Using Multivariate Statistics

Cover......Page 1
Title Page......Page 6
Copyright Page......Page 7
Contents......Page 8
Preface......Page 32
1.1.1 The Domain of Multivariate Statistics: Numbers of IVs and DVs......Page 36
1.1.2 Experimental and Nonexperimental Research......Page 37
1.1.3 Computers and Multivariate Statistics......Page 38
1.2.1 Continuous, Discrete, and Dichotomous Data......Page 40
1.2.3 Descriptive and Inferential Statistics......Page 42
1.2.4 Orthogonality: Standard and Sequential Analyses......Page 43
1.3 Linear Combinations of Variables......Page 45
1.5 Statistical Power......Page 46
1.6.1 The Data Matrix......Page 47
1.6.2 The Correlation Matrix......Page 48
1.6.4 The Sum-of-Squares and Cross-Products Matrix......Page 49
1.7 Organization of the Book......Page 51
2.1.1 Degree of Relationship Among Variables......Page 52
2.1.2 Significance of Group Differences......Page 54
2.1.3 Prediction of Group Membership......Page 58
2.1.4 Structure......Page 60
2.1.5 Time Course of Events......Page 61
2.2 Some Further Comparisons......Page 62
2.3 A Decision Tree......Page 63
2.4 Technique Chapters......Page 66
2.5 Preliminary Check of the Data......Page 67
3.1.1 One-Sample z Test as Prototype......Page 68
3.1.2 Power......Page 71
3.2 Analysis of Variance......Page 72
3.2.1 One-Way Between-Subjects ANOVA......Page 74
3.2.2 Factorial Between-Subjects ANOVA......Page 77
3.2.3 Within-Subjects ANOVA......Page 78
3.2.4 Mixed Between-Within-Subjects ANOVA......Page 81
3.2.5 Design Complexity......Page 82
3.2.6 Specific Comparisons......Page 84
3.3 Parameter Estimation......Page 88
3.4 Effect Size......Page 89
3.5 Bivariate Statistics: Correlation and Regression......Page 90
3.5.1 Correlation......Page 91
3.5.2 Regression......Page 92
3.6 Chi-Square Analysis......Page 93
4 Cleaning Up Your Act: Screening Data Prior to Analysis......Page 95
4.1.2 Honest Correlations......Page 96
4.1.3 Missing Data......Page 97
4.1.4 Outliers......Page 107
4.1.5 Normality, Linearity, and Homoscedasticity......Page 113
4.1.6 Common Data Transformations......Page 121
4.1.7 Multicollinearity and Singularity......Page 123
4.1.8 A Checklist and Some Practical Recommendations......Page 126
4.2.1 Screening Ungrouped Data......Page 127
4.2.2 Screening Grouped Data......Page 140
5.1 General Purpose and Description......Page 152
5.2.1 Degree of Relationship......Page 154
5.2.5 Contingencies Among IVs......Page 155
5.2.8 Parameter Estimates......Page 156
5.3.1 Theoretical Issues......Page 157
5.3.2 Practical Issues......Page 158
5.4.1 General Linear Equations......Page 164
5.4.2 Matrix Equations......Page 166
5.4.3 Computer Analyses of Small-Sample Example......Page 168
5.5.1 Standard Multiple Regression......Page 171
5.5.2 Sequential Multiple Regression......Page 172
5.5.3 Statistical (Stepwise) Regression......Page 173
5.5.4 Choosing Among Regression Strategies......Page 178
5.6.1 Importance of IVs......Page 179
5.6.2 Statistical Inference......Page 184
5.6.3 Adjustment of R[sup(2)]......Page 189
5.6.4 Suppressor Variables......Page 190
5.6.5 Regression Approach to ANOVA......Page 191
5.6.6 Centering When Interactions and Powers of IVs Are Included......Page 193
5.6.7 Mediation in Causal Sequence......Page 195
5.7 Complete Examples of Regression Analysis......Page 196
5.7.1 Evaluation of Assumptions......Page 197
5.7.2 Standard Multiple Regression......Page 204
5.7.3 Sequential Regression......Page 210
5.7.4 Example of Standard Multiple Regression With Missing Values Multiply Imputed......Page 216
5.8.1 IBM SPSS Package......Page 225
5.8.2 SAS System......Page 230
5.8.3 SYSTAT System......Page 231
6.1 General Purpose and Description......Page 232
6.2.2 Interactions Among IVs......Page 235
6.2.6 Parameter Estimates......Page 236
6.3.1 Theoretical Issues......Page 237
6.3.2 Practical Issues......Page 238
6.4 Fundamental Equations for Analysis of Covariance......Page 240
6.4.1 Sums of Squares and Cross-Products......Page 241
