summary

This book serves as an ideal textbook and reference book for students and researchers in the behavioral sciences and education. It includes a diagram of each design that illustrates how subjects are assigned to treatments, the use of boldface type to emphasize new terms, summaries of the advantages and disadvantages of the designs, and a plethora of review exercises. The most obvious change in the fourth edition is the sequence of the chapters. Other changes include an expanded coverage of exploratory data analysis, measures of practical significance, determination of sample size and power, and one degree-of-freedom measures. The latest advances in the rapidly expanding area of multiple comparisons are described in Chapter 5 along with recommendations for their use. Improved procedures for testing the tenability of assumptions in analysis of variance are described in Chapters 3, 4, and 8. This edition demonstrates the flexibility of the cell means model for analyzing data with missing observations and missing cells.

Table of Contents

Preface	p. xi
About the Author	p. xiii
Research Strategies and the Control of Nuisance Variables	p. 1
Introduction	p. 1
Formulation of Plans for the Collection and Analysis of Data	p. 2
Research Strategies	p. 6
Other Research Strategies	p. 9
Threats to Valid Inference Making	p. 16
Other Threats to Valid Inference Making	p. 19
Controlling Nuisance Variables and Minimizing Threats to Valid Inference Making	p. 21
Ethical Treatment of Subjects	p. 24
Review Exercises	p. 26
Experimental Designs: An Overview	p. 30
Introduction	p. 30
Overview of Some Basic Experimental Designs	p. 30
Classification of Analysis of Variance Designs	p. 45
Selecting an Appropriate Design	p. 48
Review of Statistical Inference	p. 49
Review Exercises	p. 70
Fundamental Assumptions in Analysis of Variance	p. 77
Sampling Distributions in Analysis of Variance	p. 77
Partition of the Total Sum of Squares	p. 86
Expectation of the Mean Squares	p. 92
The F Statistic in Analysis of Variance	p. 95
Effects of Failure to Meet Assumptions in Analysis of Variance	p. 96
Transformations	p. 103
Other Procedures for Dealing With Nonnormality, Unequal Variances, and Outliers	p. 108
Supplement for Section 3.3	p. 111
Review Exercises	p. 117
Completely Randomized Design	p. 125
Description of the Design	p. 125
Exploratory Data Analysis	p. 127
Computational Example for CR-4 Design	p. 131
Measures of Strength of Association and Effect Size	p. 134
Power and the Determination of Sample Size	p. 138
Random-Effects Model	p. 145
Advantages and Disadvantages of CR-p Design	p. 146
Review Exercises	p. 146
Multiple Comparison Tests	p. 154
Introduction to Multiple Comparison Tests	p. 154
Procedures for Testing p - 1 a Priori Orthogonal Contrasts	p. 170
Procedures for Testing p - 1 Contrasts Involving a Control Group Mean	p. 176
Procedures for Testing C a Priori Nonorthogonal Contrasts	p. 179
Procedures for Testing All Pairwise Contrasts	p. 187
Testing All Contrasts Suggested by an Inspection of the Data	p. 198
Other Multiple Comparison Procedures	p. 200
Comparison of Multiple Comparison Procedures	p. 201
Review Exercises	p. 201
Trend Analysis	p. 209
Introduction to Tests for Trends	p. 209
Test for the Linear Trend Contrast	p. 211
Tests for Higher-Order Trend Contrasts	p. 218
Linear and Curvilinear Correlation	p. 225
Variance Accounted for by Mean Contrasts	p. 225
Review Exercises	p. 227
General Linear Model Approach to ANOVA	p. 233
Comparison of Analysis of Variance and Multiple Regression	p. 233
Operations With Vectors and Matrices	p. 234
General Linear Model	p. 244
Estimating the Parameters in a Regression Model	p. 247
