Using multivariate statistics:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston ; Munich [u.a.]
Pearson
2007
|
| Ausgabe: | 5. ed., internat. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XXVIII, 980 S. graph. Darst. |
| ISBN: | 0205465250 0205459382 9780205465255 |
Internformat
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| 100 | 1 | |a Tabachnick, Barbara G. |d 1936- |e Verfasser |0 (DE-588)131432389 |4 aut | |
| 245 | 1 | 0 | |a Using multivariate statistics |c Barbara G. Tabachnick ; Linda S. Fidell |
| 250 | |a 5. ed., internat. ed. | ||
| 264 | 1 | |a Boston ; Munich [u.a.] |b Pearson |c 2007 | |
| 300 | |a XXVIII, 980 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Analyse multivariée | |
| 650 | 7 | |a Analyse multivariée |2 rasuqam | |
| 650 | 7 | |a Análise multivariada |2 larpcal | |
| 650 | 4 | |a Análisis multivariable | |
| 650 | 7 | |a Estatística |2 larpcal | |
| 650 | 4 | |a Statistique mathématique | |
| 650 | 7 | |a Statistique mathématique |2 rasuqam | |
| 650 | 4 | |a Multivariate analysis | |
| 650 | 0 | 7 | |a Multivariate Analyse |0 (DE-588)4040708-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Statistik |0 (DE-588)4056995-0 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804138017827323904 |
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| adam_text | FIFTH EDITION USING MULTIVARIATE STATISTICS BARBARA G. TABACHNICK
CALIFORNIA STATE UNIVERSITY, NORTHRIDGE LINDA S. FIDELL CALIFORNIA STATE
UNIVERSITY, NORTHRIDGE BOSTON * NEW YORK * SAN FRANCISCO MEXICO CITY *
MONTREAL * TORONTO * LONDON * MADRID * MUNICH * PARIS HONG KONG *
SINGAPORE * TOKYO * CAPE TOWN * SYDNEY CONTENTS PREFACE XXVII
INTRODUCTION 1 1.1 MULTIVARIATE STATISTICS: WHY? 1 1.1.1 THE DOMAIN OF
MULTIVARIATE STATISTICS: NUMBERS OF IVS AND DVS 1 1.1.2 EXPERIMENTAL AND
NONEXPERIMENTAL RESEARCH 2 1.1.3 COMPUTERS AND MULTIVARIATE STATISTICS 4
1.1.4 GARBAGE IN, ROSES OUT? 5 1.2 SOME USEFUL DEFINITIONS 5 1.2.1
CONTINUOUS, DISCRETE, AND DICHOTOMOUS DATA 5 1.2.2 SAMPLES AND
POPULATIONS 7 1.2.3 DESCRIPTIVE AND INFERENTIAL STATISTICS 7 1.2.4
ORTHOGONALITY: STANDARD AND SEQUENTIAL ANALYSES 8 1.3 LINEAR
COMBINATIONS OF VARIABLES 10 1.4 NUMBER AND NATUREOF VARIABLES TOLNCLUDE
11 1.5 STATISTICAL POWER 11 1.6 DATA APPROPRIATE FOR MULTIVARIATE
STATISTICS 12 1.6.1 THE DATA MATRIX 12 1.6.2 THE CORRELATION MATRIX 13
1.6.3 THE VARIANCE-COVARIANCE MATRIX 14 1.6.4 THE SUM-OF-SQUARES AND
CROSS-PRODUCTS MATRIX 14 1.6.5 RESIDUAIS 16 1.7 ORGANIZATION OF THE BOOK
16 A GUIDE TO STATISTICAL TECHNIQUES: USING THE BOOK 17 2.1 RESEARCH
QUESTIONS AND ASSOCIATED TECHNIQUES 17 2.1.1 DEGREE OF RELATIONSHIP
AMONG VARIABLES 17 2.1.1.1 BIVARIATER 17 2.1.1.2 MULTIPLE/? 18 2.1.1.3
SEQUENTIAL/? 18 2.1.1.4 CANONICAL/? 18 2.1.1.5 MULTIWAY FREQUENCY
ANALYSIS 19 2.1.1.6 MULTILEVEL MODELING 19 CONTENTS 2.1.2 SIGNIFICANCE
OF GROUP DIFFERENCES 19 2.1.2.1 ONE-WAY ANOVA AND T TEST 19 2.1.2.2
ONE-WAY ANCOVA 20 2.1.2.3 FACTORIAL ANOVA 20 2.1.2.4 FACTORIAL ANCOVA 20
2.1.2.5 HOTELLING S T 2 21 2.1.2.6 ONE-WAY MANOVA 21 2.1.2.7 ONE-WAY
MANCOVA 21 2.1.2.8 FACTORIAL MANOVA 22 2.1.2.9 FACTORIAL MANCOVA 22
2.1.2.10 PROFILE ANALYSIS OF REPEATED MEASURES 23 2.1.3 PREDICTION OF
GROUP MEMBERSHIP 23 2.1.3.1 ONE-WAY DISCRIMINANT 23 2.1.3.2 SEQUENTIAL
ONE-WAY DISCRIMINANT 24 2.1.3.3 MULTIWAY FREQUENCY ANALYSIS (LOGIT) 24
2.1.3.4 LOGISTIC REGRESSION 24 2.1.3.5 SEQUENTIAL LOGISTIC REGRESSION 25
2.1.3.6 FACTORIAL DISCRIMINANT ANALYSIS 25 2.1.3.7 SEQUENTIAL FACTORIAL
DISCRIMINANT ANALYSIS 25 2.1.4 STRUCTURE 25 2.1.4.1 PRINCIPAL COMPONENTS
25 2.1.4.2 FACTOR ANALYSIS 26 2.1.4.3 STRUCTURAL EQUATION MODELING 26
2.1.5 TIME COURSE OF EVENTS 26 2.1.5.1 SURVIVAL/FAILURE ANALYSIS 26
2.1.5.2 TIME-SERIES ANALYSIS 27 2.2 SOME FURTHER COMPARISONS 27 2.3 A
DECISION TREE 28 2.4 TECHNIQUE CHAPTERS 31 2.5 PRELIMINARY CHECK OF THE
DATA 32 REVIEW OF UNIVARIATE AND BIVARIATE STATISTICS 33 3.1 HYPOTHESIS
TESTING 33 3.1.1 ONE-SAMPLE Z TEST AS PROTOTYPE 33 3.1.2 POWER 36 3.1.3
EXTENSIONS OF THE MODEL 37 3.1.4 CONTROVERSY SURROUNDMG SIGNIFICANCE
TESTING 37 3.2 ANALYSIS OFVARIANCE 37 3.2.1 ONE-WAY BETWEEN-SUBJECTS
ANOVA 39 3.2.2 FACTORIAL BETWEEN-SUBJECTS ANOVA 42 3.2.3 WITHIN-SUBJECTS
ANOVA 43 3.2.4 MIXED BETWEEN-WITHIN-SUBJECTS ANOVA 46 CONTENTS 3.2.5
DESIGN COMPLEXITY 47 3.2.5.1 NESTING 47 3.2.5.2 LATIN-SQUARE DESIGNS 47
3.2.5.3 UNEQUAL N AND NONORTHOGONALITY 48 3.2.5.4 FIXED AND RANDOM
EFFECTS 49 3.2.6 SPECIFIC COMPARISONS 49 3.2.6.1 WEIGHTING COEFFICIENTS
FOR COMPARISONS 50 3.2.6.2 ORTHOGONALITYOF WEIGHTING COEFFICIENTS 50
3.2.6.3 OBTAINED F FOR COMPARISONS 51 3.2.6.4 CRITICAL F FOR PLANNED
COMPARISONS 52 3.2.6.5 CRITICAL F FOR POST HOC COMPARISONS 53 3.3
PARAMETER ESTIMATION 53 3.4 EFFECT SIZE 54 3.5 BIVARIATE STATISTICS:
CORRELATION AND REGRESSION 56 3.5.1 CORRELATION 56 3.5.2 REGRESSION 57
3.6 CHI-SQUARE ANALYSIS 58 CLEANING UP YOUR ACT: SCREENING DATA PRIOR TO
ANALYSIS 60 4.1 IMPORTANT ISSUES IN DATA SCREENING 61 4.1.1 ACCURACY OF
DATA FILE 61 4.1.2 HONEST CORRELATIONS 61 4.1.2.1 INFLATED CORRELATION
61 4.1.2.2 DEFLATED CORRELATION 61 4.1.3 MISSING DATA 62 4.1.3.1
DELETING CASES OR VARIABLES 63 4.1.3.2 ESTIMATING MISSINGDATA 66 4.1.3.3
USING A MISSING DATA CORRELATION MATRIX 70 4.1.3.4 TREATING MISSING DATA
AS DATA 71 4.1.3.5 REPEATING ANALYSES WITH AND WITHOUT MISSING DATA
4.1.3.6 CHOOSING AMONG METHODS FOR DEALING WITH MISSING DATA 71 4.1.4
OUTLIERS 72 4.1.4.1 DETECTING UNIVARIATE AND MULTIVARIATE OUTLIERS 73
4.1.4.2 DESCRIBING OUTLIERS 76 4.1.4.3 REDUCING THE INFLUENCE OF
OUTLIERS 77 4.1.4.4 OUTLIERS IN A SOLUTION 77 4.1.5 NORMALITY,
LINEARITY, AND HOMOSCEDASTICITY 78 4.1.5.1 NORMALITY 79 4.1.5.2
LINEARITY 83 4.1.5.3 HOMOSCEDASTICITY, HOMOGENEITY OFVARIANCE, AND
HOMOGENEITY OF VARIANCE-COVARIANCE MATRICES 85 CONTENTS 4.1.6 COMMON
DATA TRANSFORMATIONS 86 4.1.7 MULTICOLLINEARITY AND SINGULARITY 88 4.1.8
A CHECKLIST AND SOME PRACTICAL RECOMMENDATIONS 91 4.2 COMPLETE EXAMPLES
OF DATA SCREENING 92 4.2.1 SCREENING UNGROUPED DATA 92 4.2.1.1 ACCURACY
OF INPUT, MISSING DATA, DISTRIBUTIONS, AND UNIVARIATE OUTLIERS 93
4.2.1.2 LINEARITY AND HOMOSCEDASTICITY 96 4.2.1.3 TRANSFORMATION 98
4.2.1.4 DETECTING MULTIVARIATE OUTLIERS 99 4.2.1.5 VARIABLES CAUSING
CASES TO BE OUTLIERS 100 4.2.1.6 MULTICOLLINEARITY 104 4.2.2 SCREENING
GROUPED DATA 105 4.2.2.1 ACCURACY OF INPUT, MISSING DATA, DISTRIBUTIONS,
HOMOGENEITY OF VARIANCE, AND UNIVARIATE OUTLIERS 105 4.2.2.2 LINEARITY
110 4.2.2.3 MULTIVARIATE OUTLIERS 111 4.2.2.4 VARIABLES CAUSING CASES TO
BE OUTLIERS 113 4.2.2.5 MULTICOLLINEARITY 114 MULTIPLE REGRESSION 117
5.1 GENERAL PURPOSE AND DESCRIPTION 117 5.2 KINDS OF RESEARCH QUESTIONS
118 5.2.1 DEGREE OF RELATIONSHIP 119 5.2.2 IMPORTANCE OF IVS 119 5.2.3
ADDINGIVS 119 5.2.4 CHANGING IVS 120 5.2.5 CONTINGENCIES AMONG IVS 120
5.2.6 COMPARING SETS OF IVS 120 5.2.7 PREDICTING DV SCORES FOR MEMBERS
OFA NEW SAMPLE 120 5.2.8 PARAMETER ESTIMATES 121 5.3 LIMITATIONS TO
REGRESSION ANALYSES 121 5.3.1 THEORETICAL ISSUES 122 5.3.2 PRACTICAL
ISSUES 123 5.3.2.1 RATIO OF CASES TO IVS 123 5.3.2.2 ABSENCE OF OUTLIERS
AMONG THE IVS AND ON THE DV 124 5.3.2.3 ABSENCE OF MULTICOLLINEARITY AND
SINGULARITY 124 5.3.2.4 NORMALITY, LINEARITY, HOMOSCEDASTICITY OF
RESIDUALS 125 5.3.2.5 INDEPENDENCEOF ERRORS 128 5.3.2.6 ABSENCE OF
OUTLIERS IN THE SOLUTION 128 5.4 FUNDAMENTAL EQUATIONS FOR MULTIPLE
REGRESSION 128 5.4.1 GENERAL LINEAR EQUATIONS 129 5.4.2 MATRIX EQUATIONS
131 5.4.3 COMPUTER ANALYSES OF SMALL-SAMPLE EXAMPLE 134 CONTENTS VII 5.5
MAJOR TYPES OF MULTIPLE REGRESSION 136 5.5.1 STANDARD MULTIPLE
REGRESSION 136 5.5.2 SEQUENTIAL MULTIPLE REGRESSION 138 5.5.3
STATISTICAL (STEPWISE) REGRESSION 138 5.5.4 CHOOSING AMONG REGRESSION
STRATEGIES 143 5.6 SOME IMPORTANT ISSUES 144 5.6.1 IMPORTANCE OF IVS 144
5.6.1.1 STANDARD MULTIPLE REGRESSION 146 5.6.1.2 SEQUENTIAL OR
STATISTICAL REGRESSION 146 5.6.2 STATISTICAL INFERENCE 146 5.6.2.1 TEST
FOR MULTIPLEI? 147 5.6.2.2 TEST OF REGRESSION COMPONENTS 148 5.6.2.3
TEST OF ADDED SUBSET OF IVS 149 5.6.2.4 CONFIDENCE LIMITS AROUND B AND
MULTIPLE R 2 150 5.6.2.5 COMPARING TWO SETS OF PREDICTORS 152 5.6.3
ADJUSTMENTOFTF 2 153 5.6.4 SUPPRESSOR VARIABLES 154 5.6.5 REGRESSION
APPROACH TO ANOVA 155 5.6.6 CENTERING WHEN INTERACTIONS AND POWERS OF
IVS ARE INCLUDED 157 5.6.7 MEDIATION IN CAUSAL SEQUENCES 159 5.7
COMPLETE EXAMPLES OF REGRESSION ANALYSIS 161 5.7.1 EVALUATION OF
ASSUMPTIONS 161 5.7.1.1 RATIO OFCASESTO IVS 161 5.7.1.2 NORMALITY,
LINEARITY, HOMOSCEDASTICITY, AND INDEPENDENCE OF RESIDUAIS 161 5.7.1.3
OUTLIERS 165 5.7.1.4 MULTICOLLINEARITY AND SINGULARITY 167 5.7.2
STANDARD MULTIPLE REGRESSION 167 5.7.3 SEQUENTIAL REGRESSION 174 5.7.4
EXAMPLE OF STANDARD MULTIPLE REGRESSION WITH MISSING VALUES MULTIPLY
IMPUTED 179 5.8 COMPARISON OF PROGRAMS 188 5.8.1 SPSSPACKAGE 188 5.8.2
SAS SYSTEM 191 5.8.3 SYSTAT SYSTEM 194 ANALYSIS OF COVARIANCE 195 6.1
GENERAL PURPOSE AND DESCRIPTION 195 6.2 KINDS OF RESEARCH QUESTIONS 198
6.2.1 MAIN EFFECTS OF IVS 198 6.2.2 INTERACTIONS AMONG IVS 198 6.2.3
SPECIFIC COMPARISONS AND TREND ANALYSIS 199 6.2.4 EFFECTS OFCOVARIATES
199 CONTENTS 6.2.5 EFFECT SIZE 199 6.2.6 PARAMETER ESTIMATES 199 6.3
LIMITATIONS TO ANALYSIS OF COVARIANCE 200 6.3.1 THEORETICAL ISSUES 200
6.3.2 PRACTICAL ISSUES 201 6.3.2.1 UNEQUAL SAMPLE SIZES, MISSING DATA,
AND RATIO OF CASES TO IVS 201 6.3.2.2 ABSENCEOFOUTLIERS 201 6.3.2.3
ABSENCE OF MULTICOLLINEARITY AND SINGULARITY 201 6.3.2.4 NORMALITY OF
SAMPLING DISTRIBUTIONS 202 6.3.2.5 HOMOGENEITY OF VARIANCE 202 6.3.2.6
LINEARITY 202 6.3.2.7 HOMOGENEITY OF REGRESSION 202 6.3.2.8 RELIABILITY
