Experimental Design : Procedures for the Behavioral Sciences

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

Prefacep. xi
About the Authorp. xiii
Research Strategies and the Control of Nuisance Variablesp. 1
Introductionp. 1
Formulation of Plans for the Collection and Analysis of Datap. 2
Research Strategiesp. 6
Other Research Strategiesp. 9
Threats to Valid Inference Makingp. 16
Other Threats to Valid Inference Makingp. 19
Controlling Nuisance Variables and Minimizing Threats to Valid Inference Makingp. 21
Ethical Treatment of Subjectsp. 24
Review Exercisesp. 26
Experimental Designs: An Overviewp. 30
Introductionp. 30
Overview of Some Basic Experimental Designsp. 30
Classification of Analysis of Variance Designsp. 45
Selecting an Appropriate Designp. 48
Review of Statistical Inferencep. 49
Review Exercisesp. 70
Fundamental Assumptions in Analysis of Variancep. 77
Sampling Distributions in Analysis of Variancep. 77
Partition of the Total Sum of Squaresp. 86
Expectation of the Mean Squaresp. 92
The F Statistic in Analysis of Variancep. 95
Effects of Failure to Meet Assumptions in Analysis of Variancep. 96
Transformationsp. 103
Other Procedures for Dealing With Nonnormality, Unequal Variances, and Outliersp. 108
Supplement for Section 3.3p. 111
Review Exercisesp. 117
Completely Randomized Designp. 125
Description of the Designp. 125
Exploratory Data Analysisp. 127
Computational Example for CR-4 Designp. 131
Measures of Strength of Association and Effect Sizep. 134
Power and the Determination of Sample Sizep. 138
Random-Effects Modelp. 145
Advantages and Disadvantages of CR-p Designp. 146
Review Exercisesp. 146
Multiple Comparison Testsp. 154
Introduction to Multiple Comparison Testsp. 154
Procedures for Testing p - 1 a Priori Orthogonal Contrastsp. 170
Procedures for Testing p - 1 Contrasts Involving a Control Group Meanp. 176
Procedures for Testing C a Priori Nonorthogonal Contrastsp. 179
Procedures for Testing All Pairwise Contrastsp. 187
Testing All Contrasts Suggested by an Inspection of the Datap. 198
Other Multiple Comparison Proceduresp. 200
Comparison of Multiple Comparison Proceduresp. 201
Review Exercisesp. 201
Trend Analysisp. 209
Introduction to Tests for Trendsp. 209
Test for the Linear Trend Contrastp. 211
Tests for Higher-Order Trend Contrastsp. 218
Linear and Curvilinear Correlationp. 225
Variance Accounted for by Mean Contrastsp. 225
Review Exercisesp. 227
General Linear Model Approach to ANOVAp. 233
Comparison of Analysis of Variance and Multiple Regressionp. 233
Operations With Vectors and Matricesp. 234
General Linear Modelp. 244
Estimating the Parameters in a Regression Modelp. 247
Regression Model Approach to ANOVAp. 253
Alternative Conception of the Test of 1 = 2 = … = h-1 = 0p. 262
Cell Means Model Approach to ANOVAp. 266
Summaryp. 272
Review Exercisesp. 272
Randomized Block Designsp. 280
Description of Randomized Block Designp. 280
Computational Example for RB-p Designp. 288
Alternative Models for RB-p Designp. 296
Some Assumptions Underlying RB-p Designp. 303
Procedures for Testing Differences Among Meansp. 314
Tests for Trendsp. 319
Relative Efficiency of Randomized Block Designp. 321
Cell Mean Model Approach to the RB-p Designp. 322
Generalized Randomized Block Designp. 336
Advantages and Disadvantages of RB-p and GRB-p Designsp. 343
Review Exercisesp. 344
Completely Randomized Factorial Design With Two Treatmentsp. 357
Introduction to Factorial Designsp. 357
Description of Completely Randomized Factorial Designp. 357
Computational Example for CRF-pq Designp. 360
Experimental Design Model for CRF-pq Designp. 368
Procedures for Testing Differences Among Meansp. 372
More on the Interpretation of Interactionsp. 373
Tests for Trendsp. 386
Estimating Strength of Association, Effect Size, Power, and Sample Sizep. 395
Rules for Deriving Expected Values of Mean Squaresp. 400
Quasi F Statisticsp. 404
Preliminary Tests on the Model and Pooling Proceduresp. 406
Analysis of Completely Randomized Factorial Designs With n = 1p. 409
Cell Means Model Approach to Completely Randomized Factorial Designp. 411
Analysis of Completely Randomized Factorial Designs With Missing Observations and Empty Cellsp. 422
Advantages and Disadvantages of Factorial Designsp. 431
Review Exercisesp. 432
Completely Randomized Factorial Design With Three or More Treatments and Randomized Block Factorial Designp. 439
Introduction to CRF-pqr Designp. 439
Computational Example for CRF-pqr Designp. 441
Patterns Underlying Sum-of-Squares Formulasp. 448
Formulating Coefficient Matrices for the Cell Means Modelp. 451
Introduction to Randomized Block Factorial Designp. 458
Computational Example for RBF-pq Designp. 460
Expected Value of Mean Squares and the Sphericity Conditionsp. 465
Cell Means Model Approach to Randomized Block Factorial Designp. 469
Minimizing Time and Location Effects by Using a Randomized Block Factorial Designp. 484