6.4.2 Significance Test and Effect Size......Page 245
6.4.3 Computer Analyses of Small-Sample Example......Page 246
6.5.1 Choosing Covariates......Page 248
6.5.2 Evaluation of Covariates......Page 249
6.5.4 Design Complexity......Page 250
6.5.5 Alternatives to ANCOVA......Page 258
6.6.1 Evaluation of Assumptions......Page 260
6.6.2 Analysis of Covariance......Page 267
6.7.3 SYSTAT System......Page 277
7.1 General Purpose and Description......Page 280
7.2 Kinds of Research Questions......Page 283
7.2.3 Importance of DVs......Page 284
7.2.7 Effects of Covariates......Page 285
7.3.1 Theoretical Issues......Page 286
7.3.2 Practical Issues......Page 287
7.4.1 Multivariate Analysis of Variance......Page 290
7.4.2 Computer Analyses of Small-Sample Example......Page 298
7.4.3 Multivariate Analysis of Covariance......Page 301
7.5.2 Criteria for Statistical Inference......Page 305
7.5.3 Assessing DVs......Page 306
7.5.4 Specific Comparisons and Trend Analysis......Page 310
7.5.5 Design Complexity......Page 311
7.6.1 Evaluation of Assumptions......Page 314
7.6.2 Multivariate Analysis of Variance......Page 322
7.6.3 Multivariate Analysis of Covariance......Page 333
7.7.1 IBM SPSS Package......Page 345
7.7.3 SYSTAT System......Page 348
8.1 General Purpose and Description......Page 349
8.2.1 Parallelism of Profiles......Page 350
8.2.6 Effect Size......Page 351
8.3.2 Practical Issues......Page 352
8.4 Fundamental Equations for Profile Analysis......Page 354
8.4.1 Differences in Levels......Page 355
8.4.2 Parallelism......Page 356
8.4.3 Flatness......Page 359
8.4.4 Computer Analyses of Small-Sample Example......Page 360
8.5.1 Univariate Versus Multivariate Approach to Repeated Measures......Page 366
8.5.2 Contrasts in Profile Analysis......Page 368
8.5.3 Doubly Multivariate Designs......Page 378
8.5.5 Imputation of Missing Values......Page 382
8.6.1 Profile Analysis of Subscales of the WISC......Page 383
8.6.2 Doubly Multivariate Analysis of Reaction Time......Page 397
8.7 Comparison of Programs......Page 408
8.7.2 SAS System......Page 409
8.7.3 SYSTAT System......Page 411
9.1 General Purpose and Description......Page 412
9.2.2 Number of Significant Discriminant Functions......Page 415
9.2.6 Effect Size......Page 416
9.2.9 Estimation of Group Means......Page 417
9.3.2 Practical Issues......Page 418
9.4.1 Derivation and Test of Discriminant Functions......Page 421
9.4.2 Classification......Page 424
9.4.3 Computer Analyses of Small-Sample Example......Page 426
9.5.1 Direct Discriminant Analysis......Page 432
9.5.3 Stepwise (Statistical) Discriminant Analysis......Page 433
9.6.1 Statistical Inference......Page 434
9.6.3 Interpreting Discriminant Functions......Page 435
9.6.4 Evaluating Predictor Variables......Page 438
9.6.5 Effect Size......Page 439
9.6.6 Design Complexity: Factorial Designs......Page 440
9.6.7 Use of Classification Procedures......Page 441
9.7.1 Evaluation of Assumptions......Page 444
9.7.2 Direct Discriminant Analysis......Page 449
9.8.2 SAS System......Page 467
9.8.3 SYSTAT System......Page 473
10.1 General Purpose and Description......Page 474
10.2.2 Importance of Predictors......Page 476
10.2.6 Significance of Prediction with Covariates......Page 477
10.3.1 Theoretical Issues......Page 478
10.3.2 Practical Issues......Page 479
10.4 Fundamental Equations for Logistic Regression......Page 481
10.4.1 Testing and Interpreting Coefficients......Page 482
10.4.2 Goodness of Fit......Page 483
10.4.4 Interpretation and Analysis of Residuals......Page 485
10.4.5 Computer Analyses of Small-Sample Example......Page 486
10.5 Types of Logistic Regression......Page 490
10.5.3 Statistical (Stepwise) Logistic Regression......Page 491
10.5.4 Probit and Other Analyses......Page 493
10.6.1 Statistical Inference......Page 494
10.6.2 Effect Size for a Model......Page 497
10.6.3 Interpretation of Coefficients Using Odds......Page 498
10.6.4 Coding Outcome and Predictor Categories......Page 500
