1 CONCEPTS AND EXAMPLES OF RESEARCH 1
1-1 Concepts 1
1-2 Examples 2
1-3 Concluding Remarks 5
References 6
2 CLASSIFICATION OF VARIABLES AND THE CHOICE OF ANALYSIS 7
2-1 Classification of Variables 7
2-2 Overlapping of Classification Schemes 11
2-3 Choice of Analysis 11
References 13
3 BASIC STATISTICS:A REVIEW 14
3-1 Preview 14
3-2 Descriptive Statistics 15
3-3 Random Variables and Distributions 16
3-4 Sampling Distributions of t,χ2,and F 19
3-5 Statistical Inference:Estimation 21
3-6 Statistical Inference:Hypothesis Testing 24
3-7 Error Rates,Power,and Sample Size 28
Problems 30
References 33
4 INTRODUCTION TO REGRESSION ANALYSIS 34
4-1 Preview 34
4-2 Association versus Causality 35
4-3 Statistical versus Deterministic Models 37
4-4 Concluding Remarks 38
References 38
5 STRAIGHT-LINE REGRESSION ANALYSIS 39
5-1 Preview 39
5-2 Regression with a Single Independent Variable 39
5-3 Mathematical Properties of a Straight Line 42
5-4 Statistical Assumptions for a Straight-line Model 43
5-5 Determining the Best-fitting Straight Line 47
5-6 Measure of the Quality of the Straight-line Fit and Estimate of σ2 51
5-7 Inferences About the Slope and Intercept 52
5-8 Interpretations of Tests for Slope and Intercept 54
5-9 Inferences About the Regression Line μY|X=β0+β1X 57
5-10 Prediction of a New Value of Y at X0 59
5-11 Assessing the Appropriateness of the Straight-line Model 60
Problems 60
References 87
6 THE CORRELATION COEFFICIENT AND STRAIGHT-LINE REGRESSION ANALYSIS 88
6-1 Definition of r 88
6-2 r as a Measure of Association 89
6-3 The Bivariate Normal Distribution 90
6-4 r and the Strength of the Straight-line Relationship 93
6-5 What r Does Not Measure 95
6-6 Tests of Hypotheses and Confidence Intervals for the Correlation Coefficient 96
6-7 Testing for the Equality of Two Correlations 99
Problems 101
References 103
7 THE ANALYSIS-OF-VARIANCE TABLE 104
7-1 Preview 104
7-2 The ANOVA Table for Straight-line Regression 104
Problems 108
8 MULTIPLE REGRESSION ANALYSIS:GENERAL CONSIDERATIONS 111
8-1 Preview 111
8-2 Multiple Regression Models 112
8-3 Graphical Look at the Problem 113
8-4 Assumptions of Multiple Regression 115
8-5 Determining the Best Estimate of the Multiple Regression Equation 118
8-6 The ANOVA Table for Multiple Regression 119
8-7 Numerical Examples 121
Problems 123
References 135
9 TESTING HYPOTHESES IN MULTIPLE REGRESSION 136
9-1 Preview 136
9-2 Test for Significant Overall Regression 137
9-3 Partial F Test 138
9-4 Multiple Partial F Test 143
9-5 Strategies for Using Partial F Tests 145
9-6 Tests Involving the Intercept 150
Problems 151
References 159
10 CORRELATIONS:MULTIPLE,PARTIAL,AND MULTIPLE PARTIAL 160
10-1 Preview 160
10-2 Correlation Matrix 161
10-3 Multiple Correlation Coefficient 162
10-4 Relationship of RY|X1,X2,…,Xk to the Multivariate Normal Distribution 164
10-5 Partial Correlation Coefficient 165
10-6 Alternative Representation of the Regression Model 172
10-7 Multiple Partial Correlation 172
10-8 Concluding Remarks 174
Problems 174
Reference 185
11 CONFOUNDING AND INTERACTION IN REGRESSION 186
11-1 Preview 186
11-2 Overview 186
11-3 Interaction in Regression 188
11-4 Confounding in Regression 194
11-5 Summary and Conclusions 199
Problems 199
Reference 211