Review Exercisesp. 485
Hierarchical Designsp. 489
Introduction to Hierarchical Designsp. 489
Computational Example for CKH-pq(A) Designp. 492
Experimental Design Model for CRH-pq(A) Designp. 496
Procedures for Testing Differences Among Meansp. 498
Estimating Strength of Association, Effect Size, Power, and Sample Sizep. 500
Description of Other Completely Randomized Hierarchical Designsp. 502
Cell Means Model for Completely Randomized Hierarchical Designp. 515
Cell Means Model for Randomized Block Hierarchical! Designp. 521
Advantages and Disadvantages of Hierarchical Designsp. 530
Review Exercisesp. 531
Split-Plot Factorial Design: Design With Group-Treatment Confoundingp. 541
Description of Split-Plot Factorial Designp. 541
Computational Example for SW-pq Designp. 544
Experimental Design Model for SPF-pq Designp. 550
Some Assumptions Underlying SFF-pq Designp. 555
Procedures for Testing Differences Among Meansp. 560
Procedures for Testing Hypotheses About Simple Main Effects and Treatment-Contrast Interactionsp. 566
Relative Efficiency of Split-Plot Factorial Designp. 569
Computational Procedures for SPF-prq Designp. 570
Computational Procedures for SW-prtq Designp. 579
Computational Procedures for SPF-pqr Designp. 583
Computational Procedures for STF-pqrt Designp. 590
Computational Procedures for SW-prqt Designp. 595
Evaluation of Sequence Effectsp. 595
Cell Means Model Approach to SPF-pg Designp. 597
Advantages and Disadvantages of Split-Plot Factorial Designsp. 613
Review Exercisesp. 613
Analysis of Covariancep. 621
Introduction to Analysis of Covariancep. 621
Rationale Underlying Covariate Adjustmentp. 625
Layout and Computational Procedures for CRAC-p Designp. 633
Some Assumptions Underlying CRAC-p Designp. 637
Procedures for Testing Differences Among Means in CRAC-p Designp. 640
Analysis With Two Covariatesp. 642
Analysis of Covariance for Randomized Block Designp. 646
Analysis of Covariance for Factorial Designsp. 648
Covariance Versus Stratificationp. 654
Regression Model Approach to Analysis of Covariancep. 656
Cell Means Model Approach to Analysis of Covariancep. 660
Advantages and Disadvantages of Analysis of Covariancep. 663
Review Exercisesp. 664
Latin Square and Related Designsp. 671
Description of Latin Square Designp. 671
Construction and Randomization of Latin Squaresp. 672
Computational Example for Latin Square Designp. 675
Computational Procedures for n = 1p. 681
Experimental Design Model for Latin Square Designp. 684
Procedures for Testing Differences Among Meansp. 687
Relative Efficiency of Latin Square Design With n = 1p. 687
Analysis of Covariance for Latin Square Designp. 690
Cell Means Model Approach to Latin Square Designp. 692
Graeco-Latin Square Designp. 700
Hyper-Graeco-Latin Square Designsp. 702
Crossover Designp. 703
Advantages and Disadvantages of Designs Based on a Latin Squarep. 710
Review Exercisesp. 711
Confounded Factorial Designs: Designs With Group-Interaction Confoundingp. 719
Group-Interaction Confoundingp. 719
Use of Modular Arithmetic in Constructing Confounded Designsp. 722
Computational Procedures for RBCF-22 Designp. 726
Experimental Design Model for RBCF-22 Designp. 729
Layout and Analysis for RBCF-23 Designp. 732
Complete Versus Partial Confoundingp. 739
Computational Procedures for RBPF-23 Designp. 740
Computational Procedures for RBCF-32 and RBPF-32 Designsp. 749
Analysis Procedures for Higher-Order Confounded Designsp. 760
Alternative Notation and Computational Systemsp. 772
Computational Procedures for RBPF-322 Designp. 775
Cell Means Model Approach to RBCF-pk Designp. 785
Group-Interaction Confounding by Means of a Latin Squarep. 787
Advantages and Disadvantages of Confounding in Factorial Designsp. 793
Review Exercisesp. 796
Fractional Factorial Designs: Designs With Treatment-Interaction Confoundingp. 803
Introduction to Fractional Factorial Designsp. 803
General Procedures for Constructing Completely Randomized Fractional Factorial Designsp. 805
Computational Procedures for CRFF-24-1 Designp. 810
Computational Procedures for CRFF-34-1 Designp. 814
Cell Means Model for CRFF-pk-i Designp. 820
General Procedures for Constructing RBFF-pk-i Designsp. 823
Other Types of CRFF and RBFF Designsp. 824
Introduction to Latin Square Fractional Factorial Designsp. 825
Computational Procedures for LSFF-pp2 Designp. 828
Computational Procedures for LSFF-p3t Designp. 832
Computational Procedures for LSFF-p4u Designp. 838
Computational Procedures for GLSFF-p3 Designp. 840
Advantages and Disadvantages of Fractional Factorial Designsp. 841
Review Exercisesp. 842
Rules of Summationp. 847
Rules of Expectation, Variance, and Covariancep. 852
Orthogonal Coefficients for Unequal Intervals and Unequal nsp. 858
Matrix Algebrap. 863
Tablesp. 891
Answers to Starred Exercisesp. 952
Referencesp. 1035
Indexp. 1048
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