A primer of multivariate statistics:
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| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
Mahwah [u.a.]
Erlbaum
2001
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| Edition: | 3. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene Nachdrucke |
| Physical Description: | XX, 609 S. |
| ISBN: | 0805832106 |
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MARC
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| 245 | 1 | 0 | |a A primer of multivariate statistics |c Richard J. Harris |
| 250 | |a 3. ed. | ||
| 264 | 1 | |a Mahwah [u.a.] |b Erlbaum |c 2001 | |
| 300 | |a XX, 609 S. | ||
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| adam_text | Contents
1 The Forest before the Trees
1.0 Why Statistics? 1
1.01 Statistics as a Form of Social Control 1
1.02 Objections to Null Hypothesis Significance Testing 2
1.03 Should Significance Tests be Banned? 3
1.04 Math Modeling s the Ultimate Answer 5
1.05 Some Recent Developments in Univariate Statistics 6
1.0.5.1 The MIDS and FEDs criteria as alternatives to power calculation 7
Table 1.1 Fraction of Population Effect Size That Must Be Statistically
Significant in Order to Achieve a Given Level of Power for Your
Significance Test 9
1.0.5.2 Prior Information Confidence Intervals (PICIs) 9
1.1 Why Multivariate Statistics? 10
1.1.1 Bonferroni Adjustment: An Alternative to Multivariate Statistics. 13
1.1.2 Why Isn t Bonferroni Adjustment Enough? 14
1.2 A Heuristic Survey of Statistical Techniques 14
Table 1.2 Statistical Techniques 16
1.2.1 Student s t test 17
1.2.2 One Way Analysis of Variance 18
1.2.3 Hotelling s f 21
Example 1.1 Anglo versus Chicano Early Memories 23
1.2.4 One Way Multivariate Analysis of Variance 24
Example 1.2 Inferring Social Motives from Behavior 25
1.2.5 Higher Order Analysis of Variance 26
1.2.6 Higher Order Manova 27
Example 1.3 Fat, Four eyed, and Female 28
1.2.7 Pearson r and Bivariate Regression 28
1.2.8 Multiple Correlation and Regression 31
Example 1.4 Chicano Role Models, GPA, and MRA 33
1.2.9 Path Analysis 34
1.2.10 Canonical Correlation 35
Figure 1.1 Multivariate Analyses of Between Set Relationships 36
Example 1.5 Television Viewing and Fear of Victimization 37
1.2.11 Analysis of Covariance 38
1.2.12 Principal Component Analysis 40
1.2.13 Factor Analysis 42
Example 1.6 Measuring Perceived Deindividuation 44
1.2.14 Structural Equation Modeling 44
xii Contents
1.3 Learning to Use Multivariate Statistics 45
1.3.1 A Taxonomy of Linear Combinatons 45
1.3.1.1 Averages of subsets of the measures 45
1.3.1.2 Profiles 47
1.3.1.3 Contrasts 47
1.3.2 Why the Rest of the Book? 51
Quiz 1 See How Much You Know after Reading Just One Chapter! 55
Sample Answers to Quiz 1 56
2 Multiple Regression: Predicting One Variable
from Many
Data Set 1 58
2.1 The Model 59
2.2 Choosing Weights 62
2.2.1 Least Squares Criterion 62
Table 2.1 Multiple Regression Analyses of Data Set 1 66
Table 2.2 Data Set lb: A Presumptuous Data Set 68
2.2.2 Maximum Correlation Criterion 69
2.2.3 The Utility of Matrix Algebra 70
2.2.4 Independence of Irrelevant Parameters 72
2.3 Relating the Sample Equation to the Population Equation 74
Table 2.3 Summary of Significance Tests for Multiple Regression 77
2.3.1 Rx versus Sx versus x x as the Basis for MRA 81
Table 2.4 Alternative MRA Formulae 84
2.3.2 Specific Comparisons 84
2.3.3 Illustrating Significance Tests 86
Example 2.1 Locus of Control, the CPQ, and Hyperactivity 86
Computer break 2 1: CPQ vs. LOC, CPT C, CPT E 89
2.3.4 Stepwise Multiple Regression Analysis 95
Example 2.1 Revisited 96
2.4 Computer Programs for Multiple Regression 96
2.4.1 Computer Logic and Organization 97
2.4.2 Sage Advice on Use of Computer Programs 98