10.6.5 Number and Type of Outcome Categories......Page 501
10.6.6 Classification of Cases......Page 504
10.6.7 Hierarchical and Nonhierarchical Analysis......Page 505
10.7 Complete Examples of Logistic Regression......Page 507
10.7.1 Evaluation of Limitations......Page 508
10.7.2 Direct Logistic Regression with Two-Category Outcome and Continuous Predictors......Page 512
10.7.3 Sequential Logistic Regression with Three Categories of Outcome......Page 519
10.8.1 IBM SPSS Package......Page 537
10.8.2 SAS System......Page 543
10.8.3 SYSTAT System......Page 544
11.1 General Purpose and Description......Page 545
11.2.3 Survival Time With Covariates......Page 547
11.3.2 Practical Issues......Page 548
11.4 Fundamental Equations for Survival Analysis......Page 550
11.4.1 Life Tables......Page 551
11.4.3 Hazard and Density Functions......Page 553
11.4.4 Plot of Life Tables......Page 554
11.4.5 Test for Group Differences......Page 555
11.4.6 Computer Analyses of Small-Sample Example......Page 557
11.5.1 Actuarial and Product-Limit Life Tables and Survivor Functions......Page 563
11.5.2 Prediction of Group Survival Times From Covariates......Page 564
11.6.1 Proportionality of Hazards......Page 574
11.6.2 Censored Data......Page 576
11.6.3 Effect Size and Power......Page 577
11.6.4 Statistical Criteria......Page 578
11.6.5 Predicting Survival Rate......Page 579
11.7 Complete Example of Survival Analysis......Page 580
11.7.1 Evaluation of Assumptions......Page 582
11.7.2 Cox Regression Survival Analysis......Page 590
11.8.1 SAS System......Page 598
11.8.2 IBM SPSS Package......Page 604
11.8.3 SYSTAT System......Page 605
12.1 General Purpose and Description......Page 606
12.2.3 Importance of Canonical Variates......Page 608
12.3.1 Theoretical Limitations......Page 609
12.3.2 Practical Issues......Page 610
12.4 Fundamental Equations for Canonical Correlation......Page 611
12.4.1 Eigenvalues and Eigenvectors......Page 613
12.4.2 Matrix Equations......Page 615
12.4.3 Proportions of Variance Extracted......Page 619
12.4.4 Computer Analyses of Small-Sample Example......Page 620
12.5.1 Importance of Canonical Variates......Page 626
12.6 Complete Example of Canonical Correlation......Page 627
12.6.1 Evaluation of Assumptions......Page 628
12.6.2 Canonical Correlation......Page 630
12.7.2 IBM SPSS Package......Page 644
12.7.3 SYSTAT System......Page 646
13.1 General Purpose and Description......Page 647
13.2.1 Number of Factors......Page 650
13.3.1 Theoretical Issues......Page 651
13.3.2 Practical Issues......Page 652
13.4 Fundamental Equations for Factor Analysis......Page 655
13.4.1 Extraction......Page 657
13.4.2 Orthogonal Rotation......Page 660
13.4.3 Communalities, Variance, and Covariance......Page 661
13.4.4 Factor Scores......Page 662
13.4.5 Oblique Rotation......Page 665
13.4.6 Computer Analyses of Small-Sample Example......Page 667
13.5.1 Factor Extraction Techniques......Page 672
13.5.2 Rotation......Page 677
13.6 Some Important Issues......Page 682
13.6.2 Adequacy of Extraction and Number of Factors......Page 683
13.6.3 Adequacy of Rotation and Simple Structure......Page 686
13.6.4 Importance and Internal Consistency of Factors......Page 687
13.6.5 Interpretation of Factors......Page 689
13.6.6 Factor Scores......Page 690
13.7 Complete Example of FA......Page 691
13.7.1 Evaluation of Limitations......Page 692
13.7.2 Principal Factors Extraction With Varimax Rotation......Page 696
13.8.2 SAS System......Page 711
13.8.3 SYSTAT System......Page 715
14.1 General Purpose and Description......Page 716
14.2.5 Parameter Estimates......Page 720
14.2.8 Longitudinal Differences......Page 721
14.3.1 Theoretical Issues......Page 722
14.3.2 Practical Issues......Page 723
14.4.1 Covariance Algebra......Page 724
14.4.2 Model Hypotheses......Page 726
14.4.3 Model Specification......Page 728
14.4.4 Model Estimation......Page 730
14.4.5 Model Evaluation......Page 734
14.4.6 Computer Analysis of Small-Sample Example......Page 736