Regression Model Approach to ANOVA	p. 253
Alternative Conception of the Test of ß1 = ß2 = … = ßh-1 = 0	p. 262
Cell Means Model Approach to ANOVA	p. 266
Summary	p. 272
Review Exercises	p. 272
Randomized Block Designs	p. 280
Description of Randomized Block Design	p. 280
Computational Example for RB-p Design	p. 288
Alternative Models for RB-p Design	p. 296
Some Assumptions Underlying RB-p Design	p. 303
Procedures for Testing Differences Among Means	p. 314
Tests for Trends	p. 319
Relative Efficiency of Randomized Block Design	p. 321
Cell Mean Model Approach to the RB-p Design	p. 322
Generalized Randomized Block Design	p. 336
Advantages and Disadvantages of RB-p and GRB-p Designs	p. 343
Review Exercises	p. 344
Completely Randomized Factorial Design With Two Treatments	p. 357
Introduction to Factorial Designs	p. 357
Description of Completely Randomized Factorial Design	p. 357
Computational Example for CRF-pq Design	p. 360
Experimental Design Model for CRF-pq Design	p. 368
Procedures for Testing Differences Among Means	p. 372
More on the Interpretation of Interactions	p. 373
Tests for Trends	p. 386
Estimating Strength of Association, Effect Size, Power, and Sample Size	p. 395
Rules for Deriving Expected Values of Mean Squares	p. 400
Quasi F Statistics	p. 404
Preliminary Tests on the Model and Pooling Procedures	p. 406
Analysis of Completely Randomized Factorial Designs With n = 1	p. 409
Cell Means Model Approach to Completely Randomized Factorial Design	p. 411
Analysis of Completely Randomized Factorial Designs With Missing Observations and Empty Cells	p. 422
Advantages and Disadvantages of Factorial Designs	p. 431
Review Exercises	p. 432
Completely Randomized Factorial Design With Three or More Treatments and Randomized Block Factorial Design	p. 439
Introduction to CRF-pqr Design	p. 439
Computational Example for CRF-pqr Design	p. 441
Patterns Underlying Sum-of-Squares Formulas	p. 448
Formulating Coefficient Matrices for the Cell Means Model	p. 451
Introduction to Randomized Block Factorial Design	p. 458
Computational Example for RBF-pq Design	p. 460
Expected Value of Mean Squares and the Sphericity Conditions	p. 465
Cell Means Model Approach to Randomized Block Factorial Design	p. 469
Minimizing Time and Location Effects by Using a Randomized Block Factorial Design	p. 484
Review Exercises	p. 485
Hierarchical Designs	p. 489
Introduction to Hierarchical Designs	p. 489
Computational Example for CKH-pq(A) Design	p. 492
Experimental Design Model for CRH-pq(A) Design	p. 496
Procedures for Testing Differences Among Means	p. 498
Estimating Strength of Association, Effect Size, Power, and Sample Size	p. 500
Description of Other Completely Randomized Hierarchical Designs	p. 502
Cell Means Model for Completely Randomized Hierarchical Design	p. 515
Cell Means Model for Randomized Block Hierarchical! Design	p. 521
Advantages and Disadvantages of Hierarchical Designs	p. 530
Review Exercises	p. 531
Split-Plot Factorial Design: Design With Group-Treatment Confounding	p. 541
Description of Split-Plot Factorial Design	p. 541
Computational Example for SW-p·q Design	p. 544
Experimental Design Model for SPF-p·q Design	p. 550
Some Assumptions Underlying SFF-p·q Design	p. 555
Procedures for Testing Differences Among Means	p. 560
Procedures for Testing Hypotheses About Simple Main Effects and Treatment-Contrast Interactions	p. 566
Relative Efficiency of Split-Plot Factorial Design	p. 569
Computational Procedures for SPF-pr·q Design	p. 570
Computational Procedures for SW-prt·q Design	p. 579
Computational Procedures for SPF-p·qr Design	p. 583
Computational Procedures for STF-p·qrt Design	p. 590