OF COVARIATES 203 6.4 FUNDAMENTAL EQUATIONS FOR ANALYSIS OF COVARIANCE
203 6.4.1 SUMS OF SQUARES AND CROSS PRODUCTS 204 6.4.2 SIGNIFTCANCE TEST
AND EFFECT SIZE 208 6.4.3 COMPUTER ANALYSES OF SMALL-SAMPLE EXAMPLE 209
6.5 SOME IMPORTANT ISSUES 211 6.5.1 CHOOSING COVARIATES 211 6.5.2
EVALUATION OF COVARIATES 212 6.5.3 TEST FOR HOMOGENEITY OF REGRESSION
213 6.5.4 DESIGN COMPLEXITY 213 6.5.4.1 WITHIN-SUBJECTS AND MIXED
WITHIN-BETWEEN DESIGNS 214 6.5.4.2 UNEQUAL SAMPLE SIZES 217 6.5.4.3
SPECIFIC COMPARISONS AND TREND ANALYSIS 218 6.5.4.4 EFFECT SIZE 221
6.5.5 ALTERNATIVES TOANCOVA 221 6.6 COMPLETE EXAMPLE OF ANALYSIS OF
COVARIANCE 223 6.6.1 EVALUATION OF ASSUMPTIONS 223 6.6.1.1 UNEQUAL N AND
MISSING DATA 224 6.6.1.2 NORMALITY 224 6.6.1.3 LINEARITY 224 6.6.1.4
OUTLIERS 224 6.6.1.5 MULTICOLLINEARITY AND SINGULARITY 227 6.6.1.6
HOMOGENEITY OF VARIANCE 228 6.6.1.7 HOMOGENEITY OF REGRESSION 230
6.6.1.8 RELIABILITY OF COVARIATES 230 6.6.2 ANALYSIS OF COVARIANCE 230
6.6.2.1 MAIN ANALYSIS 230 6.6.2.2 EVALUATION OF COVARIATES 235 6.6.2.3
HOMOGENEITY OF REGRESSION RUN 237 6.7 COMPARISON OF PROGRAMS 240 6.7.1
SPSS PACKAGE 240 CONTENTS 6.7.2 SAS SYSTEM 240 6.7.3 SYSTAT SYSTEM 240
MULTIVARIATE ANALYSIS OF VARIANCE AND COVARIANCE 243 7.1 GENERAL PURPOSE
AND DESCRIPTION 243 7.2 KINDS OF RESEARCH QUESTIONS 247 7.2.1 MAIN
EFFECTS OFIVS 247 7.2.2 INTERACTIONS AMONG IVS 247 7.2.3 IMPORTANCEOFDVS
247 7.2.4 PARAMETER ESTIMATES 248 7.2.5 SPECIFIC COMPARISONS AND TREND
ANALYSIS 248 7.2.6 EFFECT SIZE 248 7.2.7 EFFECTS OFCOVARIATES 248 7.2.8
REPEATED-MEASURES ANALYSIS OF VARIANCE 249 7.3 LIMITATIONS TO
MULTIVARIATE ANALYSIS OF VARIANCE AND COVARIANCE 249 7.3.1 THEORETICAL
ISSUES 249 7.3.2 PRACTICAL ISSUES 250 7.3.2.1 UNEQUAL SAMPLE SIZES,
MISSING DATA, AND POWER 250 7.3.2.2 MULTIVARIATE NORMALITY 251 7.3.2.3
ABSENCEOFOUTLIERS 251 7.3.2.4 HOMOGENEITY OFVARIANCE-COVARIANCEMATRICES
251 7.3.2.5 LINEARITY 252 7.3.2.6 HOMOGENEITY OF REGRESSION 252 7.3.2.7
RELIABILITY OFCOVARIATES 253 7.3.2.8 ABSENCE OF MULTICOLLINEARITY AND
SINGULARITY 253 7.4 FUNDAMENTAL EQUATIONS FOR MULTIVARIATE ANALYSIS OF
VARIANCE AND COVARIANCE 253 7.4.1 MULTIVARIATE ANALYSIS OF VARIANCE 253
7.4.2 COMPUTER ANALYSES OF SMALL-SAMPLE EXAMPLE 261 7.4.3 MULTIVARIATE
ANALYSIS OF COVARIANCE 264 7.5 SOME IMPORTANT ISSUES 268 7.5.1 MANOVA
VS. ANOVAS 268 7.5.2 CRITERIA FOR STATISTICAL INFERENCE 269 7.5.3
ASSESSING DVS 270 7.5.3.1 UNIVARIATEF 270 7.5.3.2 ROY-BARGMANN STEPDOWN
ANALYSIS 271 7.5.3.3 USING DISCRIMINANT ANALYSIS 272 7.5.3.4 CHOOSING
AMONG STRATEGIES FOR ASSESSING DVS 273 7.5.4 SPECIFIC COMPARISONS AND
TREND ANALYSIS 273 7.5.5 DESIGN COMPLEXITY 274 7.5.5.1 WITHIN-SUBJECTS
AND BETWEEN-WITHIN DESIGNS 274 7.5.5.2 UNEQUAL SAMPLE SIZES 276 CONTENTS
7.6 COMPLETE EXAMPLES OF MULTIVARIATE ANALYSIS OF VARIANCE AND
COVARIANCE 277 7.6.1 EVALUATION OF ASSUMPTIONS 277 7.6.1.1 UNEQUAL
SAMPLE SIZES AND MISSING DATA 277 7.6.1.2 MULTIVARIATE NORMALITY 279
7.6.1.3 LINEARITY 279 7.6.1.4 OUTLIERS 279 7.6.1.5 HOMOGENEITY OF
VARIANCE-COVARIANCE MATRICES 280 7.6.1.6 HOMOGENEITY OF REGRESSION 281
7.6.1.7 RELIABILITY OF COVARIATES 284 7.6.1.8 MULTICOLLINEARITY AND
SINGULARITY 285 7.6.2 MULTIVARIATE ANALYSIS OF VARIANCE 285 7.6.3
MULTIVARIATE ANALYSIS OF COVARIANCE 296 7.6.3.1 ASSESSING COVARIATES 296
7.6.3.2 ASSESSING DVS 296 7.7 COMPARISON OF PROGRAMS 307 7.7.1
SPSSPACKAGE 307 7.7.2 SAS SYSTEM 310 7.7.3 SYSTAT SYSTEM 310 PROFILE
ANALYSIS: THE MULTIVARIATE APPROACH TO REPEATED MEASURES 311 8.1 GENERAL
PURPOSE AND DESCRIPTION 311 8.2 KINDS OF RESEARCH QUESTIONS 312 8.2.1
PARALLELISMOF PROFILES 312 8.2.2 OVERALL DIFFERENCE AMONG GROUPS 8.2.3
FLATNESSOF PROFILES 313 8.2.4 CONTRASTS FOLLOWING PROFILE ANALYSIS 8.2.5
PARAMETER ESTIMATES 313 8.2.6 EFFECT SIZE 314 8.3 LIMITATIONS TO PROFILE
ANALYSIS 314 8.3.1 THEORETICAL ISSUES 314 8.3.2 PRACTICAL ISSUES 315
8.3.2.1 SAMPLE SIZE, MISSING DATA, AND POWER 315 8.3.2.2 MULTIVARIATE
NORMALITY 315 8.3.2.3 ABSENCE OF OUTLIERS 315 8.3.2.4 HOMOGENEITY OF
VARIANCE-COVARIANCE MATRICES 315 8.3.2.5 LINEARITY 316 8.3.2.6 ABSENCE
OF MULTICOLLINEARITY AND SINGULARITY 316 8.4 FUNDAMENTAL EQUATIONS FOR
PROFILE ANALYSIS 316 8.4.1 DIFFERENCES IN LEVELS 316 8.4.2 PARALLELISM
318 313 313 CONTENTS XI 8.4.3 FLATNESS 321 8.4.4 COMPUTER ANALYSES OF
SMALL-SAMPLE EXAMPLE 323 8.5 SOME IMPORTANT ISSUES 329 8.5.1 UNIVARIATE
VS. MULTIVARIATE APPROACH TO REPEATED MEASURES 329 8.5.2 CONTRASTS IN
PROFILE ANALYSIS 331 8.5.2.1 PARALLELISM AND FLATNESS SIGNIFICANT,
LEVELS NOT SIGNIFICANT (SIMPLE-EFFECTS ANALYSIS) 333 8.5.2.2 PARALLELISM
AND LEVELS SIGNIFICANT, FLATNESS NOT SIGNIFICANT (SIMPLE-EFFECTS
ANALYSIS) 336 8.5.2.3 PARALLELISM, LEVELS, AND FLATNESS SIGNIFICANT
(INTERACTION CONTRASTS) 339 8.5.2.4 ONLY PARALLELISM SIGNIFICANT 339
8.5.3 DOUBLY-MULTIVARIATE DESIGNS 339 8.5.4 CLASSIFYING PROFILES 345
8.5.5 IMPUTATION OF MISSING VALUES 345 8.6 COMPLETE EXAMPLES OF PROFILE
ANALYSIS 346 8.6.1 PROFILE ANALYSIS OF SUBSCALES OF THE WISC 346 8.6.1.1
EVALUATION OF ASSUMPTIONS 346 8.6.1.2 PROFILE ANALYSIS 351 8.6.2
DOUBLY-MULTIVARIATE ANALYSIS OF REACTION TIME 360 8.6.2.1 EVALUATION OF
ASSUMPTIONS 360 8.6.2.2 DOUBLY-MULTIVARIATE ANALYSIS OF SLOPE AND
INTERCEPT 363 8.7 COMPARISON OF PROGRAMS 371 8.7.1 SPSSPACKAGE 373 8.7.2
SAS SYSTEM 373 8.7.3 SYSTAT SYSTEM 374 DISCRIMINANT ANALYSIS 375 9.1
GENERAL PURPOSE AND DESCRIPTION 375 9.2 KINDS OF RESEARCH QUESTIONS 378
9.2.1 SIGNIFICANCE OF PREDICTION 378 9.2.2 NUMBER OF SIGNIFICANT
DISCRIMINANT FUNCTIONS 378 9.2.3 DIMENSIONS OF DISCRIMINATION 379 9.2.4
CLASSIFICATION FUNCTIONS 379 9.2.5 ADEQUACYOF CLASSIFICATION 379 9.2.6
EFFECT SIZE 379 9.2.7 IMPORTANCE OF PREDICTOR VARIABLES 380 9.2.8
SIGNIFICANCE OF PREDICTION WITH COVARIATES 380 9.2.9 ESTIMATION OF GROUP
MEANS 380 9.3 LIMITATIONS TO DISCRIMINANT ANALYSIS 381 9.3.1 THEORETICAL
ISSUES 381 XUE CONTENTS 9.3.2 PRACTICAL ISSUES 381 9.3.2.1 UNEQUAL SAMPLE
SIZES, MISSING DATA, AND POWER 381 9.3.2.2 MULJIVARIATE NORMALITY 382
9.3.2.3 ABSENCEOFOUTLIERS 382 9.3.2.4 HOMOGENEITY
OFVARIANCE-COVARIANCEMATRICES 382 9.3.2.5 LINEARITY 383 9.3.2.6 ABSENCE
OF MULTICOLLINEARITY AND SINGULARITY 383 9.4 FUNDAMENTAL EQUATIONS FOR
DISCRIMINANT ANALYSIS 384 9.4.1 DERIVATION AND TEST OF DISCRIMINANT
FUNCTIONS 384 9.4.2 CLASSIFICATION 387 9.4.3 COMPUTER ANALYSES OF
SMALL-SAMPLE EXAMPLE 389 9.5 TYPES OF DISCRIMINANT FUNCTION ANALYSES 395
9.5.1 DIRECT DISCRIMINANT ANALYSIS 395 9.5.2 SEQUENTIAL DISCRIMINANT
ANALYSIS 396 9.5.3 STEPWISE (STATISTICAL) DISCRIMINANT ANALYSIS 396 9.6
SOME IMPORTANT ISSUES 397 9.6.1 STATISTICAL INFERENCE 397 9.6.1.1
CRITERIA FOR OVERALL STATISTICAL SIGNIFICANCE 397 9.6.1.2 STEPPING
METHODS 397 9.6.2 NUMBER OF DISCRIMINANT FUNCTIONS 398 9.6.3
INTERPRETING DISCRIMINANT FUNCTIONS 398 9.6.3.1 DISCRIMINANT FUNCTION
PLOTS 398 9.6.3.2 STRUCTURE MATRIX OFLOADINGS 400 9.6.4 EVALUATING
PREDICTOR VARIABLES 401 9.6.5 EFFECT SIZE 402 9.6.6 DESIGN COMPLEXITY:
FACTORIAL DESIGNS 403 9.6.7 USE OF CLASSIFICATION PROCEDURES 404 9.6.7.1
CROSS-VALIDATION AND NEW CASES 405 9.6.7.2 JACKKNIFED CLASSIFICATION 405
9.6.7.3 EVALUATING IMPROVEMENT IN CLASSIFICATION 405 9.7 COMPLETE
EXAMPLE OF DISCRIMINANT ANALYSIS 407 9.7.1 EVALUATION OF ASSUMPTIONS 407
9.7.1.1 UNEQUAL SAMPLE SIZES AND MISSING DATA 407 9.7.1.2 MULTIVARIATE
NORMALITY 408 9.7.1.3 LINEARITY 408 9.7.1.4 OUTLIERS 408 9.7.1.5
HOMOGENEITY OFVARIANCE-COVARIANCEMATRICES 411 9.7.1.6 MULTICOLLINEARITY
AND SINGULARITY 411 9.7.2 DIRECT DISCRIMINANT ANALYSIS 412 9.8
COMPARISON OF PROGRAMS 430 9.8.1 SPSSPACKAGE 430 9.8.2 SAS SYSTEM 430
9.8.3 SYSTAT SYSTEM 436 CONTENTS XIII LOGISTIC REGRESSION 437 10.1
GENERAL PURPOSE AND DESCRIPTION 437 10.2 KINDS OF RESEARCH QUESTIONS 439
10.2.1 PREDICTION OF GROUP MEMBERSHIP OR OUTCOME 439 10.2.2 IMPORTANCE
OFPREDICTORS 439 10.2.3 INTERACTIONS AMONG PREDICTORS 440 10.2.4
PARAMETER ESTIMATES 440 10.2.5 CLASSIFICATION OF CASES 440 10.2.6
SIGNIFICANCE OF PREDICTION WITH COVARIATES 440 10.2.7 EFFECT SIZE 441
10.3 LIMITATIONS TO LOGISTIC REGRESSION ANALYSIS 441 10.3.1 THEORETICAL
ISSUES 441 10.3.2 PRACTICAL ISSUES 442 10.3.2.1 RATIO OF CASES TO
VARIABLES 442 10.3.2.2 ADEQUACY OF EXPECTED FREQUENCIES AND POWER 442
10.3.2.3 LINEARITY IN THE LOGIT 443 10.3.2.4 ABSENCE OF
MULTICOLLINEARITY 443 10.3.2.5 ABSENCE OF OUTLIERS IN THE SOLUTION 443
10.3.2.6 INDEPENDENCE OF ERRORS 443 10.4 FUNDAMENTAL EQUATIONS FOR
LOGISTIC REGRESSION 444 10.4.1 TESTING AND INTERPRETING COEFFICIENTS 445
10.4.2 GOODNESS-OF-FIT 446 10.4.3 COMPARING MODELS 448 10.4.4
INTERPRETATION AND ANALYSIS OF RESIDUAIS 448 10.4.5 COMPUTER ANALYSES OF
SMALL-SAMPLE EXAMPLE 449 10.5 TYPES OF LOGISTIC REGRESSION 453 10.5.1
DIRECT LOGISTIC REGRESSION 454 10.5.2 SEQUENTIAL LOGISTIC REGRESSION 454
10.5.3 STATISTICAL (STEPWISE) LOGISTIC REGRESSION 454 10.5.4 PROBIT AND
OTHER ANALYSES 456 10.6 SOME IMPORTANT ISSUES 457 10.6.1 STATISTICAL
INFERENCE 457 10.6.1.1 ASSESSING GOODNESS-OF-FIT OF MODELS 457 10.6.1.2
TESTS OFLNDIVIDUAL VARIABLES 459 10.6.2 EFFECT SIZE FOR A MODEL 460
10.6.3 INTERPRETATION OF COEFFICIENTS USING ODDS 461 10.6.4 CODING
OUTCOME AND PREDICTOR CATEGORIES 464 10.6.5 NUMBER AND TYPE OF OUTCOME
CATEGORIES 464 10.6.6 CLASSIFICATION OF CASES 468 10.6.7 HIERARCHICAL
AND NONHIERARCHICAL ANALYSIS 468 CONTENTS 10.6.8 IMPORTANCE OF
PREDICTORS 469 10.6.9 LOGISTIC REGRESSION FOR MATCHED GROUPS 469 10.7
COMPLETE EXAMPLES OF LOGISTIC REGRESSION 469 10.7.1 EVALUATION OF
LIMITATIONS 470 10.7.1.1 RATIO OF CASES TO VARIABLES AND MISSING DATA
470 10.7.1.2 MULTICOLLINEARITY 473 10.7.1.3 OUTLIERS IN THE SOLUTION 474