14.5.1 Model Identification......Page 749
14.5.2 Estimation Techniques......Page 752
14.5.3 Assessing the Fit of the Model......Page 755
14.5.4 Model Modification......Page 761
14.5.5 Reliability and Proportion of Variance......Page 768
14.5.6 Discrete and Ordinal Data......Page 769
14.5.7 Multiple Group Models......Page 770
14.5.8 Mean and Covariance Structure Models......Page 771
14.6.1 Confirmatory Factor Analysis of the WISC......Page 772
14.6.2 SEM of Health Data......Page 790
14.7.2 LISREL......Page 813
14.7.4 SAS System......Page 820
15.1 General Purpose and Description......Page 821
15.2.3 Cross-Level Interactions......Page 824
15.2.8 Path Analysis at Individual and Group Levels......Page 825
15.3.1 Theoretical Issues......Page 826
15.3.2 Practical Issues......Page 827
15.4 Fundamental Equations......Page 829
15.4.1 Intercepts-Only Model......Page 832
15.4.2 Model With a First-Level Predictor......Page 837
15.4.3 Model With Predictors at First and Second Levels......Page 846
15.5.1 Repeated Measures......Page 853
15.5.3 Latent Variables......Page 858
15.5.4 Nonnormal Outcome Variables......Page 859
15.5.5 Multiple Response Models......Page 860
15.6.1 Intraclass Correlation......Page 861
15.6.2 Centering Predictors and Changes in Their Interpretations......Page 862
15.6.4 Random and Fixed Intercepts and Slopes......Page 865
15.6.5 Statistical Inference......Page 869
15.6.6 Effect Size......Page 871
15.6.7 Estimation Techniques and Convergence Problems......Page 872
15.6.8 Exploratory Model Building......Page 873
15.7.1 Evaluation of Assumptions......Page 874
15.7.2 Multilevel Modeling......Page 879
15.8.1 SAS System......Page 891
15.8.3 HLM Program......Page 895
15.8.5 SYSTAT System......Page 896
16.1 General Purpose and Description......Page 897
16.2.1 Associations Among Variables......Page 898
16.2.5 Effect Size......Page 899
16.3.2 Practical Issues......Page 900
16.4 Fundamental Equations for Multiway Frequency Analysis......Page 902
16.4.1 Screening for Effects......Page 903
16.4.2 Modeling......Page 910
16.4.3 Evaluation and Interpretation......Page 913
16.4.4 Computer Analyses of Small-Sample Example......Page 918
16.5.2 Statistical Criteria......Page 925
16.5.3 Strategies for Choosing a Model......Page 926
16.6.2 Hierarchical Log-Linear Analysis......Page 928
16.7 Comparison of Programs......Page 945
16.7.1 IBM SPSS Package......Page 948
16.7.3 SYSTAT System......Page 949
17.2.1 Bivariate Form......Page 950
17.2.2 Simple Multivariate Form......Page 951
17.2.3 Full Multivariate Form......Page 954
17.3 Alternative Research Strategies......Page 957
Appendix A: A Skimpy Introduction to Matrix Algebra......Page 962
A.3 Multiplication or Division of a Matrix by a Constant......Page 963
A.5 Multiplication, Transposes, and Square Roots of Matrices......Page 964
A.6 Matrix “Division” (Inverses and Determinants)......Page 966
A.7 Eigenvalues and Eigenvectors: Procedures for Consolidating Variance From a Matrix......Page 968
B.1 Women’s Health and Drug Study......Page 972
B.2 Sexual Attraction Study......Page 973
B.3 Learning Disabilities Data Bank......Page 976
B.5 Field Studies of Noise-Induced Sleep Disturbance......Page 977
B.7 Impact of Seat Belt Law......Page 978
Appendix C: Statistical Tables......Page 979
C.1 Normal Curve Areas......Page 980
C.2 Critical Values of the t Distribution for α = .05 and .01, Two-Tailed Test......Page 981
C.3 Critical Values of the F Distribution......Page 982
C.4 Critical Values of Chi Square (X[sup(2)])......Page 987
C.5 Critical Values for Squared Multiple Correlation (R[sup(2)]) in Forward Stepwise Selection: α = .05......Page 988
C.6 Critical Values for F[sub(MAX)] (S[sup(2)] MAX/S[sup(2)] [sub(MIN)]) Distribution for α =.05 and .01......Page 990
References......Page 991
C......Page 1000
D......Page 1001
E......Page 1002
F......Page 1003
I......Page 1004
M......Page 1007
N......Page 1009
O......Page 1010
P......Page 1012
S......Page 1013
T......Page 1017
Z......Page 1018