12-1 Preview 212
12-2 Simple Approaches to Diagnosing Problems in Data 212
12 REGRESSION DIAGNOSTICS 212
12-3 Residual Analysis 216
12-4 Treating Outliers 228
12-5 Collinearity 237
12-6 Scaling Problems 248
12-7 Treating Collinearity and Scaling Problems 248
12-8 Alternate Strategies of Analysis 249
12-9 An Important Caution 252
Problems 253
References 279
13 POLYNOMIAL REGRESSION 281
13-1 Preview 281
13-2 Polynomial Models 282
13-3 Least-squares Procedure for Fitting a Parabola 282
13-5 Inferences Associated with Second-order Polynomial Regression 284
13-4 ANOVA Table for Second-order Polynomial Regression 284
13-6 Example Requiring a Second-order Model 286
13-7 Fitting and Testing Higher-order Models 290
13-8 Lack-of-fit Tests 290
13-9 Orthogonal Polynomials 292
13-10 Strategies for Choosing a Polynomial Model 301
Problems 302
14-2 Definitions 317
14-1 Preview 317
14 DUMMY VARIABLES IN REGRESSION 317
14-3 Rule for Defining Dummy Variables 318
14-4 Comparing Two Straight-line Regression Equations:An Example 319
14-5 Questions for Comparing Two Straight Lines 320
14-6 Methods of Comparing Two Straight Lines 321
14-7 MethodⅠ:Using Separate Regression Fits to Compare Two Straight Lines 322
14-8 MethodⅡ:Using a Single Regression Equation to Compare Two Straight Lines 327
14-10 Testing Strategies and Interpretation:Comparing Two Straight Lines 330
14-9 Comparison of Methods Ⅰ and Ⅱ 330
14-11 Other Dummy Variable Models 332
14-12 Comparing Four Regression Equations 334
14-13 Comparing Several Regression Equations Involving Two Nominal Variables 336
Problems 338
References 360
15 ANALYSIS OF COVARIANCE AND OTHER METHODS FOR ADJUSTING CONTINUOUS DATA 361
15-1 Preview 361
15-2 Adjustment Problem 361
15-3 Analysis of Covariance 363
15-4 Assumption of Parallelism:A Potential Drawback 365
15-5 Analysis of Covariance:Several Groups and Several Covariates 366
15-6 Comments and Cautions 368
15-7 Summary 371
Problems 371
Reference 385
16 SELECTING THE BEST REGRESSION EQUATION 386
16-1 Preview 386
16-2 Steps in Selecting the Best Regression Equation 387
16-3 Step 1:Specifying the Maximum Model 387
16-4 Step 2:Specifying a Criterion for Selecting a Model 390
16-5 Step 3:Specifying a Strategy for Selecting Variables 392
16-6 Step 4:Conducting the Analysis 401
16-7 Step 5:Evaluating Reliability with Split Samples 401
16-8 Example Analysis of Actual Data 403
16-9 Issues in Selecting the Most Valid Model 409
Problems 409
References 422
17 ONE-WAY ANALYSIS OF VARIANCE 423
17-1 Preview 423
17-2 One-way ANOVA:The Problem,Assumptions,and Data Configuration 426
17-3 Methodology for One-way Fixed-effects ANOVA 429
17-4 Regression Model for Fixed-effects One-way ANOVA 435
17-5 Fixed-effects Model for One-way ANOVA 438
17-6 Random-effects Model for One-way ANOVA 440
17-7 Multiple-comparison Procedures for Fixed-effects One-way ANOVA 443
17-8 Choosing a Multiple-comparison Technique 456
17-9 Orthogonal Contrasts and Partitioning an ANOVA Sum of Squares 457
Problems 463
References 483
18 RANDOMIZED BLOCKS:SPECIAL CASE OF TWO-WAY ANOVA 484
18-1 Preview 484
18-2 Equivalent Analysis of a Matched Pairs Experiment 488
18-3 Principle of Blocking 491
18-4 Analysis of a Randomized-blocks Experiment 493