10.7.2 DIRECT LOGISTIC REGRESSION WITH TWO-CATEGORY OUTCOME AND
CONTINUOUS PREDICTORS 474 10.7.2.1 LIMITATION: LINEARITY IN THE LOGIT
474 10.7.2.2 DIRECT LOGISTIC REGRESSION WITH TWO-CATEGORY OUTCOME 10.7.3
SEQUENTIAL LOGISTIC REGRESSION WITH THREE CATEGORIES OF OUTCOME 481
10.7.3.1 LIMITATIONS OF MULTINOMIAL LOGISTIC REGRESSION 481 10.7.3.2
SEQUENTIAL MULTINOMIAL LOGISTIC REGRESSION 481 10.8 COMPARISONS OF
PROGRAMS 499 10.8.1 SPSSPACKAGE 499 10.8.2 SAS SYSTEM 504 10.8.3 SYSTAT
SYSTEM 504 SURVIVAL/FAILURE ANALYSIS 506 11.1 GENERAL PURPOSE AND
DESCRIPTION 506 11.2 KINDS OF RESEARCH QUESTIONS 507 11.2.1 PROPORTIONS
SURVIVING AT VARIOUS TIMES 507 11.2.2 GROUP DIFFERENCES IN SURVIVAL 508
11.2.3 SURVIVAL TIME WITH COVARIATES 508 11.2.3.1 TREATMENT EFFECTS 508
11.2.3.2 IMPORTANCE OF COVARIATES 508 11.2.3.3 PARAMETER ESTIMATES 508
11.2.3.4 CONTINGENCIES AMONG COVARIATES 508 11.2.3.5 EFFECT SIZE AND
POWER 509 11.3 LIMITATIONS TO SURVIVAL ANALYSIS 509 11.3.1 THEORETICAL
ISSUES 509 11.3.2 PRACTICAL ISSUES 509 11.3.2.1 SAMPLE SIZE AND MISSING
DATA 509 11.3.2.2 NORMALITY OF SAMPLING DISTRIBUTIONS, LINEARITY, AND
HOMOSCEDASTICITY 510 11.3.2.3 ABSENCEOF OUTLIERS 510 11.3.2.4
DIFFERENCES BETWEEN WITHDRAWN AND REMAINING CASES 510 11.3.2.5 CHANGE IN
SURVIVAL CONDITIONS OVER TIME 510 11.3.2.6 PROPORTIONALITY OF HAZARDS
510 11.3.2.7 ABSENCE OF MULTICOLLINEARITY 510 CONTENTS XV 11.4
FUNDAMENTAL EQUATIONS FOR SURVIVAL ANALYSIS 511 11.4.1 LIFETABLES 511
11.4.2 STANDARD ERROR OF CUMULATIVE PROPORTION SURVIVING 513 11.4.3
HAZARD AND DENSITY FUNCTIONS 514 11.4.4 PLOTOFLIFETABLES 515 11.4.5 TEST
FOR GROUP DIFFERENCES 515 11.4.6 COMPUTER ANALYSES OF SMALL-SAMPLE
EXAMPLE 517 11.5 TYPES OF SURVIVAL ANALYSES 524 11.5.1 ACTUARIAL AND
PRODUCT-LIMIT LIFE TABLES AND SURVIVOR FUNCTIONS 524 11.5.2 PREDICTION
OF GROUP SURVIVAL TIMES FROM COVARIATES 524 11.5.2.1 DIRECT, SEQUENTIAL,
AND STATISTICAL ANALYSIS 527 11.5.2.2 COX PROPORTIONAL-HAZARDS MODEL 527
11.5.2.3 ACCELERATED FAILURE-TIME MODELS 529 11.5.2.4 CHOOSING A METHOD
535 11.6 SOME IMPORTANT ISSUES 535 11.6.1 PROPORTIONALITY OF HAZARDS 535
11.6.2 CENSOREDDATA 537 11.6.2.1 RIGHT-CENSORED DATA 537 11.6.2.2
OTHERFORMSOFCENSORING 537 11.6.3 EFFECT SIZE AND POWER 538 11.6.4
STATISTICAL CRITERIA 539 11.6.4.1 TEST STATISTICS FOR GROUP DIFFERENCES
IN SURVIVAL FUNCTIONS 539 11.6.4.2 TEST STATISTICS FOR PREDICTION FROM
COVARIATES 540 11.6.5 PREDICTING SURVIVAL RATE 540 11.6.5.1 REGRESSION
COEFFICIENTS (PARAMETER ESTIMATES) 540 11.6.5.2 ODDSRATIOS 540 11.6.5.3
EXPECTED SURVIVAL RATES 541 11.7 COMPLETE EXAMPLE OF SURVIVAL ANALYSIS
541 11.7.1 EVALUATION OF ASSUMPTIONS 543 11.7.1.1 ACCURACY OF INPUT,
ADEQUACY OF SAMPLE SIZE, MISSING DATA, AND DISTRIBUTIONS 543 11.7.1.2
OUTLIERS 545 11.7.1.3 DIFFERENCES BETWEEN WITHDRAWN AND REMAINING CASES
549 11.7.1.4 CHANGE IN SURVIVAL EXPERIENCE OVER TIME 549 11.7.1.5
PROPORTIONALITY OF HAZARDS 549 11.7.1.6 MULTICOLLINEARITY 551 11.7.2 COX
REGRESSION SURVIVAL ANALYSIS 551 11.7.2.1 EFFECT OFDRUGTREATMENT 552
11.7.2.2 EVALUATION OF OTHER COVARIATES 552 11.8 COMPARISON OF PROGRAMS
559 11.8.1 SAS SYSTEM 559 11.8.2 SPSSPACKAGE 559 11.8.3 SYSTAT SYSTEM
566 CONTENTS CANONICAL CORRELATION 567 12.1 GENERAL PURPOSE AND
DESCRIPTION 567 12.2 KINDS OF RESEARCH QUESTIONS 568 12.2.1 NUMBER OF
CANONICAL VARIATE PAIRS 568 12.2.2 INTERPRETATION OF CANONICAL VARIATES
569 12.2.3 IMPORTANCE OF CANONICAL VARIATES 569 12.2.4 CANONICAL VARIATE
SCORES 569 12.3 LIMITATIONS 569 12.3.1 THEORETICAL LIMITATIONS 569
12.3.2 PRACTICAL ISSUES 570 12.3.2.1 RATIO OFCASESTOIVS 570 12.3.2.2
NORMALITY, LINEARITY, AND HOMOSCEDASTICITY 570 12.3.2.3 MISSINGDATA 571
12.3.2.4 ABSENCE OF OUTLIERS 571 12.3.2.5 ABSENCE OF MULTICOLLINEARITY
AND SINGULARITY 571 12.4 FUNDAMENTAL EQUATIONS FOR CANONICAL CORRELATION
572 12.4.1 EIGENVALUES AND EIGENVECTORS 573 12.4.2 MATRIX EQUATIONS 575
12.4.3 PROPORTIONS OFVARIANCEEXTRACTED 579 12.4.4 COMPUTER ANALYSES OF
SMALL-SAMPLE EXAMPLE 580 12.5 SOME IMPORTANT ISSUES 586 12.5.1
IMPORTANCE OF CANONICAL VARIATES 586 12.5.2 INTERPRETATION OF CANONICAL
VARIATES 587 12.6 COMPLETE EXAMPLE OF CANONICAL CORRELATION 587 12.6.1
EVALUATION OF ASSUMPTIONS 588 12.6.1.1 MISSINGDATA 588 12.6.1.2
NORMALITY, LINEARITY, AND HOMOSCEDASTICITY 588 12.6.1.3 OUTLIERS 591
12.6.1.4 MULTICOLLINEARITY AND SINGULARITY 595 12.6.2 CANONICAL
CORRELATION 595 12.7 COMPARISON OF PROGRAMS 604 12.7.1 SAS SYSTEM 604
12.7.2 SPSSPACKAGE 604 12.7.3 SYSTAT SYSTEM 606 PRINCIPAL COMPONENTS AND
FACTOR ANALYSIS 607 13.1 GENERAL PURPOSE AND DESCRIPTION 607 13.2 KINDS
OF RESEARCH QUESTIONS 610 13.2.1 NUMBER OF FACTORS 610 CONTENTS XVUE
13.2.2 NATURE OF FACTORS 611 13.2.3 IMPORTANCE OF SOLUTIONS AND FACTORS
611 13.2.4 TESTING THEORY IN FA 611 13.2.5 ESTIMATING SCORES ON FACTORS
611 13.3 LIMITATIONS 611 13.3.1 THEORETICAL ISSUES 611 13.3.2 PRACTICAL
ISSUES 612 13.3.2.1 SAMPLE SIZE AND MISSING DATA 613 13.3.2.2 NORMALITY
613 13.3.2.3 LINEARITY 613 13.3.2.4 ABSENCE OF OUTLIERS AMONG CASES 613
13.3.2.5 ABSENCE OF MULTICOLLINEARITY AND SINGULARITY 614 13.3.2.6
FACTORABILITYOFR 614 13.3.2.7 ABSENCE OF OUTLIERS AMONG VARIABLES 614
13.4 FUNDAMENTAL EQUATIONS FOR FACTOR ANALYSIS 615 13.4.1 EXTRACTION 616
13.4.2 ORTHOGONAL ROTATION 620 13.4.3 COMMUNALITIES, VARIANCE, AND
COVARIANCE 621 13.4.4 FACTOR SCORES 622 13.4.5 OBLIQUE ROTATION 625
13.4.6 COMPUTER ANALYSES OF SMALL-SAMPLE EXAMPLE 628 13.5 MAJOR TYPES OF
FACTOR ANALYSES 633 13.5.1 FACTOR EXTRACTION TECHNIQUES 633 13.5.1.1
PCAVS. FA 634 13.5.1.2 PRINCIPAL COMPONENTS 635 13.5.1.3 PRINCIPAL
FACTORS 636 13.5.1.4 IMAGE FACTOR EXTRACTION 636 13.5.1.5 MAXIMUM
LIKELIHOOD FACTOR EXTRACTION 636 13.5.1.6 UNWEIGHTED LEAST SQUARES
FACTORING 636 13.5.1.7 GENERALIZED (WEIGHTED) LEAST SQUARES FACTORING
637 13.5.1.8 ALPHA FACTORING 637 13.5.2 ROTATION 637 13.5.2.1 ORTHOGONAL
ROTATION 638 13.5.2.2 OBLIQUE ROTATION 638 13.5.2.3 GEOMETRIE
INTERPRETATION 640 13.5.3 SOME PRACTICAL RECOMMENDATIONS 642 13.6 SOME
IMPORTANT ISSUES 643 13.6.1 ESTIMATES OF COMMUNALITIES 643 13.6.2
ADEQUACY OF EXTRACTION AND NUMBER OF FACTORS 644 13.6.3 ADEQUACY OF
ROTATION AND SIMPLE STRUCTURE 646 13.6.4 IMPORTANCE AND INTERNAL
CONSISTENCY OF FACTORS 647 13.6.5 INTERPRETATION OF FACTORS 649 13.6.6
FACTOR SCORES 650 13.6.7 COMPARISONS AMONG SOLUTIONS AND GROUPS 651
CONTENTS 13.7 COMPLETEEXAMPLEOFFA 651 13.7.1 EVALUATIONOF LIMITATIONS
652 13.7.1.1 SAMPLE SIZE AND MISSING DATA 652 13.7.1.2 NORMALITY 652
13.7.1.3 LINEARITY 652 13.7.1.4 OUTLIERS 652 13.7.1.5 MULTICOLLINEARITY
AND SINGULARITY 657 13.7.1.6 OUTLIERS AMONG VARIABLES 657 13.7.2
PRINCIPAL FACTORS EXTRACTION WITH VARIMAX ROTATION 657 13.8 COMPARISON
OF PROGRAMS 671 13.8.1 SPSSPACKAGE 674 13.8.2 SAS SYSTEM 675 13.8.3
SYSTAT SYSTEM 675 STRUCTURAL EQUATION MODELING 676 14.1 GENERAL PURPOSE
AND DESCRIPTION 676 14.2 KINDS OF RESEARCH QUESTIONS 680 14.2.1
ADEQUACYOF THE MODEL 680 14.2.2 TESTING THEORY 680 14.2.3 AMOUNT OF
VARIANCE IN THE VARIABLES ACCOUNTED FOR BY THE FACTORS 680 14.2.4
RELIABILITY OF THE INDICATORS 680 14.2.5 PARAMETER ESTIMATES 680 14.2.6
INTERVENING VARIABLES 681 14.2.7 GROUP DIFFERENCES 681 14.2.8
LONGITUDINAL DIFFERENCES 681 14.2.9 MULTILEVEL MODELING 681 14.3
LIMITATIONS TO STRUCTURAL EQUATION MODELING 682 14.3.1 THEORETICAL
ISSUES 682 14.3.2 PRACTICAL ISSUES 682 14.3.2.1 SAMPLE SIZE AND MISSING
DATA 682 14.3.2.2 MULTIVARIATE NORMALITY AND ABSENCE OF OUTLIERS 683
14.3.2.3 LINEARITY 683 14.3.2.4 ABSENCE OF MULTICOLLINEARITY AND
SINGULARITY 683 14.3.2.5 RESIDUAIS 684 14.4 FUNDAMENTAL EQUATIONS FOR
STRUCTURAL EQUATIONS MODELING 684 14.4.1 COVARIANCE ALGEBRA 684 14.4.2
MODEL HYPOTHESES 686 14.4.3 MODEL SPECIFICATION 688 14.4.4 MODEL
ESTIMATION 690 14.4.5 MODEL EVALUATION 694 14.4.6 COMPUTER ANALYSIS OF
SMALL-SAMPLE EXAMPLE 696 15 CONTENTS XIX 14.5 SOME IMPORTANT ISSUES 709
14.5.1 MODEL IDENTIFICATION 709 14.5.2 ESTIMATION TECHNIQUES 713
14.5.2.1 ESTIMATION METHODS AND SAMPLE SIZE 714 14.5.2.2 ESTIMATION
METHODS AND NONNORMALITY 714 14.5.2.3 ESTIMATION METHODS AND DEPENDENCE
715 14.5.2.4 SOME RECOMMENDATIONS FOR CHOICE OF ESTIMATION METHOD 715
14.5.3 ASSESSING THE FIT OF THE MODEL 715 14.5.3.1 COMPARATIVE FIT
INDICES 716 14.5.3.2 ABSOLUTE FIT INDEX 718 14.5.3.3 INDICES OF
PROPORTION OF VARIANCE ACCOUNTED 718 14.5.3.4 DEGREE OF PARSIMONY FIT
INDICES 719 14.5.3.5 RESIDUAL-BASED FIT INDICES 720 14.5.3.6 CHOOSING
AMONG FIT INDICES 720 14.5.4 MODEL MODIFICATION 721 14.5.4.1 CHI-SQUARE
DIFFERENCE TEST 721 14.5.4.2 LAGRANGE MULTIPLIER (LM) TEST 721 14.5.4.3
WALD TEST 723 14.5.4.4 SOME CAVEATS AND HINTS ON MODEL MODIFICATION 728
14.5.5 RELIABILITY AND PROPORTION OF VARIANCE 728 14.5.6 DISCRETE AND
ORDINAL DATA 729 14.5.7 MULTIPLE GROUP MODELS 730 14.5.8 MEAN AND
COVARIANCE STRUCTURE MODELS 731 14.6 COMPLETE EXAMPLES OF STRUCTURAL
EQUATION MODELING ANALYSIS 732 14.6.1 CONFIRMATORY FACTOR ANALYSIS OF
THE WISC 732 14.6.1.1 MODEL SPECIFICATION FOR CFA 732 14.6.1.2
EVALUATION OF ASSUMPTIONS FOR CFA 733 14.6.1.3 CFA MODEL ESTIMATION AND
PRELIMINARY EVALUATION 734 14.6.1.4 MODEL MODIFICATION 743 14.6.2 SEM OF
HEALTH DATA 750 14.6.2.1 SEM MODEL SPECIFICATION 750 14.6.2.2 EVALUATION
OF ASSUMPTIONS FOR SEM 751 14.6.2.3 SEM MODEL ESTIMATION AND PRELIMINARY
EVALUATION 755 14.6.2.4 MODEL MODIFICATION 759 14.7 COMPARISON OF
PROGRAMS 773 14.7.1 EQS 773 14.7.2 LISREL 773 14.7.3 AMOS 780 14.7.4 SAS
SYSTEM 780 MULTILEVEL LINEAR MODELING 781 15.1 GENERAL PURPOSE AND
DESCRIPTION 781 CONTENTS 15.2 KINDS OF RESEARCH QUESTIONS 784 15.2.1
GROUP DIFFERENCES IN MEANS 784 15.2.2 GROUP DIFFERENCES IN SLOPES 784