Computational Procedures for SW-pr·qt Design	p. 595
Evaluation of Sequence Effects	p. 595
Cell Means Model Approach to SPF-p·g Design	p. 597
Advantages and Disadvantages of Split-Plot Factorial Designs	p. 613
Review Exercises	p. 613
Analysis of Covariance	p. 621
Introduction to Analysis of Covariance	p. 621
Rationale Underlying Covariate Adjustment	p. 625
Layout and Computational Procedures for CRAC-p Design	p. 633
Some Assumptions Underlying CRAC-p Design	p. 637
Procedures for Testing Differences Among Means in CRAC-p Design	p. 640
Analysis With Two Covariates	p. 642
Analysis of Covariance for Randomized Block Design	p. 646
Analysis of Covariance for Factorial Designs	p. 648
Covariance Versus Stratification	p. 654
Regression Model Approach to Analysis of Covariance	p. 656
Cell Means Model Approach to Analysis of Covariance	p. 660
Advantages and Disadvantages of Analysis of Covariance	p. 663
Review Exercises	p. 664
Latin Square and Related Designs	p. 671
Description of Latin Square Design	p. 671
Construction and Randomization of Latin Squares	p. 672
Computational Example for Latin Square Design	p. 675
Computational Procedures for n = 1	p. 681
Experimental Design Model for Latin Square Design	p. 684
Procedures for Testing Differences Among Means	p. 687
Relative Efficiency of Latin Square Design With n = 1	p. 687
Analysis of Covariance for Latin Square Design	p. 690
Cell Means Model Approach to Latin Square Design	p. 692
Graeco-Latin Square Design	p. 700
Hyper-Graeco-Latin Square Designs	p. 702
Crossover Design	p. 703
Advantages and Disadvantages of Designs Based on a Latin Square	p. 710
Review Exercises	p. 711
Confounded Factorial Designs: Designs With Group-Interaction Confounding	p. 719
Group-Interaction Confounding	p. 719
Use of Modular Arithmetic in Constructing Confounded Designs	p. 722
Computational Procedures for RBCF-22 Design	p. 726
Experimental Design Model for RBCF-22 Design	p. 729
Layout and Analysis for RBCF-23 Design	p. 732
Complete Versus Partial Confounding	p. 739
Computational Procedures for RBPF-23 Design	p. 740
Computational Procedures for RBCF-32 and RBPF-32 Designs	p. 749
Analysis Procedures for Higher-Order Confounded Designs	p. 760
Alternative Notation and Computational Systems	p. 772
Computational Procedures for RBPF-322 Design	p. 775
Cell Means Model Approach to RBCF-pk Design	p. 785
Group-Interaction Confounding by Means of a Latin Square	p. 787
Advantages and Disadvantages of Confounding in Factorial Designs	p. 793
Review Exercises	p. 796
Fractional Factorial Designs: Designs With Treatment-Interaction Confounding	p. 803
Introduction to Fractional Factorial Designs	p. 803
General Procedures for Constructing Completely Randomized Fractional Factorial Designs	p. 805
Computational Procedures for CRFF-24-1 Design	p. 810
Computational Procedures for CRFF-34-1 Design	p. 814
Cell Means Model for CRFF-pk-i Design	p. 820
General Procedures for Constructing RBFF-pk-i Designs	p. 823
Other Types of CRFF and RBFF Designs	p. 824
Introduction to Latin Square Fractional Factorial Designs	p. 825
Computational Procedures for LSFF-p·p2 Design	p. 828
Computational Procedures for LSFF-p3t Design	p. 832
Computational Procedures for LSFF-p4u Design	p. 838
Computational Procedures for GLSFF-p3 Design	p. 840
Advantages and Disadvantages of Fractional Factorial Designs	p. 841
Review Exercises	p. 842
Rules of Summation	p. 847
Rules of Expectation, Variance, and Covariance	p. 852
Orthogonal Coefficients for Unequal Intervals and Unequal ns	p. 858
Matrix Algebra	p. 863
Tables	p. 891
Answers to Starred Exercises	p. 952
References	p. 1035
Index	p. 1048
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