18-5 ANOVA Table for a Randomized-blocks Experiment 495
18-6 Regression Models for a Randomized-blocks Experiment 499
18-7 Fixed-effects ANOVA Model for a Randomized-blocks Experiment 502
Problems 503
References 515
19 TWO-WAY ANOVA WITH EQUAL CELL NUMBERS 516
19-1 Preview 516
19-2 Using a Table of Cell Mcans 518
19-3 General Methodology 522
19-4 F Tests for Two-way ANOVA 527
19-5 Regression Model for Fixed-effects Two-way ANOVA 530
19-6 Interactions in Two-way ANOVA 534
19-7 Random- and Mixed-effects Two-way ANOVA Models 541
Problems 544
References 560
20 TWO-WAY ANOVA WITH UNEQUAL CELL NUMBERS 561
20-1 Preview 561
20-2 Problems with Unequal Cell Numbers:Nonorthogonality 563
20-3 Regression Approach for Unequal Cell Sample Sizes 567
20-4 Higher-way ANOVA 571
Problems 572
References 588
21 ANALYSIS OF REPEATED MEASURES DATA 589
21-1 Preview 589
21-2 Examples 590
21-3 General Approach for Repeated Measures ANOVA 592
21-4 Overview of Selected Repeated Measures Designs and ANOVA-based Analyses 594
21-5 Repeated Measures ANOVA for Unbalanced Data 611
21-6 Other Approaches to Analyzing Repeated Measures Data 612
Appendix 2l-A Examples of SAS s GLM and MIXED Procedures 613
Problems 616
References 638
22-1 Preview 639
22-2 The Principle of Maximum Likelihood 639
22 THE METHOD OF MAXIMUM LIKELIHOOD 639
22-3 Statistical Inference via Maximum Likelihood 642
22-4 Summary 652
Problems 653
References 655
23 LOGISTIC REGRESSION ANALYSIS 656
23-1 Preview 656
23-2 The Logistic Model 656
23-3 Estimating the Odds Ratio Using Logistic Regression 658
23-4 A Numerical Example of Logistic Regression 664
23-5 Theoretical Considerations 671
23-6 An Example of Conditional ML Estimation Involving Pair-matched Data with Unmatched Covariates 677
23-7 Summary 681
Problems 682
References 686
24-2 The Poisson Distribution 687
24 POISSON REGRESSION ANALYSIS 687
24-1 Preview 687
24-3 An Example of Poisson Regression 688
24-4 Poisson Regression:General Considerations 690
24-5 Measures of Goodness of Fit 694
24-6 Continuation of Skin Cancer Data Example 696
24-7 A Second Illustration of Poisson Regression Analysis 701
24-8 Summary 704
Problems 705
References 709
A APPENDIX A—TABLES 711
A-1 Standard Normal Cumulative Probabilities 712
A-2 Percentiles of the t Distribution 715
A-3 Percentiles of the Chi-square Distribution 716
A-4 Percentiles of the F Distribution 717
A-5 Values of?ln? 724
A-6 Upper α Point of Studentized Range 726
A-7 Orthogonal Polynomial Coefficients 728
A-8 BonferToni Corrected Jackknife and Studentized Residual Critical Values 729
A-9 Critical Values for Leverages 730
A-10 Critical Values for the Maximum of N Values of Cook s d(i)times(n-k-1) 731
B APPENDIX B—MATRICES AND THEIR RELATIONSHIP TO REGRESSION ANALYSIS 732
C APPENDIX C—ANOVA INFORMATION FOR FOUR COMMON BALANCED REPEATED MEASURES DESIGNS 744
C-1 Balanced Repeated Measures Design with One Crossover Factor (Treatments) 744
C-2 Balanced Repeated Measures Design with Two Crossover Factors 746
C-3 Balanced Repeated Measures Design with One Nest Factor (Treatments) 750
C-4 Balanced Repeated Measures Design with One Crossover Factor and One Nest Factor 752
C-5 Balanced Two-group Pre/Posttest Design 755
References 757
D SOLUTIONS TO EXERCISES 758
INDEX 787