15.2.3 CROSS-LEVEL INTERACTIONS 785 15.2.4 META-ANALYSIS 785 15.2.5
RELATIVE STRENGTH OF PREDICTORS AT VARIOUS LEVELS 785 15.2.6 INDIVIDUAL
AND GROUP STRUCTURE 785 15.2.7 PATH ANALYSIS AT INDIVIDUAL AND GROUP
LEVELS 786 15.2.8 ANALYSIS OF LONGITUDINAL DATA 786 15.2.9 MULTILEVEL
LOGISTIC REGRESSION 786 15.2.10 MULTIPLE RESPONSE ANALYSIS 786 15.3
LIMITATIONS TO MULTILEVEL LINEAR MODELING 786 15.3.1 THEORETICAL ISSUES
786 15.3.2 PRACTICAL ISSUES 787 15.3.2.1 SAMPLE SIZE, UNEQUAL-N, AND
MISSING DATA 787 15.3.2.2 INDEPENDENCE OF ERRORS 788 15.3.2.3 ABSENCE OF
MULTICOLLINEARITY AND SINGULARITY 789 15.4 FUNDAMENTAL EQUATIONS 789
15.4.1 INTERCEPTS-ONLY MODEL 792 15.4.1.1 THE INTERCEPTS-ONLY MODEL:
LEVEL-1 EQUATION 793 15.4.1.2 THE INTERCEPTS-ONLY MODEL: LEVEL-2
EQUATION 793 15.4.1.3 COMPUTER ANALYSIS OF INTERCEPTS-ONLY MODEL 794
15.4.2 MODEL WITH A FIRST-LEVEL PREDICTOR 799 15.4.2.1 LEVEL-1 EQUATION
FOR A MODEL WITH A LEVEL-1 PREDICTOR 799 15.4.2.2 LEVEL-2 EQUATIONS FOR
A MODEL WITH A LEVEL-1 PREDICTOR 801 15.4.2.3 COMPUTERANALYSIS OFA MODEL
WITHA LEVEL-1 PREDICTOR 802 15.4.3 MODEL WITH PREDICTORS AT FIRST AND
SECOND LEVELS 807 15.4.3.1 LEVEL-1 EQUATION FOR MODEL WITH PREDICTORS AT
BOTH LEVELS 807 15.4.3.2 LEVEL-2 EQUATIONS FOR MODEL WITH PREDICTORS AT
BOTH LEVELS 807 15.4.3.3 COMPUTER ANALYSES OF MODEL WITH PREDICTORS AT
FIRST AND SECOND LEVELS 808 15.5 TYPESOFMLM 814 15.5.1 REPEATED MEASURES
814 15.5.2 HIGHER-ORDER MLM 819 15.5.3 LATENT VARIABLES 819 15.5.4
NONNORMAL OUTCOME VARIABLES 820 15.5.5 MULTIPLE RESPONSE MODELS 821 15.6
SOME IMPORTANT ISSUES 822 15.6.1 INTRACLASS CORRELATION 822 15.6.2
CENTERING PREDICTORS AND CHANGES IN THEIR INTERPRETATIONS 823 15.6.3
INTERACTIONS 826 15.6.4 RANDOM AND FIXED INTERCEPTS AND SLOPES 826
CONTENTS XXI 15.6.5 STATISTICAL INFERENCE 830 15.6.5.1 ASSESSING MODELS
830 15.6.5.2 TESTS OF INDIVIDUAL EFFECTS 831 15.6.6 EFFECT SIZE 832
15.6.7 ESTIMATION TECHNIQUES AND CONVERGENCE PROBLEMS 833 15.6.8
EXPLORATORY MODEL BUILDING 834 15.7 COMPLETEEXAMPLEOFMLM 835 15.7.1
EVALUATION OF ASSUMPTIONS 835 15.7.1.1 SAMPLE SIZES, MISSING DATA, AND
DISTRIBUTIONS 835 15.7.1.2 OUTLIERS 838 15.7.1.3 MULTICOLLINEARITY AND
SINGULARITY 839 15.7.1.4 INDEPENDENCE OF ERRORS: INTRACLASS CORRELATIONS
839 15.7.2 MULTILEVEL MODELING 840 15.8 COMPARISON OF PROGRAMS 852
15.8.1 SAS SYSTEM 852 15.8.2 SPSSPACKAGE 856 15.8.3 HLM PROGRAM 856
15.8.4 MLWIN PROGRAM 857 15.8.5 SYSTAT SYSTEM 857 MULTIWAY FREQUENCY
ANALYSIS 858 16.1 GENERAL PURPOSE AND DESCRIPTION 858 16.2 KINDS OF
RESEARCH QUESTIONS 859 16.2.1 ASSOCIATIONS AMONG VARIABLES 859 16.2.2
EFFECT ON A DEPENDENT VARIABLE 860 16.2.3 PARAMETER ESTIMATES 860 16.2.4
IMPORTANCEOF EFFECTS 860 16.2.5 EFFECT SIZE 860 16.2.6 SPECIFIC
COMPARISONS AND TREND ANALYSIS 860 16.3 LIMITATIONS TO MULTIWAY
FREQUENCY ANALYSIS 861 16.3.1 THEORETICAL ISSUES 861 16.3.2 PRACTICAL
ISSUES 861 16.3.2.1 INDEPENDENCE 861 16.3.2.2 RATIO OFCASESTO VARIABLES
861 16.3.2.3 ADEQUACY OF EXPECTED FREQUENCIES 862 16.3.2.4 ABSENCE OF
OUTLIERS IN THE SOLUTION 863 16.4 FUNDAMENTAL EQUATIONS FOR MULTIWAY
FREQUENCY ANALYSIS 863 16.4.1 SCREENING FOR EFFECTS 864 16.4.1.1 TOTAL
EFFECT 865 16.4.1.2 FIRST-ORDER EFFECTS 866 16.4.1.3 SECOND-ORDER
EFFECTS 867 16.4.1.4 THIRD-ORDER EFFECT 871 CONTENTS 16.4.2 MODELING 871
16.4.3 EVALUATION AND INTERPRETATION 874 16.4.3.1 RESIDUAIS 874 16.4.3.2
PARAMETER ESTIMATES 874 16.4.4 COMPUTER ANALYSES OF SMALL-SAMPLE EXAMPLE
880 16.5 SOME IMPORTANT ISSUES 887 16.5.1 HIERARCHICAL AND
NONHIERARCHICAL MODELS 887 16.5.2 STATISTICAL CRITERIA 888 16.5.2.1
TESTS OF MODELS 888 16.5.2.2 TESTS OFLNDIVIDUAL EFFECTS 888 16.5.3
STRATEGIES FOR CHOOSING A MODEL 889 16.5.3.1 SPSS HILOGLINEAR
(HIERARCHICAL) 889 16.5.3.2 SPSS GENLOG (GENERAL LOG-LINEAR) 889
16.5.3.3 SAS CATMOD AND SPSS LOGLINEAR (GENERAL LOG-LINEAR) 890 16.6
COMPLETE EXAMPLE OF MULTIWAY FREQUENCY ANALYSIS 890 16.6.1 EVALUATION OF
ASSUMPTIONS: ADEQUACY OF EXPECTED FREQUENCIES 890 16.6.2 HIERARCHICAL
LOG-LINEAR ANALYSIS 891 16.6.2.1 PRELIMINARY MODEL SCREENING 891
16.6.2.2 STEPWISE MODEL SELECTION 893 16.6.2.3 ADEQUACY OF FIT 895
16.6.2.4 INTERPRETATION OF THE SELECTED MODEL 901 16.7 COMPARISON OF
PROGRAMS 908 16.7.1 SPSSPACKAGE 911 16.7.2 SAS SYSTEM 912 16.7.3 SYSTAT
SYSTEM 912 AN OVERVIEW OF THE GENERAL LINEAR MODEL 913 17.1 LINEARITY
AND THE GENERAL LINEAR MODEL 913 17.2 BIVARIATE TO MULTIVARIATE
STATISTICS AND OVERVIEW OFTECHNIQUES 913 17.2.1 BIVARIATE FORM 913
17.2.2 SIMPLE MULTIVARIATE FORM 914 17.2.3 FUELL MULTIVARIATE FORM 917
17.3 ALTERNATIVE RESEARCH STRATEGIES 918 TIME-SERIES ANALYSIS (AVAILABLE
ONLINE AT WWW.ABLONGMAN.COM/TABACHNICK5E) 18-1 18.1 GENERAL PURPOSE AND
DESCRIPTION 18-1 CONTENTS XX111 18.2 KINDS OF RESEARCH QUESTIONS 18-3
18.2.1 PATTERN OF AUTOCORRELATION 18-5 18.2.2 SEASONAL CYCLES AND TRENDS
18-5 18.2.3 FORECASTING 18-5 18.2.4 EFFECT OF AN INTERVENTION 18-5
18.2.5 COMPARING TIME SERIES 18-5 18.2.6 TIME SERIES WITH COVARIATES
18-6 18.2.7 EFFECT SIZE AND POWER 18-6 18.3 ASSUMPTIONS OF TIME-SERIES
ANALYSIS 18-6 18.3.1 THEORETICAL ISSUES 18-6 18.3.2 PRACTICAL ISSUES
18-6 18.3.2.1 NORMALITY OF DISTRIBUTIONS OF RESIDUALS 18-6 18.3.2.2
HOMOGENEITY OFVARIANCE AND ZERO MEAN OF RESIDUALS 18-7 18.3.2.3
INDEPENDENCE OF RESIDUALS 18-7 18.3.2.4 ABSENCE OF OUTLIERS 18-7 18.4
FUNDAMENTAL EQUATIONS FOR TIME-SERIES ARIMA MODELS 18-7 18.4.1
IDENTIFICATION ARIMA (P, D, Q) MODELS 18-8 18.4.1.1 TREND COMPONENTS, D:
MAKING THE PROCESS STATIONARY 18-8 18.4.1.2 AUTO-REGRESSIVE COMPONENTS
18-11 18.4.1.3 MOVING AVERAGE COMPONENTS 18-12 18.4.1.4 MIXED MODELS
18-13 18.4.1.5 ACFSANDPACFS 18-13 18.4.2 ESTIMATING MODEL PARAMETERS
18-16 18.4.3 DIAGNOSING A MODEL 18-19 18.4.4 COMPUTER ANALYSIS OF
SMALL-SAMPLE TIME-SERIES EXAMPLE 18-19 18.5 TYPESOF TIME-SERIES ANALYSES
18-27 18.5.1 MODELS WITH SEASONAL COMPONENTS 18-27 18.5.2 MODELS WITH
INTERVENTIONS 18-30 18.5.2.1 ABRUPT, PERMANENT EFFECTS 18-32 18.5.2.2
ABRUPT, TEMPORARY EFFECTS 18-32 18.5.2.3 GRADUAL, PERMANENT EFFECTS
18-38 18.5.2.4 MODELS WITH MULTIPLE INTERVENTIONS 18-38 18.5.3 ADDING
CONTINUOUS VARIABLES 18-38 18.6 SOME IMPORTANT ISSUES 18-41 18.6.1
PATTERNSOF ACFSANDPACFS 18-41 18.6.2 EFFECT SIZE 18-44 18.6.3
FORECASTING 18-45 18.6.4 STATISTICAL METHODS FOR COMPARING TWO MODELS
18-45 18.7 COMPLETE EXAMPLE OF A TIME-SERIES ANALYSIS 18-47 18.7.1
EVALUATION OF ASSUMPTIONS 18-48 18.7.1.1 NORMALITY OF SAMPLING
DISTRIBUTIONS 18-48 18.7.1.2 HOMOGENEITY OFVARIANCE 18-48 18.7.1.3
OUTLIERS 18-48 XXIV CONTENTS 18.7.2 BASELINE MODEL IDENTIFICATION AND
ESTIMATION 18-48 18.7.3 BASELINE MODEL DIAGNOSIS 18-49 18.7.4
INTERVENTION ANALYSIS 18-55 18.7.4.1 MODEL DIAGNOSIS 18-55 18.7.4.2
MODEL INTERPRETATION 18-56 18.8 COMPARISON OF PROGRAMS 18-60 18.8.1
SPSSPACKAGE 18-61 18.8.2 SAS SYSTEM 18-61 18.8.3 SYSTAT SYSTEM 18-61 A
SKIMPY INTRODUCTION TO MATRIX ALGEBRA 924 A.L THE TRACEOFA MATRIX 925
A.2 ADDITION OR SUBTRACTION OF A CONSTANT TO A MATRIX 925 A.3
MULTIPLICATION OR DIVISION OF A MATRIX BY A CONSTANT 925 A.4 ADDITION
AND SUBTRACTION OF TWO MATRICES 926 A.5 MULTIPLICATION, TRANSPOSES, AND
SQUARE ROOTS OF MATRICES 927 A.6 MATRIX DIVISION (INVERSES AND
DETERMINANTS) 929 A.7 EIGENVALUES AND EIGENVECTORS: PROCEDURES FOR
CONSOLIDATING VARIANCE FROM A MATRIX 930 RESEARCH DESIGNS FOR COMPLETE
EXAMPLES 934 B.L WOMEN S HEALTH AND DRUG STUDY 934 B.2 SEXUAL ATTRACTION
STUDY 935 B.3 LEARNING DISABILITIES DATA BANK 938 B.4 REACTION TIME TO
IDENTIFY FIGURES 939 B.5 FIELD STUDIES OF NOISE-INDUCED SLEEP
DISTURBANCE 939 B.6 CLINICAL TRIAL FOR PRIMARY BILIARY CIRRHOSIS 940 B.7
IMPACTOF SEAT BELT LAW 940 APPENDIX ^ STATISTICAL TABLES 941 C.L NORMAL
CURVE AREAS 942 C.2 CRITICAL VALUES OF THE T DISTRIBUTION FOR A = .05
AND .01, TWO-TAILED TEST 943 APPENDIX R APPENDIX B CONTENTS XXV C.3
CRITICAL VALUES OFTHEF DISTRIBUTION 944 C.4 CRITICAL VALUES OF CHI
SQUARE (/ 2 ) 949 C.5 CRITICAL VALUES FOR SQUARED MULTIPLE CORRELATION
(R 2 ) IN FORWARD STEPWISE SELECTION 950 C.6 CRITICAL VALUES FOR F MAX
(S^AX/^MIN) DISTRIBUTION FOR A = .05 AND .01 952 REFERENCES 953 INDEX
963
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FIFTH EDITION USING MULTIVARIATE STATISTICS BARBARA G. TABACHNICK
CALIFORNIA STATE UNIVERSITY, NORTHRIDGE LINDA S. FIDELL CALIFORNIA STATE
UNIVERSITY, NORTHRIDGE BOSTON * NEW YORK * SAN FRANCISCO MEXICO CITY *
MONTREAL * TORONTO * LONDON * MADRID * MUNICH * PARIS HONG KONG *
SINGAPORE * TOKYO * CAPE TOWN * SYDNEY CONTENTS PREFACE XXVII
INTRODUCTION 1 1.1 MULTIVARIATE STATISTICS: WHY? 1 1.1.1 THE DOMAIN OF
MULTIVARIATE STATISTICS: NUMBERS OF IVS AND DVS 1 1.1.2 EXPERIMENTAL AND
NONEXPERIMENTAL RESEARCH 2 1.1.3 COMPUTERS AND MULTIVARIATE STATISTICS 4
1.1.4 GARBAGE IN, ROSES OUT? 5 1.2 SOME USEFUL DEFINITIONS 5 1.2.1
CONTINUOUS, DISCRETE, AND DICHOTOMOUS DATA 5 1.2.2 SAMPLES AND
POPULATIONS 7 1.2.3 DESCRIPTIVE AND INFERENTIAL STATISTICS 7 1.2.4
ORTHOGONALITY: STANDARD AND SEQUENTIAL ANALYSES 8 1.3 LINEAR
COMBINATIONS OF VARIABLES 10 1.4 NUMBER AND NATUREOF VARIABLES TOLNCLUDE
11 1.5 STATISTICAL POWER 11 1.6 DATA APPROPRIATE FOR MULTIVARIATE
STATISTICS 12 1.6.1 THE DATA MATRIX 12 1.6.2 THE CORRELATION MATRIX 13
1.6.3 THE VARIANCE-COVARIANCE MATRIX 14 1.6.4 THE SUM-OF-SQUARES AND
CROSS-PRODUCTS MATRIX 14 1.6.5 RESIDUAIS 16 1.7 ORGANIZATION OF THE BOOK
16 A GUIDE TO STATISTICAL TECHNIQUES: USING THE BOOK 17 2.1 RESEARCH
QUESTIONS AND ASSOCIATED TECHNIQUES 17 2.1.1 DEGREE OF RELATIONSHIP
AMONG VARIABLES 17 2.1.1.1 BIVARIATER 17 2.1.1.2 MULTIPLE/? 18 2.1.1.3
SEQUENTIAL/? 18 2.1.1.4 CANONICAL/? 18 2.1.1.5 MULTIWAY FREQUENCY
ANALYSIS 19 2.1.1.6 MULTILEVEL MODELING 19 CONTENTS 2.1.2 SIGNIFICANCE
OF GROUP DIFFERENCES 19 2.1.2.1 ONE-WAY ANOVA AND T TEST 19 2.1.2.2
ONE-WAY ANCOVA 20 2.1.2.3 FACTORIAL ANOVA 20 2.1.2.4 FACTORIAL ANCOVA 20
2.1.2.5 HOTELLING'S T 2 21 2.1.2.6 ONE-WAY MANOVA 21 2.1.2.7 ONE-WAY
MANCOVA 21 2.1.2.8 FACTORIAL MANOVA 22 2.1.2.9 FACTORIAL MANCOVA 22
2.1.2.10 PROFILE ANALYSIS OF REPEATED MEASURES 23 2.1.3 PREDICTION OF
GROUP MEMBERSHIP 23 2.1.3.1 ONE-WAY DISCRIMINANT 23 2.1.3.2 SEQUENTIAL
ONE-WAY DISCRIMINANT 24 2.1.3.3 MULTIWAY FREQUENCY ANALYSIS (LOGIT) 24
2.1.3.4 LOGISTIC REGRESSION 24 2.1.3.5 SEQUENTIAL LOGISTIC REGRESSION 25
2.1.3.6 FACTORIAL DISCRIMINANT ANALYSIS 25 2.1.3.7 SEQUENTIAL FACTORIAL
DISCRIMINANT ANALYSIS 25 2.1.4 STRUCTURE 25 2.1.4.1 PRINCIPAL COMPONENTS
25 2.1.4.2 FACTOR ANALYSIS 26 2.1.4.3 STRUCTURAL EQUATION MODELING 26
2.1.5 TIME COURSE OF EVENTS 26 2.1.5.1 SURVIVAL/FAILURE ANALYSIS 26
2.1.5.2 TIME-SERIES ANALYSIS 27 2.2 SOME FURTHER COMPARISONS 27 2.3 A
DECISION TREE 28 2.4 TECHNIQUE CHAPTERS 31 2.5 PRELIMINARY CHECK OF THE
DATA 32 REVIEW OF UNIVARIATE AND BIVARIATE STATISTICS 33 3.1 HYPOTHESIS
TESTING 33 3.1.1 ONE-SAMPLE Z TEST AS PROTOTYPE 33 3.1.2 POWER 36 3.1.3
EXTENSIONS OF THE MODEL 37 3.1.4 CONTROVERSY SURROUNDMG SIGNIFICANCE
TESTING 37 3.2 ANALYSIS OFVARIANCE 37 3.2.1 ONE-WAY BETWEEN-SUBJECTS
ANOVA 39 3.2.2 FACTORIAL BETWEEN-SUBJECTS ANOVA 42 3.2.3 WITHIN-SUBJECTS
ANOVA 43 3.2.4 MIXED BETWEEN-WITHIN-SUBJECTS ANOVA 46 CONTENTS 3.2.5
DESIGN COMPLEXITY 47 3.2.5.1 NESTING 47 3.2.5.2 LATIN-SQUARE DESIGNS 47
3.2.5.3 UNEQUAL N AND NONORTHOGONALITY 48 3.2.5.4 FIXED AND RANDOM
EFFECTS 49 3.2.6 SPECIFIC COMPARISONS 49 3.2.6.1 WEIGHTING COEFFICIENTS
FOR COMPARISONS 50 3.2.6.2 ORTHOGONALITYOF WEIGHTING COEFFICIENTS 50
3.2.6.3 OBTAINED F FOR COMPARISONS 51 3.2.6.4 CRITICAL F FOR PLANNED
COMPARISONS 52 3.2.6.5 CRITICAL F FOR POST HOC COMPARISONS 53 3.3
PARAMETER ESTIMATION 53 3.4 EFFECT SIZE 54 3.5 BIVARIATE STATISTICS:
CORRELATION AND REGRESSION 56 3.5.1 CORRELATION 56 3.5.2 REGRESSION 57
3.6 CHI-SQUARE ANALYSIS 58 CLEANING UP YOUR ACT: SCREENING DATA PRIOR TO
ANALYSIS 60 4.1 IMPORTANT ISSUES IN DATA SCREENING 61 4.1.1 ACCURACY OF
DATA FILE 61 4.1.2 HONEST CORRELATIONS 61 4.1.2.1 INFLATED CORRELATION
61 4.1.2.2 DEFLATED CORRELATION 61 4.1.3 MISSING DATA 62 4.1.3.1
DELETING CASES OR VARIABLES 63 4.1.3.2 ESTIMATING MISSINGDATA 66 4.1.3.3
USING A MISSING DATA CORRELATION MATRIX 70 4.1.3.4 TREATING MISSING DATA
AS DATA 71 4.1.3.5 REPEATING ANALYSES WITH AND WITHOUT MISSING DATA
4.1.3.6 CHOOSING AMONG METHODS FOR DEALING WITH MISSING DATA 71 4.1.4
OUTLIERS 72 4.1.4.1 DETECTING UNIVARIATE AND MULTIVARIATE OUTLIERS 73
4.1.4.2 DESCRIBING OUTLIERS 76 4.1.4.3 REDUCING THE INFLUENCE OF
OUTLIERS 77 4.1.4.4 OUTLIERS IN A SOLUTION 77 4.1.5 NORMALITY,
LINEARITY, AND HOMOSCEDASTICITY 78 4.1.5.1 NORMALITY 79 4.1.5.2
LINEARITY 83 4.1.5.3 HOMOSCEDASTICITY, HOMOGENEITY OFVARIANCE, AND
HOMOGENEITY OF VARIANCE-COVARIANCE MATRICES 85 CONTENTS 4.1.6 COMMON
DATA TRANSFORMATIONS 86 4.1.7 MULTICOLLINEARITY AND SINGULARITY 88 4.1.8
A CHECKLIST AND SOME PRACTICAL RECOMMENDATIONS 91 4.2 COMPLETE EXAMPLES
OF DATA SCREENING 92 4.2.1 SCREENING UNGROUPED DATA 92 4.2.1.1 ACCURACY
OF INPUT, MISSING DATA, DISTRIBUTIONS, AND UNIVARIATE OUTLIERS 93
4.2.1.2 LINEARITY AND HOMOSCEDASTICITY 96 4.2.1.3 TRANSFORMATION 98
4.2.1.4 DETECTING MULTIVARIATE OUTLIERS 99 4.2.1.5 VARIABLES CAUSING
CASES TO BE OUTLIERS 100 4.2.1.6 MULTICOLLINEARITY 104 4.2.2 SCREENING
GROUPED DATA 105 4.2.2.1 ACCURACY OF INPUT, MISSING DATA, DISTRIBUTIONS,
HOMOGENEITY OF VARIANCE, AND UNIVARIATE OUTLIERS 105 4.2.2.2 LINEARITY
110 4.2.2.3 MULTIVARIATE OUTLIERS 111 4.2.2.4 VARIABLES CAUSING CASES TO
BE OUTLIERS 113 4.2.2.5 MULTICOLLINEARITY 114 MULTIPLE REGRESSION 117
5.1 GENERAL PURPOSE AND DESCRIPTION 117 5.2 KINDS OF RESEARCH QUESTIONS
118 5.2.1 DEGREE OF RELATIONSHIP 119 5.2.2 IMPORTANCE OF IVS 119 5.2.3
ADDINGIVS 119 5.2.4 CHANGING IVS 120 5.2.5 CONTINGENCIES AMONG IVS 120
5.2.6 COMPARING SETS OF IVS 120 5.2.7 PREDICTING DV SCORES FOR MEMBERS
OFA NEW SAMPLE 120 5.2.8 PARAMETER ESTIMATES 121 5.3 LIMITATIONS TO
REGRESSION ANALYSES 121 5.3.1 THEORETICAL ISSUES 122 5.3.2 PRACTICAL
ISSUES 123 5.3.2.1 RATIO OF CASES TO IVS 123 5.3.2.2 ABSENCE OF OUTLIERS
AMONG THE IVS AND ON THE DV 124 5.3.2.3 ABSENCE OF MULTICOLLINEARITY AND
SINGULARITY 124 5.3.2.4 NORMALITY, LINEARITY, HOMOSCEDASTICITY OF
RESIDUALS 125 5.3.2.5 INDEPENDENCEOF ERRORS 128 5.3.2.6 ABSENCE OF
OUTLIERS IN THE SOLUTION 128 5.4 FUNDAMENTAL EQUATIONS FOR MULTIPLE
REGRESSION 128 5.4.1 GENERAL LINEAR EQUATIONS 129 5.4.2 MATRIX EQUATIONS
131 5.4.3 COMPUTER ANALYSES OF SMALL-SAMPLE EXAMPLE 134 CONTENTS VII 5.5
MAJOR TYPES OF MULTIPLE REGRESSION 136 5.5.1 STANDARD MULTIPLE
REGRESSION 136 5.5.2 SEQUENTIAL MULTIPLE REGRESSION 138 5.5.3
STATISTICAL (STEPWISE) REGRESSION 138 5.5.4 CHOOSING AMONG REGRESSION
STRATEGIES 143 5.6 SOME IMPORTANT ISSUES 144 5.6.1 IMPORTANCE OF IVS 144
5.6.1.1 STANDARD MULTIPLE REGRESSION 146 5.6.1.2 SEQUENTIAL OR
STATISTICAL REGRESSION 146 5.6.2 STATISTICAL INFERENCE 146 5.6.2.1 TEST
FOR MULTIPLEI? 147 5.6.2.2 TEST OF REGRESSION COMPONENTS 148 5.6.2.3
TEST OF ADDED SUBSET OF IVS 149 5.6.2.4 CONFIDENCE LIMITS AROUND B AND
MULTIPLE R 2 150 5.6.2.5 COMPARING TWO SETS OF PREDICTORS 152 5.6.3
ADJUSTMENTOFTF 2 153 5.6.4 SUPPRESSOR VARIABLES 154 5.6.5 REGRESSION
APPROACH TO ANOVA 155 5.6.6 CENTERING WHEN INTERACTIONS AND POWERS OF
IVS ARE INCLUDED 157 5.6.7 MEDIATION IN CAUSAL SEQUENCES 159 5.7
COMPLETE EXAMPLES OF REGRESSION ANALYSIS 161 5.7.1 EVALUATION OF
ASSUMPTIONS 161 5.7.1.1 RATIO OFCASESTO IVS 161 5.7.1.2 NORMALITY,
LINEARITY, HOMOSCEDASTICITY, AND INDEPENDENCE OF RESIDUAIS 161 5.7.1.3
OUTLIERS 165 5.7.1.4 MULTICOLLINEARITY AND SINGULARITY 167 5.7.2
STANDARD MULTIPLE REGRESSION 167 5.7.3 SEQUENTIAL REGRESSION 174 5.7.4
EXAMPLE OF STANDARD MULTIPLE REGRESSION WITH MISSING VALUES MULTIPLY
IMPUTED 179 5.8 COMPARISON OF PROGRAMS 188 5.8.1 SPSSPACKAGE 188 5.8.2
SAS SYSTEM 191 5.8.3 SYSTAT SYSTEM 194 ANALYSIS OF COVARIANCE 195 6.1
GENERAL PURPOSE AND DESCRIPTION 195 6.2 KINDS OF RESEARCH QUESTIONS 198
6.2.1 MAIN EFFECTS OF IVS 198 6.2.2 INTERACTIONS AMONG IVS 198 6.2.3
SPECIFIC COMPARISONS AND TREND ANALYSIS 199 6.2.4 EFFECTS OFCOVARIATES
199 CONTENTS 6.2.5 EFFECT SIZE 199 6.2.6 PARAMETER ESTIMATES 199 6.3
LIMITATIONS TO ANALYSIS OF COVARIANCE 200 6.3.1 THEORETICAL ISSUES 200
6.3.2 PRACTICAL ISSUES 201 6.3.2.1 UNEQUAL SAMPLE SIZES, MISSING DATA,
AND RATIO OF CASES TO IVS 201 6.3.2.2 ABSENCEOFOUTLIERS 201 6.3.2.3
ABSENCE OF MULTICOLLINEARITY AND SINGULARITY 201 6.3.2.4 NORMALITY OF
SAMPLING DISTRIBUTIONS 202 6.3.2.5 HOMOGENEITY OF VARIANCE 202 6.3.2.6
LINEARITY 202 6.3.2.7 HOMOGENEITY OF REGRESSION 202 6.3.2.8 RELIABILITY
OF COVARIATES 203 6.4 FUNDAMENTAL EQUATIONS FOR ANALYSIS OF COVARIANCE
203 6.4.1 SUMS OF SQUARES AND CROSS PRODUCTS 204 6.4.2 SIGNIFTCANCE TEST
AND EFFECT SIZE 208 6.4.3 COMPUTER ANALYSES OF SMALL-SAMPLE EXAMPLE 209
6.5 SOME IMPORTANT ISSUES 211 6.5.1 CHOOSING COVARIATES 211 6.5.2
EVALUATION OF COVARIATES 212 6.5.3 TEST FOR HOMOGENEITY OF REGRESSION
213 6.5.4 DESIGN COMPLEXITY 213 6.5.4.1 WITHIN-SUBJECTS AND MIXED
WITHIN-BETWEEN DESIGNS 214 6.5.4.2 UNEQUAL SAMPLE SIZES 217 6.5.4.3
SPECIFIC COMPARISONS AND TREND ANALYSIS 218 6.5.4.4 EFFECT SIZE 221
6.5.5 ALTERNATIVES TOANCOVA 221 6.6 COMPLETE EXAMPLE OF ANALYSIS OF
COVARIANCE 223 6.6.1 EVALUATION OF ASSUMPTIONS 223 6.6.1.1 UNEQUAL N AND
MISSING DATA 224 6.6.1.2 NORMALITY 224 6.6.1.3 LINEARITY 224 6.6.1.4
OUTLIERS 224 6.6.1.5 MULTICOLLINEARITY AND SINGULARITY 227 6.6.1.6
HOMOGENEITY OF VARIANCE 228 6.6.1.7 HOMOGENEITY OF REGRESSION 230
6.6.1.8 RELIABILITY OF COVARIATES 230 6.6.2 ANALYSIS OF COVARIANCE 230
6.6.2.1 MAIN ANALYSIS 230 6.6.2.2 EVALUATION OF COVARIATES 235 6.6.2.3
HOMOGENEITY OF REGRESSION RUN 237 6.7 COMPARISON OF PROGRAMS 240 6.7.1
SPSS PACKAGE 240 CONTENTS 6.7.2 SAS SYSTEM 240 6.7.3 SYSTAT SYSTEM 240
MULTIVARIATE ANALYSIS OF VARIANCE AND COVARIANCE 243 7.1 GENERAL PURPOSE
AND DESCRIPTION 243 7.2 KINDS OF RESEARCH QUESTIONS 247 7.2.1 MAIN
EFFECTS OFIVS 247 7.2.2 INTERACTIONS AMONG IVS 247 7.2.3 IMPORTANCEOFDVS
247 7.2.4 PARAMETER ESTIMATES 248 7.2.5 SPECIFIC COMPARISONS AND TREND
ANALYSIS 248 7.2.6 EFFECT SIZE 248 7.2.7 EFFECTS OFCOVARIATES 248 7.2.8
REPEATED-MEASURES ANALYSIS OF VARIANCE 249 7.3 LIMITATIONS TO
MULTIVARIATE ANALYSIS OF VARIANCE AND COVARIANCE 249 7.3.1 THEORETICAL
ISSUES 249 7.3.2 PRACTICAL ISSUES 250 7.3.2.1 UNEQUAL SAMPLE SIZES,
MISSING DATA, AND POWER 250 7.3.2.2 MULTIVARIATE NORMALITY 251 7.3.2.3
ABSENCEOFOUTLIERS 251 7.3.2.4 HOMOGENEITY OFVARIANCE-COVARIANCEMATRICES
251 7.3.2.5 LINEARITY 252 7.3.2.6 HOMOGENEITY OF REGRESSION 252 7.3.2.7
RELIABILITY OFCOVARIATES 253 7.3.2.8 ABSENCE OF MULTICOLLINEARITY AND
SINGULARITY 253 7.4 FUNDAMENTAL EQUATIONS FOR MULTIVARIATE ANALYSIS OF
VARIANCE AND COVARIANCE 253 7.4.1 MULTIVARIATE ANALYSIS OF VARIANCE 253
7.4.2 COMPUTER ANALYSES OF SMALL-SAMPLE EXAMPLE 261 7.4.3 MULTIVARIATE
ANALYSIS OF COVARIANCE 264 7.5 SOME IMPORTANT ISSUES 268 7.5.1 MANOVA
VS. ANOVAS 268 7.5.2 CRITERIA FOR STATISTICAL INFERENCE 269 7.5.3
ASSESSING DVS 270 7.5.3.1 UNIVARIATEF 270 7.5.3.2 ROY-BARGMANN STEPDOWN
ANALYSIS 271 7.5.3.3 USING DISCRIMINANT ANALYSIS 272 7.5.3.4 CHOOSING
AMONG STRATEGIES FOR ASSESSING DVS 273 7.5.4 SPECIFIC COMPARISONS AND
TREND ANALYSIS 273 7.5.5 DESIGN COMPLEXITY 274 7.5.5.1 WITHIN-SUBJECTS
AND BETWEEN-WITHIN DESIGNS 274 7.5.5.2 UNEQUAL SAMPLE SIZES 276 CONTENTS
7.6 COMPLETE EXAMPLES OF MULTIVARIATE ANALYSIS OF VARIANCE AND
COVARIANCE 277 7.6.1 EVALUATION OF ASSUMPTIONS 277 7.6.1.1 UNEQUAL
SAMPLE SIZES AND MISSING DATA 277 7.6.1.2 MULTIVARIATE NORMALITY 279
7.6.1.3 LINEARITY 279 7.6.1.4 OUTLIERS 279 7.6.1.5 HOMOGENEITY OF
VARIANCE-COVARIANCE MATRICES 280 7.6.1.6 HOMOGENEITY OF REGRESSION 281
7.6.1.7 RELIABILITY OF COVARIATES 284 7.6.1.8 MULTICOLLINEARITY AND
SINGULARITY 285 7.6.2 MULTIVARIATE ANALYSIS OF VARIANCE 285 7.6.3
MULTIVARIATE ANALYSIS OF COVARIANCE 296 7.6.3.1 ASSESSING COVARIATES 296
7.6.3.2 ASSESSING DVS 296 7.7 COMPARISON OF PROGRAMS 307 7.7.1
SPSSPACKAGE 307 7.7.2 SAS SYSTEM 310 7.7.3 SYSTAT SYSTEM 310 PROFILE
ANALYSIS: THE MULTIVARIATE APPROACH TO REPEATED MEASURES 311 8.1 GENERAL
PURPOSE AND DESCRIPTION 311 8.2 KINDS OF RESEARCH QUESTIONS 312 8.2.1
PARALLELISMOF PROFILES 312 8.2.2 OVERALL DIFFERENCE AMONG GROUPS 8.2.3
FLATNESSOF PROFILES 313 8.2.4 CONTRASTS FOLLOWING PROFILE ANALYSIS 8.2.5
PARAMETER ESTIMATES 313 8.2.6 EFFECT SIZE 314 8.3 LIMITATIONS TO PROFILE
ANALYSIS 314 8.3.1 THEORETICAL ISSUES 314 8.3.2 PRACTICAL ISSUES 315
8.3.2.1 SAMPLE SIZE, MISSING DATA, AND POWER 315 8.3.2.2 MULTIVARIATE
NORMALITY 315 8.3.2.3 ABSENCE OF OUTLIERS 315 8.3.2.4 HOMOGENEITY OF
VARIANCE-COVARIANCE MATRICES 315 8.3.2.5 LINEARITY 316 8.3.2.6 ABSENCE
OF MULTICOLLINEARITY AND SINGULARITY 316 8.4 FUNDAMENTAL EQUATIONS FOR
PROFILE ANALYSIS 316 8.4.1 DIFFERENCES IN LEVELS 316 8.4.2 PARALLELISM
318 313 313 CONTENTS XI 8.4.3 FLATNESS 321 8.4.4 COMPUTER ANALYSES OF
SMALL-SAMPLE EXAMPLE 323 8.5 SOME IMPORTANT ISSUES 329 8.5.1 UNIVARIATE
VS. MULTIVARIATE APPROACH TO REPEATED MEASURES 329 8.5.2 CONTRASTS IN
PROFILE ANALYSIS 331 8.5.2.1 PARALLELISM AND FLATNESS SIGNIFICANT,
LEVELS NOT SIGNIFICANT (SIMPLE-EFFECTS ANALYSIS) 333 8.5.2.2 PARALLELISM
AND LEVELS SIGNIFICANT, FLATNESS NOT SIGNIFICANT (SIMPLE-EFFECTS
ANALYSIS) 336 8.5.2.3 PARALLELISM, LEVELS, AND FLATNESS SIGNIFICANT
(INTERACTION CONTRASTS) 339 8.5.2.4 ONLY PARALLELISM SIGNIFICANT 339
8.5.3 DOUBLY-MULTIVARIATE DESIGNS 339 8.5.4 CLASSIFYING PROFILES 345
8.5.5 IMPUTATION OF MISSING VALUES 345 8.6 COMPLETE EXAMPLES OF PROFILE
ANALYSIS 346 8.6.1 PROFILE ANALYSIS OF SUBSCALES OF THE WISC 346 8.6.1.1
EVALUATION OF ASSUMPTIONS 346 8.6.1.2 PROFILE ANALYSIS 351 8.6.2
DOUBLY-MULTIVARIATE ANALYSIS OF REACTION TIME 360 8.6.2.1 EVALUATION OF
ASSUMPTIONS 360 8.6.2.2 DOUBLY-MULTIVARIATE ANALYSIS OF SLOPE AND
INTERCEPT 363 8.7 COMPARISON OF PROGRAMS 371 8.7.1 SPSSPACKAGE 373 8.7.2
SAS SYSTEM 373 8.7.3 SYSTAT SYSTEM 374 DISCRIMINANT ANALYSIS 375 9.1
GENERAL PURPOSE AND DESCRIPTION 375 9.2 KINDS OF RESEARCH QUESTIONS 378
9.2.1 SIGNIFICANCE OF PREDICTION 378 9.2.2 NUMBER OF SIGNIFICANT
DISCRIMINANT FUNCTIONS 378 9.2.3 DIMENSIONS OF DISCRIMINATION 379 9.2.4
CLASSIFICATION FUNCTIONS 379 9.2.5 ADEQUACYOF CLASSIFICATION 379 9.2.6
EFFECT SIZE 379 9.2.7 IMPORTANCE OF PREDICTOR VARIABLES 380 9.2.8
SIGNIFICANCE OF PREDICTION WITH COVARIATES 380 9.2.9 ESTIMATION OF GROUP
MEANS 380 9.3 LIMITATIONS TO DISCRIMINANT ANALYSIS 381 9.3.1 THEORETICAL
ISSUES 381 XUE CONTENTS 9.3.2 PRACTICAL ISSUES 381 9.3.2.1 UNEQUAL SAMPLE
SIZES, MISSING DATA, AND POWER 381 9.3.2.2 MULJIVARIATE NORMALITY 382
9.3.2.3 ABSENCEOFOUTLIERS 382 9.3.2.4 HOMOGENEITY
OFVARIANCE-COVARIANCEMATRICES 382 9.3.2.5 LINEARITY 383 9.3.2.6 ABSENCE
OF MULTICOLLINEARITY AND SINGULARITY 383 9.4 FUNDAMENTAL EQUATIONS FOR
DISCRIMINANT ANALYSIS 384 9.4.1 DERIVATION AND TEST OF DISCRIMINANT
FUNCTIONS 384 9.4.2 CLASSIFICATION 387 9.4.3 COMPUTER ANALYSES OF
SMALL-SAMPLE EXAMPLE 389 9.5 TYPES OF DISCRIMINANT FUNCTION ANALYSES 395
9.5.1 DIRECT DISCRIMINANT ANALYSIS 395 9.5.2 SEQUENTIAL DISCRIMINANT
ANALYSIS 396 9.5.3 STEPWISE (STATISTICAL) DISCRIMINANT ANALYSIS 396 9.6
SOME IMPORTANT ISSUES 397 9.6.1 STATISTICAL INFERENCE 397 9.6.1.1
CRITERIA FOR OVERALL STATISTICAL SIGNIFICANCE 397 9.6.1.2 STEPPING
METHODS 397 9.6.2 NUMBER OF DISCRIMINANT FUNCTIONS 398 9.6.3
INTERPRETING DISCRIMINANT FUNCTIONS 398 9.6.3.1 DISCRIMINANT FUNCTION
PLOTS 398 9.6.3.2 STRUCTURE MATRIX OFLOADINGS 400 9.6.4 EVALUATING
PREDICTOR VARIABLES 401 9.6.5 EFFECT SIZE 402 9.6.6 DESIGN COMPLEXITY:
FACTORIAL DESIGNS 403 9.6.7 USE OF CLASSIFICATION PROCEDURES 404 9.6.7.1
CROSS-VALIDATION AND NEW CASES 405 9.6.7.2 JACKKNIFED CLASSIFICATION 405
9.6.7.3 EVALUATING IMPROVEMENT IN CLASSIFICATION 405 9.7 COMPLETE
EXAMPLE OF DISCRIMINANT ANALYSIS 407 9.7.1 EVALUATION OF ASSUMPTIONS 407
9.7.1.1 UNEQUAL SAMPLE SIZES AND MISSING DATA 407 9.7.1.2 MULTIVARIATE
NORMALITY 408 9.7.1.3 LINEARITY 408 9.7.1.4 OUTLIERS 408 9.7.1.5
HOMOGENEITY OFVARIANCE-COVARIANCEMATRICES 411 9.7.1.6 MULTICOLLINEARITY
AND SINGULARITY 411 9.7.2 DIRECT DISCRIMINANT ANALYSIS 412 9.8
COMPARISON OF PROGRAMS 430 9.8.1 SPSSPACKAGE 430 9.8.2 SAS SYSTEM 430
9.8.3 SYSTAT SYSTEM 436 CONTENTS XIII LOGISTIC REGRESSION 437 10.1
GENERAL PURPOSE AND DESCRIPTION 437 10.2 KINDS OF RESEARCH QUESTIONS 439
10.2.1 PREDICTION OF GROUP MEMBERSHIP OR OUTCOME 439 10.2.2 IMPORTANCE
OFPREDICTORS 439 10.2.3 INTERACTIONS AMONG PREDICTORS 440 10.2.4
PARAMETER ESTIMATES 440 10.2.5 CLASSIFICATION OF CASES 440 10.2.6
SIGNIFICANCE OF PREDICTION WITH COVARIATES 440 10.2.7 EFFECT SIZE 441
10.3 LIMITATIONS TO LOGISTIC REGRESSION ANALYSIS 441 10.3.1 THEORETICAL
ISSUES 441 10.3.2 PRACTICAL ISSUES 442 10.3.2.1 RATIO OF CASES TO
VARIABLES 442 10.3.2.2 ADEQUACY OF EXPECTED FREQUENCIES AND POWER 442
10.3.2.3 LINEARITY IN THE LOGIT 443 10.3.2.4 ABSENCE OF
MULTICOLLINEARITY 443 10.3.2.5 ABSENCE OF OUTLIERS IN THE SOLUTION 443
10.3.2.6 INDEPENDENCE OF ERRORS 443 10.4 FUNDAMENTAL EQUATIONS FOR
LOGISTIC REGRESSION 444 10.4.1 TESTING AND INTERPRETING COEFFICIENTS 445
10.4.2 GOODNESS-OF-FIT 446 10.4.3 COMPARING MODELS 448 10.4.4
INTERPRETATION AND ANALYSIS OF RESIDUAIS 448 10.4.5 COMPUTER ANALYSES OF
SMALL-SAMPLE EXAMPLE 449 10.5 TYPES OF LOGISTIC REGRESSION 453 10.5.1
DIRECT LOGISTIC REGRESSION 454 10.5.2 SEQUENTIAL LOGISTIC REGRESSION 454
10.5.3 STATISTICAL (STEPWISE) LOGISTIC REGRESSION 454 10.5.4 PROBIT AND
OTHER ANALYSES 456 10.6 SOME IMPORTANT ISSUES 457 10.6.1 STATISTICAL
INFERENCE 457 10.6.1.1 ASSESSING GOODNESS-OF-FIT OF MODELS 457 10.6.1.2
TESTS OFLNDIVIDUAL VARIABLES 459 10.6.2 EFFECT SIZE FOR A MODEL 460
10.6.3 INTERPRETATION OF COEFFICIENTS USING ODDS 461 10.6.4 CODING
OUTCOME AND PREDICTOR CATEGORIES 464 10.6.5 NUMBER AND TYPE OF OUTCOME
CATEGORIES 464 10.6.6 CLASSIFICATION OF CASES 468 10.6.7 HIERARCHICAL
AND NONHIERARCHICAL ANALYSIS 468 CONTENTS 10.6.8 IMPORTANCE OF
PREDICTORS 469 10.6.9 LOGISTIC REGRESSION FOR MATCHED GROUPS 469 10.7
COMPLETE EXAMPLES OF LOGISTIC REGRESSION 469 10.7.1 EVALUATION OF
LIMITATIONS 470 10.7.1.1 RATIO OF CASES TO VARIABLES AND MISSING DATA
470 10.7.1.2 MULTICOLLINEARITY 473 10.7.1.3 OUTLIERS IN THE SOLUTION 474
10.7.2 DIRECT LOGISTIC REGRESSION WITH TWO-CATEGORY OUTCOME AND
CONTINUOUS PREDICTORS 474 10.7.2.1 LIMITATION: LINEARITY IN THE LOGIT
474 10.7.2.2 DIRECT LOGISTIC REGRESSION WITH TWO-CATEGORY OUTCOME 10.7.3
SEQUENTIAL LOGISTIC REGRESSION WITH THREE CATEGORIES OF OUTCOME 481
10.7.3.1 LIMITATIONS OF MULTINOMIAL LOGISTIC REGRESSION 481 10.7.3.2
SEQUENTIAL MULTINOMIAL LOGISTIC REGRESSION 481 10.8 COMPARISONS OF
PROGRAMS 499 10.8.1 SPSSPACKAGE 499 10.8.2 SAS SYSTEM 504 10.8.3 SYSTAT
SYSTEM 504 SURVIVAL/FAILURE ANALYSIS 506 11.1 GENERAL PURPOSE AND
DESCRIPTION 506 11.2 KINDS OF RESEARCH QUESTIONS 507 11.2.1 PROPORTIONS
SURVIVING AT VARIOUS TIMES 507 11.2.2 GROUP DIFFERENCES IN SURVIVAL 508
11.2.3 SURVIVAL TIME WITH COVARIATES 508 11.2.3.1 TREATMENT EFFECTS 508
11.2.3.2 IMPORTANCE OF COVARIATES 508 11.2.3.3 PARAMETER ESTIMATES 508
11.2.3.4 CONTINGENCIES AMONG COVARIATES 508 11.2.3.5 EFFECT SIZE AND
POWER 509 11.3 LIMITATIONS TO SURVIVAL ANALYSIS 509 11.3.1 THEORETICAL
ISSUES 509 11.3.2 PRACTICAL ISSUES 509 11.3.2.1 SAMPLE SIZE AND MISSING
DATA 509 11.3.2.2 NORMALITY OF SAMPLING DISTRIBUTIONS, LINEARITY, AND
HOMOSCEDASTICITY 510 11.3.2.3 ABSENCEOF OUTLIERS 510 11.3.2.4
DIFFERENCES BETWEEN WITHDRAWN AND REMAINING CASES 510 11.3.2.5 CHANGE IN
SURVIVAL CONDITIONS OVER TIME 510 11.3.2.6 PROPORTIONALITY OF HAZARDS
510 11.3.2.7 ABSENCE OF MULTICOLLINEARITY 510 CONTENTS XV 11.4
FUNDAMENTAL EQUATIONS FOR SURVIVAL ANALYSIS 511 11.4.1 LIFETABLES 511
11.4.2 STANDARD ERROR OF CUMULATIVE PROPORTION SURVIVING 513 11.4.3
HAZARD AND DENSITY FUNCTIONS 514 11.4.4 PLOTOFLIFETABLES 515 11.4.5 TEST
FOR GROUP DIFFERENCES 515 11.4.6 COMPUTER ANALYSES OF SMALL-SAMPLE
EXAMPLE 517 11.5 TYPES OF SURVIVAL ANALYSES 524 11.5.1 ACTUARIAL AND
PRODUCT-LIMIT LIFE TABLES AND SURVIVOR FUNCTIONS 524 11.5.2 PREDICTION
OF GROUP SURVIVAL TIMES FROM COVARIATES 524 11.5.2.1 DIRECT, SEQUENTIAL,
AND STATISTICAL ANALYSIS 527 11.5.2.2 COX PROPORTIONAL-HAZARDS MODEL 527
11.5.2.3 ACCELERATED FAILURE-TIME MODELS 529 11.5.2.4 CHOOSING A METHOD
535 11.6 SOME IMPORTANT ISSUES 535 11.6.1 PROPORTIONALITY OF HAZARDS 535
11.6.2 CENSOREDDATA 537 11.6.2.1 RIGHT-CENSORED DATA 537 11.6.2.2
OTHERFORMSOFCENSORING 537 11.6.3 EFFECT SIZE AND POWER 538 11.6.4
STATISTICAL CRITERIA 539 11.6.4.1 TEST STATISTICS FOR GROUP DIFFERENCES
IN SURVIVAL FUNCTIONS 539 11.6.4.2 TEST STATISTICS FOR PREDICTION FROM
COVARIATES 540 11.6.5 PREDICTING SURVIVAL RATE 540 11.6.5.1 REGRESSION
COEFFICIENTS (PARAMETER ESTIMATES) 540 11.6.5.2 ODDSRATIOS 540 11.6.5.3
EXPECTED SURVIVAL RATES 541 11.7 COMPLETE EXAMPLE OF SURVIVAL ANALYSIS
541 11.7.1 EVALUATION OF ASSUMPTIONS 543 11.7.1.1 ACCURACY OF INPUT,
ADEQUACY OF SAMPLE SIZE, MISSING DATA, AND DISTRIBUTIONS 543 11.7.1.2
OUTLIERS 545 11.7.1.3 DIFFERENCES BETWEEN WITHDRAWN AND REMAINING CASES
549 11.7.1.4 CHANGE IN SURVIVAL EXPERIENCE OVER TIME 549 11.7.1.5
PROPORTIONALITY OF HAZARDS 549 11.7.1.6 MULTICOLLINEARITY 551 11.7.2 COX
REGRESSION SURVIVAL ANALYSIS 551 11.7.2.1 EFFECT OFDRUGTREATMENT 552
11.7.2.2 EVALUATION OF OTHER COVARIATES 552 11.8 COMPARISON OF PROGRAMS
559 11.8.1 SAS SYSTEM 559 11.8.2 SPSSPACKAGE 559 11.8.3 SYSTAT SYSTEM
566 CONTENTS CANONICAL CORRELATION 567 12.1 GENERAL PURPOSE AND
DESCRIPTION 567 12.2 KINDS OF RESEARCH QUESTIONS 568 12.2.1 NUMBER OF
CANONICAL VARIATE PAIRS 568 12.2.2 INTERPRETATION OF CANONICAL VARIATES
569 12.2.3 IMPORTANCE OF CANONICAL VARIATES 569 12.2.4 CANONICAL VARIATE
SCORES 569 12.3 LIMITATIONS 569 12.3.1 THEORETICAL LIMITATIONS 569
12.3.2 PRACTICAL ISSUES 570 12.3.2.1 RATIO OFCASESTOIVS 570 12.3.2.2
NORMALITY, LINEARITY, AND HOMOSCEDASTICITY 570 12.3.2.3 MISSINGDATA 571
12.3.2.4 ABSENCE OF OUTLIERS 571 12.3.2.5 ABSENCE OF MULTICOLLINEARITY
AND SINGULARITY 571 12.4 FUNDAMENTAL EQUATIONS FOR CANONICAL CORRELATION
572 12.4.1 EIGENVALUES AND EIGENVECTORS 573 12.4.2 MATRIX EQUATIONS 575
12.4.3 PROPORTIONS OFVARIANCEEXTRACTED 579 12.4.4 COMPUTER ANALYSES OF
SMALL-SAMPLE EXAMPLE 580 12.5 SOME IMPORTANT ISSUES 586 12.5.1
IMPORTANCE OF CANONICAL VARIATES 586 12.5.2 INTERPRETATION OF CANONICAL
VARIATES 587 12.6 COMPLETE EXAMPLE OF CANONICAL CORRELATION 587 12.6.1
EVALUATION OF ASSUMPTIONS 588 12.6.1.1 MISSINGDATA 588 12.6.1.2
NORMALITY, LINEARITY, AND HOMOSCEDASTICITY 588 12.6.1.3 OUTLIERS 591
12.6.1.4 MULTICOLLINEARITY AND SINGULARITY 595 12.6.2 CANONICAL
CORRELATION 595 12.7 COMPARISON OF PROGRAMS 604 12.7.1 SAS SYSTEM 604
12.7.2 SPSSPACKAGE 604 12.7.3 SYSTAT SYSTEM 606 PRINCIPAL COMPONENTS AND
FACTOR ANALYSIS 607 13.1 GENERAL PURPOSE AND DESCRIPTION 607 13.2 KINDS
OF RESEARCH QUESTIONS 610 13.2.1 NUMBER OF FACTORS 610 CONTENTS XVUE
13.2.2 NATURE OF FACTORS 611 13.2.3 IMPORTANCE OF SOLUTIONS AND FACTORS
611 13.2.4 TESTING THEORY IN FA 611 13.2.5 ESTIMATING SCORES ON FACTORS
611 13.3 LIMITATIONS 611 13.3.1 THEORETICAL ISSUES 611 13.3.2 PRACTICAL
ISSUES 612 13.3.2.1 SAMPLE SIZE AND MISSING DATA 613 13.3.2.2 NORMALITY
613 13.3.2.3 LINEARITY 613 13.3.2.4 ABSENCE OF OUTLIERS AMONG CASES 613
13.3.2.5 ABSENCE OF MULTICOLLINEARITY AND SINGULARITY 614 13.3.2.6
FACTORABILITYOFR 614 13.3.2.7 ABSENCE OF OUTLIERS AMONG VARIABLES 614
13.4 FUNDAMENTAL EQUATIONS FOR FACTOR ANALYSIS 615 13.4.1 EXTRACTION 616
13.4.2 ORTHOGONAL ROTATION 620 13.4.3 COMMUNALITIES, VARIANCE, AND
COVARIANCE 621 13.4.4 FACTOR SCORES 622 13.4.5 OBLIQUE ROTATION 625
13.4.6 COMPUTER ANALYSES OF SMALL-SAMPLE EXAMPLE 628 13.5 MAJOR TYPES OF
FACTOR ANALYSES 633 13.5.1 FACTOR EXTRACTION TECHNIQUES 633 13.5.1.1
PCAVS. FA 634 13.5.1.2 PRINCIPAL COMPONENTS 635 13.5.1.3 PRINCIPAL
FACTORS 636 13.5.1.4 IMAGE FACTOR EXTRACTION 636 13.5.1.5 MAXIMUM
LIKELIHOOD FACTOR EXTRACTION 636 13.5.1.6 UNWEIGHTED LEAST SQUARES
FACTORING 636 13.5.1.7 GENERALIZED (WEIGHTED) LEAST SQUARES FACTORING
637 13.5.1.8 ALPHA FACTORING 637 13.5.2 ROTATION 637 13.5.2.1 ORTHOGONAL
ROTATION 638 13.5.2.2 OBLIQUE ROTATION 638 13.5.2.3 GEOMETRIE
INTERPRETATION 640 13.5.3 SOME PRACTICAL RECOMMENDATIONS 642 13.6 SOME
IMPORTANT ISSUES 643 13.6.1 ESTIMATES OF COMMUNALITIES 643 13.6.2
ADEQUACY OF EXTRACTION AND NUMBER OF FACTORS 644 13.6.3 ADEQUACY OF
ROTATION AND SIMPLE STRUCTURE 646 13.6.4 IMPORTANCE AND INTERNAL
CONSISTENCY OF FACTORS 647 13.6.5 INTERPRETATION OF FACTORS 649 13.6.6
FACTOR SCORES 650 13.6.7 COMPARISONS AMONG SOLUTIONS AND GROUPS 651
CONTENTS 13.7 COMPLETEEXAMPLEOFFA 651 13.7.1 EVALUATIONOF LIMITATIONS
652 13.7.1.1 SAMPLE SIZE AND MISSING DATA 652 13.7.1.2 NORMALITY 652
13.7.1.3 LINEARITY 652 13.7.1.4 OUTLIERS 652 13.7.1.5 MULTICOLLINEARITY
AND SINGULARITY 657 13.7.1.6 OUTLIERS AMONG VARIABLES 657 13.7.2
PRINCIPAL FACTORS EXTRACTION WITH VARIMAX ROTATION 657 13.8 COMPARISON
OF PROGRAMS 671 13.8.1 SPSSPACKAGE 674 13.8.2 SAS SYSTEM 675 13.8.3
SYSTAT SYSTEM 675 STRUCTURAL EQUATION MODELING 676 14.1 GENERAL PURPOSE
AND DESCRIPTION 676 14.2 KINDS OF RESEARCH QUESTIONS 680 14.2.1
ADEQUACYOF THE MODEL 680 14.2.2 TESTING THEORY 680 14.2.3 AMOUNT OF
VARIANCE IN THE VARIABLES ACCOUNTED FOR BY THE FACTORS 680 14.2.4
RELIABILITY OF THE INDICATORS 680 14.2.5 PARAMETER ESTIMATES 680 14.2.6
INTERVENING VARIABLES 681 14.2.7 GROUP DIFFERENCES 681 14.2.8
LONGITUDINAL DIFFERENCES 681 14.2.9 MULTILEVEL MODELING 681 14.3
LIMITATIONS TO STRUCTURAL EQUATION MODELING 682 14.3.1 THEORETICAL
ISSUES 682 14.3.2 PRACTICAL ISSUES 682 14.3.2.1 SAMPLE SIZE AND MISSING
DATA 682 14.3.2.2 MULTIVARIATE NORMALITY AND ABSENCE OF OUTLIERS 683
14.3.2.3 LINEARITY 683 14.3.2.4 ABSENCE OF MULTICOLLINEARITY AND
SINGULARITY 683 14.3.2.5 RESIDUAIS 684 14.4 FUNDAMENTAL EQUATIONS FOR
STRUCTURAL EQUATIONS MODELING 684 14.4.1 COVARIANCE ALGEBRA 684 14.4.2
MODEL HYPOTHESES 686 14.4.3 MODEL SPECIFICATION 688 14.4.4 MODEL
ESTIMATION 690 14.4.5 MODEL EVALUATION 694 14.4.6 COMPUTER ANALYSIS OF
SMALL-SAMPLE EXAMPLE 696 15 CONTENTS XIX 14.5 SOME IMPORTANT ISSUES 709
14.5.1 MODEL IDENTIFICATION 709 14.5.2 ESTIMATION TECHNIQUES 713
14.5.2.1 ESTIMATION METHODS AND SAMPLE SIZE 714 14.5.2.2 ESTIMATION
METHODS AND NONNORMALITY 714 14.5.2.3 ESTIMATION METHODS AND DEPENDENCE
715 14.5.2.4 SOME RECOMMENDATIONS FOR CHOICE OF ESTIMATION METHOD 715
14.5.3 ASSESSING THE FIT OF THE MODEL 715 14.5.3.1 COMPARATIVE FIT
INDICES 716 14.5.3.2 ABSOLUTE FIT INDEX 718 14.5.3.3 INDICES OF
PROPORTION OF VARIANCE ACCOUNTED 718 14.5.3.4 DEGREE OF PARSIMONY FIT
INDICES 719 14.5.3.5 RESIDUAL-BASED FIT INDICES 720 14.5.3.6 CHOOSING
AMONG FIT INDICES 720 14.5.4 MODEL MODIFICATION 721 14.5.4.1 CHI-SQUARE
DIFFERENCE TEST 721 14.5.4.2 LAGRANGE MULTIPLIER (LM) TEST 721 14.5.4.3
WALD TEST 723 14.5.4.4 SOME CAVEATS AND HINTS ON MODEL MODIFICATION 728
14.5.5 RELIABILITY AND PROPORTION OF VARIANCE 728 14.5.6 DISCRETE AND
ORDINAL DATA 729 14.5.7 MULTIPLE GROUP MODELS 730 14.5.8 MEAN AND
COVARIANCE STRUCTURE MODELS 731 14.6 COMPLETE EXAMPLES OF STRUCTURAL
EQUATION MODELING ANALYSIS 732 14.6.1 CONFIRMATORY FACTOR ANALYSIS OF
THE WISC 732 14.6.1.1 MODEL SPECIFICATION FOR CFA 732 14.6.1.2
EVALUATION OF ASSUMPTIONS FOR CFA 733 14.6.1.3 CFA MODEL ESTIMATION AND
PRELIMINARY EVALUATION 734 14.6.1.4 MODEL MODIFICATION 743 14.6.2 SEM OF
HEALTH DATA 750 14.6.2.1 SEM MODEL SPECIFICATION 750 14.6.2.2 EVALUATION
OF ASSUMPTIONS FOR SEM 751 14.6.2.3 SEM MODEL ESTIMATION AND PRELIMINARY
EVALUATION 755 14.6.2.4 MODEL MODIFICATION 759 14.7 COMPARISON OF
PROGRAMS 773 14.7.1 EQS 773 14.7.2 LISREL 773 14.7.3 AMOS 780 14.7.4 SAS
SYSTEM 780 MULTILEVEL LINEAR MODELING 781 15.1 GENERAL PURPOSE AND
DESCRIPTION 781 CONTENTS 15.2 KINDS OF RESEARCH QUESTIONS 784 15.2.1
GROUP DIFFERENCES IN MEANS 784 15.2.2 GROUP DIFFERENCES IN SLOPES 784
15.2.3 CROSS-LEVEL INTERACTIONS 785 15.2.4 META-ANALYSIS 785 15.2.5
RELATIVE STRENGTH OF PREDICTORS AT VARIOUS LEVELS 785 15.2.6 INDIVIDUAL
AND GROUP STRUCTURE 785 15.2.7 PATH ANALYSIS AT INDIVIDUAL AND GROUP
LEVELS 786 15.2.8 ANALYSIS OF LONGITUDINAL DATA 786 15.2.9 MULTILEVEL
LOGISTIC REGRESSION 786 15.2.10 MULTIPLE RESPONSE ANALYSIS 786 15.3
LIMITATIONS TO MULTILEVEL LINEAR MODELING 786 15.3.1 THEORETICAL ISSUES
786 15.3.2 PRACTICAL ISSUES 787 15.3.2.1 SAMPLE SIZE, UNEQUAL-N, AND
MISSING DATA 787 15.3.2.2 INDEPENDENCE OF ERRORS 788 15.3.2.3 ABSENCE OF
MULTICOLLINEARITY AND SINGULARITY 789 15.4 FUNDAMENTAL EQUATIONS 789
15.4.1 INTERCEPTS-ONLY MODEL 792 15.4.1.1 THE INTERCEPTS-ONLY MODEL:
LEVEL-1 EQUATION 793 15.4.1.2 THE INTERCEPTS-ONLY MODEL: LEVEL-2
EQUATION 793 15.4.1.3 COMPUTER ANALYSIS OF INTERCEPTS-ONLY MODEL 794
15.4.2 MODEL WITH A FIRST-LEVEL PREDICTOR 799 15.4.2.1 LEVEL-1 EQUATION
FOR A MODEL WITH A LEVEL-1 PREDICTOR 799 15.4.2.2 LEVEL-2 EQUATIONS FOR
A MODEL WITH A LEVEL-1 PREDICTOR 801 15.4.2.3 COMPUTERANALYSIS OFA MODEL
WITHA LEVEL-1 PREDICTOR 802 15.4.3 MODEL WITH PREDICTORS AT FIRST AND
SECOND LEVELS 807 15.4.3.1 LEVEL-1 EQUATION FOR MODEL WITH PREDICTORS AT
BOTH LEVELS 807 15.4.3.2 LEVEL-2 EQUATIONS FOR MODEL WITH PREDICTORS AT
BOTH LEVELS 807 15.4.3.3 COMPUTER ANALYSES OF MODEL WITH PREDICTORS AT
FIRST AND SECOND LEVELS 808 15.5 TYPESOFMLM 814 15.5.1 REPEATED MEASURES
814 15.5.2 HIGHER-ORDER MLM 819 15.5.3 LATENT VARIABLES 819 15.5.4
NONNORMAL OUTCOME VARIABLES 820 15.5.5 MULTIPLE RESPONSE MODELS 821 15.6
SOME IMPORTANT ISSUES 822 15.6.1 INTRACLASS CORRELATION 822 15.6.2
CENTERING PREDICTORS AND CHANGES IN THEIR INTERPRETATIONS 823 15.6.3
INTERACTIONS 826 15.6.4 RANDOM AND FIXED INTERCEPTS AND SLOPES 826
CONTENTS XXI 15.6.5 STATISTICAL INFERENCE 830 15.6.5.1 ASSESSING MODELS
830 15.6.5.2 TESTS OF INDIVIDUAL EFFECTS 831 15.6.6 EFFECT SIZE 832
15.6.7 ESTIMATION TECHNIQUES AND CONVERGENCE PROBLEMS 833 15.6.8
EXPLORATORY MODEL BUILDING 834 15.7 COMPLETEEXAMPLEOFMLM 835 15.7.1
EVALUATION OF ASSUMPTIONS 835 15.7.1.1 SAMPLE SIZES, MISSING DATA, AND
DISTRIBUTIONS 835 15.7.1.2 OUTLIERS 838 15.7.1.3 MULTICOLLINEARITY AND
SINGULARITY 839 15.7.1.4 INDEPENDENCE OF ERRORS: INTRACLASS CORRELATIONS
839 15.7.2 MULTILEVEL MODELING 840 15.8 COMPARISON OF PROGRAMS 852
15.8.1 SAS SYSTEM 852 15.8.2 SPSSPACKAGE 856 15.8.3 HLM PROGRAM 856
15.8.4 MLWIN PROGRAM 857 15.8.5 SYSTAT SYSTEM 857 MULTIWAY FREQUENCY
ANALYSIS 858 16.1 GENERAL PURPOSE AND DESCRIPTION 858 16.2 KINDS OF
RESEARCH QUESTIONS 859 16.2.1 ASSOCIATIONS AMONG VARIABLES 859 16.2.2
EFFECT ON A DEPENDENT VARIABLE 860 16.2.3 PARAMETER ESTIMATES 860 16.2.4
IMPORTANCEOF EFFECTS 860 16.2.5 EFFECT SIZE 860 16.2.6 SPECIFIC
COMPARISONS AND TREND ANALYSIS 860 16.3 LIMITATIONS TO MULTIWAY
FREQUENCY ANALYSIS 861 16.3.1 THEORETICAL ISSUES 861 16.3.2 PRACTICAL
ISSUES 861 16.3.2.1 INDEPENDENCE 861 16.3.2.2 RATIO OFCASESTO VARIABLES
861 16.3.2.3 ADEQUACY OF EXPECTED FREQUENCIES 862 16.3.2.4 ABSENCE OF
OUTLIERS IN THE SOLUTION 863 16.4 FUNDAMENTAL EQUATIONS FOR MULTIWAY
FREQUENCY ANALYSIS 863 16.4.1 SCREENING FOR EFFECTS 864 16.4.1.1 TOTAL
EFFECT 865 16.4.1.2 FIRST-ORDER EFFECTS 866 16.4.1.3 SECOND-ORDER
EFFECTS 867 16.4.1.4 THIRD-ORDER EFFECT 871 CONTENTS 16.4.2 MODELING 871
16.4.3 EVALUATION AND INTERPRETATION 874 16.4.3.1 RESIDUAIS 874 16.4.3.2
PARAMETER ESTIMATES 874 16.4.4 COMPUTER ANALYSES OF SMALL-SAMPLE EXAMPLE
880 16.5 SOME IMPORTANT ISSUES 887 16.5.1 HIERARCHICAL AND
NONHIERARCHICAL MODELS 887 16.5.2 STATISTICAL CRITERIA 888 16.5.2.1
TESTS OF MODELS 888 16.5.2.2 TESTS OFLNDIVIDUAL EFFECTS 888 16.5.3
STRATEGIES FOR CHOOSING A MODEL 889 16.5.3.1 SPSS HILOGLINEAR
(HIERARCHICAL) 889 16.5.3.2 SPSS GENLOG (GENERAL LOG-LINEAR) 889
16.5.3.3 SAS CATMOD AND SPSS LOGLINEAR (GENERAL LOG-LINEAR) 890 16.6
COMPLETE EXAMPLE OF MULTIWAY FREQUENCY ANALYSIS 890 16.6.1 EVALUATION OF
ASSUMPTIONS: ADEQUACY OF EXPECTED FREQUENCIES 890 16.6.2 HIERARCHICAL
LOG-LINEAR ANALYSIS 891 16.6.2.1 PRELIMINARY MODEL SCREENING 891
16.6.2.2 STEPWISE MODEL SELECTION 893 16.6.2.3 ADEQUACY OF FIT 895
16.6.2.4 INTERPRETATION OF THE SELECTED MODEL 901 16.7 COMPARISON OF
PROGRAMS 908 16.7.1 SPSSPACKAGE 911 16.7.2 SAS SYSTEM 912 16.7.3 SYSTAT
SYSTEM 912 AN OVERVIEW OF THE GENERAL LINEAR MODEL 913 17.1 LINEARITY
AND THE GENERAL LINEAR MODEL 913 17.2 BIVARIATE TO MULTIVARIATE
STATISTICS AND OVERVIEW OFTECHNIQUES 913 17.2.1 BIVARIATE FORM 913
17.2.2 SIMPLE MULTIVARIATE FORM 914 17.2.3 FUELL MULTIVARIATE FORM 917
17.3 ALTERNATIVE RESEARCH STRATEGIES 918 TIME-SERIES ANALYSIS (AVAILABLE
ONLINE AT WWW.ABLONGMAN.COM/TABACHNICK5E) 18-1 18.1 GENERAL PURPOSE AND
DESCRIPTION 18-1 CONTENTS XX111 18.2 KINDS OF RESEARCH QUESTIONS 18-3
18.2.1 PATTERN OF AUTOCORRELATION 18-5 18.2.2 SEASONAL CYCLES AND TRENDS
18-5 18.2.3 FORECASTING 18-5 18.2.4 EFFECT OF AN INTERVENTION 18-5
18.2.5 COMPARING TIME SERIES 18-5 18.2.6 TIME SERIES WITH COVARIATES
18-6 18.2.7 EFFECT SIZE AND POWER 18-6 18.3 ASSUMPTIONS OF TIME-SERIES
ANALYSIS 18-6 18.3.1 THEORETICAL ISSUES 18-6 18.3.2 PRACTICAL ISSUES
18-6 18.3.2.1 NORMALITY OF DISTRIBUTIONS OF RESIDUALS 18-6 18.3.2.2
HOMOGENEITY OFVARIANCE AND ZERO MEAN OF RESIDUALS 18-7 18.3.2.3
INDEPENDENCE OF RESIDUALS 18-7 18.3.2.4 ABSENCE OF OUTLIERS 18-7 18.4
FUNDAMENTAL EQUATIONS FOR TIME-SERIES ARIMA MODELS 18-7 18.4.1
IDENTIFICATION ARIMA (P, D, Q) MODELS 18-8 18.4.1.1 TREND COMPONENTS, D:
MAKING THE PROCESS STATIONARY 18-8 18.4.1.2 AUTO-REGRESSIVE COMPONENTS
18-11 18.4.1.3 MOVING AVERAGE COMPONENTS 18-12 18.4.1.4 MIXED MODELS
18-13 18.4.1.5 ACFSANDPACFS 18-13 18.4.2 ESTIMATING MODEL PARAMETERS
18-16 18.4.3 DIAGNOSING A MODEL 18-19 18.4.4 COMPUTER ANALYSIS OF
SMALL-SAMPLE TIME-SERIES EXAMPLE 18-19 18.5 TYPESOF TIME-SERIES ANALYSES
18-27 18.5.1 MODELS WITH SEASONAL COMPONENTS 18-27 18.5.2 MODELS WITH
INTERVENTIONS 18-30 18.5.2.1 ABRUPT, PERMANENT EFFECTS 18-32 18.5.2.2
ABRUPT, TEMPORARY EFFECTS 18-32 18.5.2.3 GRADUAL, PERMANENT EFFECTS
18-38 18.5.2.4 MODELS WITH MULTIPLE INTERVENTIONS 18-38 18.5.3 ADDING
CONTINUOUS VARIABLES 18-38 18.6 SOME IMPORTANT ISSUES 18-41 18.6.1
PATTERNSOF ACFSANDPACFS 18-41 18.6.2 EFFECT SIZE 18-44 18.6.3
FORECASTING 18-45 18.6.4 STATISTICAL METHODS FOR COMPARING TWO MODELS
18-45 18.7 COMPLETE EXAMPLE OF A TIME-SERIES ANALYSIS 18-47 18.7.1
EVALUATION OF ASSUMPTIONS 18-48 18.7.1.1 NORMALITY OF SAMPLING
DISTRIBUTIONS 18-48 18.7.1.2 HOMOGENEITY OFVARIANCE 18-48 18.7.1.3
OUTLIERS 18-48 XXIV CONTENTS 18.7.2 BASELINE MODEL IDENTIFICATION AND
ESTIMATION 18-48 18.7.3 BASELINE MODEL DIAGNOSIS 18-49 18.7.4
INTERVENTION ANALYSIS 18-55 18.7.4.1 MODEL DIAGNOSIS 18-55 18.7.4.2
MODEL INTERPRETATION 18-56 18.8 COMPARISON OF PROGRAMS 18-60 18.8.1
SPSSPACKAGE 18-61 18.8.2 SAS SYSTEM 18-61 18.8.3 SYSTAT SYSTEM 18-61 A
SKIMPY INTRODUCTION TO MATRIX ALGEBRA 924 A.L THE TRACEOFA MATRIX 925
A.2 ADDITION OR SUBTRACTION OF A CONSTANT TO A MATRIX 925 A.3
MULTIPLICATION OR DIVISION OF A MATRIX BY A CONSTANT 925 A.4 ADDITION
AND SUBTRACTION OF TWO MATRICES 926 A.5 MULTIPLICATION, TRANSPOSES, AND
SQUARE ROOTS OF MATRICES 927 A.6 MATRIX "DIVISION" (INVERSES AND
DETERMINANTS) 929 A.7 EIGENVALUES AND EIGENVECTORS: PROCEDURES FOR
CONSOLIDATING VARIANCE FROM A MATRIX 930 RESEARCH DESIGNS FOR COMPLETE
EXAMPLES 934 B.L WOMEN'S HEALTH AND DRUG STUDY 934 B.2 SEXUAL ATTRACTION
STUDY 935 B.3 LEARNING DISABILITIES DATA BANK 938 B.4 REACTION TIME TO
IDENTIFY FIGURES 939 B.5 FIELD STUDIES OF NOISE-INDUCED SLEEP
DISTURBANCE 939 B.6 CLINICAL TRIAL FOR PRIMARY BILIARY CIRRHOSIS 940 B.7
IMPACTOF SEAT BELT LAW 940 APPENDIX \^ STATISTICAL TABLES 941 C.L NORMAL
CURVE AREAS 942 C.2 CRITICAL VALUES OF THE T DISTRIBUTION FOR A = .05
AND .01, TWO-TAILED TEST 943 APPENDIX R\ APPENDIX B CONTENTS XXV C.3
CRITICAL VALUES OFTHEF DISTRIBUTION 944 C.4 CRITICAL VALUES OF CHI
SQUARE (/ 2 ) 949 C.5 CRITICAL VALUES FOR SQUARED MULTIPLE CORRELATION
(R 2 ) IN FORWARD STEPWISE SELECTION 950 C.6 CRITICAL VALUES FOR F MAX
(S^AX/^MIN) DISTRIBUTION FOR A = .05 AND .01 952 REFERENCES 953 INDEX
963 |
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| author | Tabachnick, Barbara G. 1936- Fidell, Linda S. 1942- |
| author_GND | (DE-588)131432389 (DE-588)132341697 |
| author_facet | Tabachnick, Barbara G. 1936- Fidell, Linda S. 1942- |
| author_role | aut aut |
| author_sort | Tabachnick, Barbara G. 1936- |
| author_variant | b g t bg bgt l s f ls lsf |
| building | Verbundindex |
| bvnumber | BV035069991 |
| callnumber-first | Q - Science |
| callnumber-label | QA278 |
| callnumber-raw | QA278 |
| callnumber-search | QA278 |
| callnumber-sort | QA 3278 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | CM 4000 MR 2100 QH 234 SK 830 SK 840 |
| classification_tum | MAT 627f |
| ctrlnum | (OCoLC)62766132 (DE-599)BVBBV035069991 |
| dewey-full | 519.5/35 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5/35 |
| dewey-search | 519.5/35 |
| dewey-sort | 3519.5 235 |
| dewey-tens | 510 - Mathematics |
| discipline | Soziologie Psychologie Mathematik Wirtschaftswissenschaften |
| discipline_str_mv | Soziologie Psychologie Mathematik Wirtschaftswissenschaften |
| edition | 5. ed., internat. ed. |
| format | Book |
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| genre | (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Lehrbuch |
| id | DE-604.BV035069991 |
| illustrated | Illustrated |
| index_date | 2024-07-02T22:03:53Z |
| indexdate | 2024-07-09T21:21:30Z |
| institution | BVB |
| isbn | 0205465250 0205459382 9780205465255 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016738385 |
| oclc_num | 62766132 |
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| owner_facet | DE-355 DE-BY-UBR DE-703 DE-20 DE-1102 DE-91S DE-BY-TUM DE-92 DE-858 |
| physical | XXVIII, 980 S. graph. Darst. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Pearson |
| record_format | marc |
| spelling | Tabachnick, Barbara G. 1936- Verfasser (DE-588)131432389 aut Using multivariate statistics Barbara G. Tabachnick ; Linda S. Fidell 5. ed., internat. ed. Boston ; Munich [u.a.] Pearson 2007 XXVIII, 980 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Analyse multivariée Analyse multivariée rasuqam Análise multivariada larpcal Análisis multivariable Estatística larpcal Statistique mathématique Statistique mathématique rasuqam Multivariate analysis Multivariate Analyse (DE-588)4040708-1 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Multivariate Analyse (DE-588)4040708-1 s Statistik (DE-588)4056995-0 s 1\p DE-604 Fidell, Linda S. 1942- Verfasser (DE-588)132341697 aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016738385&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Tabachnick, Barbara G. 1936- Fidell, Linda S. 1942- Using multivariate statistics Analyse multivariée Analyse multivariée rasuqam Análise multivariada larpcal Análisis multivariable Estatística larpcal Statistique mathématique Statistique mathématique rasuqam Multivariate analysis Multivariate Analyse (DE-588)4040708-1 gnd Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4040708-1 (DE-588)4056995-0 (DE-588)4123623-3 |
| title | Using multivariate statistics |
| title_auth | Using multivariate statistics |
| title_exact_search | Using multivariate statistics |
| title_exact_search_txtP | Using multivariate statistics |
| title_full | Using multivariate statistics Barbara G. Tabachnick ; Linda S. Fidell |
| title_fullStr | Using multivariate statistics Barbara G. Tabachnick ; Linda S. Fidell |
| title_full_unstemmed | Using multivariate statistics Barbara G. Tabachnick ; Linda S. Fidell |
| title_short | Using multivariate statistics |
| title_sort | using multivariate statistics |
| topic | Analyse multivariée Analyse multivariée rasuqam Análise multivariada larpcal Análisis multivariable Estatística larpcal Statistique mathématique Statistique mathématique rasuqam Multivariate analysis Multivariate Analyse (DE-588)4040708-1 gnd Statistik (DE-588)4056995-0 gnd |
| topic_facet | Analyse multivariée Análise multivariada Análisis multivariable Estatística Statistique mathématique Multivariate analysis Multivariate Analyse Statistik Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016738385&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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