2.4.3 Computerized Multiple Regression Analysis 100
2.4.3.1 MATLAB 100
2.4.3.2 SPSS REGRESSION, Syntax Window 101
2.4.3.3 SPSS REGRESSION , Point and Click 102
2.4.3.4 SAS PROC REG and PROC RSQUARE 103
2.5 Some General Properties of Covariance Matrices 105
2.6 Measuring the Importance of the Contribution of a Single Variable 107
Table 2.5 Measures of Importance in MRA 110
Contents xiii
2.7 Anova via MRA 103
Table 2.6 Relationship Between MRA and Anova Effects Model 105
Example 2.2 In Group/Out Group Stereotypes 106
Table 2.7 Coding of MRA Level Membership Variables for Study of
Stereotypes 113
Example 2.3 Negative Shares and Equity Judgments 106
Table 2.8 Alternative Codings of MRA Predictor Variables, Equity Study 113
Example 2.4 Gender Bias in Faculty Salaries ? 116
Table 2.9 Mean Faculty Salary at Hypo. U. as f(College, Gender) 117
Table 2.10 Data for MRA Based Anova of Gender Bias Data Set 118
2.8 Alternatives to the Least Squares Criterion 121
2.9 Path Analysis 122
2.9.1 Path analytic Terminology 123
2.9.2 Preconditions for Path Analysis 124
2.9.3 Estimating and Testing Path coefficients 126
2.9.4 Decomposition of Correlations into Components 128
2.9.5 Overall Test of Goodness of fit 129
2.9.6 Examples 130
Example 2.5 Mother s Effects on Child s IQ 130
Example 2.6 Gender Bias Revisited: More Light on Suppression 134
2.9.7 Some Path Analysis References 136
Demonstration Problem 136
Answers 139
Some Real Data and a Quiz Thereon 143
Table 2.11 Data Set 2: Ratings of Conservatism of Statement 144
Answers 146
Table 2.12 Buildup of R2 for Different Orders of Addition of Predictors 146
Figure 2.1 Venn diagram of correlations among Y and four predictors 147
Path Analysis Problem 149
Answers to Path Analysis Problem 150
3 Hotelling s r2: Tests on One or Two Mean Vectors
3.1 Single Sample t and f 155
Table 3.1 Data Set 3: Divisions of Potential Prize, Experiment 3,
Harris Joyce (1980). 157
Example 3.1 162
3.2 Linearly Related Outcome Variables 165
Example 3.2 166
Table 3.2 Data Set 4: Results of Deutsch Replication 1 167
3.3 Two Sample t and t 170
3.4 Profile Analysis 173
Figure 3.1 Response vectors for groups differing in level and slope 174
xiv Contents
3.5 Discriminant Analysis 182
3.6 Relationship between T2 and MRA 184
3.7 Assumptions Underlying T2 186
3.7.1 The Assumption of Equal Covariance Matrices 186
3.7.2 Known Covariance Matrix 187
3.7.3 The Assumption of Multivariate Normality 188
3.8 Analyzing Repeated Measures Designs via T2 188
Table 3.3 Repeated Measures Anova of Data Set 3 189
Example 3.2 Blood Doping 192
Table 3.4 10K Running Time as Affected by an Infusion of One s Own Blood 192
3.9 Single Symbol Expressions for Simple Cases 196
3.10 Computerized r2 198
3.10.1 Single Sample and Two Sample f 198
3.10.2 Within Subjects Anova 199
Demonstration Problems 200
Answers 202
4 Multivariate Analysis of Variance:
Differences Among Several Groups on Several
Measures
4.1 One Way (Univariate) Analysis of Variance 210
4.1.1 The Overall Test 210
Table 4.1 Summary Table of Anova on Dependent Variable 213
4.1.2 Specific Comparisons 213
Table 4.2 Summary Table for Effects of Instructions on Frequency of DD
Outcomes 215
4.2 One Way Multivariate Analysis of Variance 218
Table 4.3 Critical Values for Contrasts Performed on Linear Combinations of
Variables 222
4.3 Multiple Profile Analysis 224
Example 4.1 Damselfish Territories 227
Table 4.4 Mean Percentage Coverage of Damselfish Territories 227
4.4 Multiple Discriminant Analysis 229
4.5 Greatest Characteristic Roots versus Multiple Root Tests in Manova 231
4.5.1 Protected Univariate Tests 233
4.5.2 Simultaneous Test Procedures and Union Intersection 234
4.5.3 Invalidity of Partitioned U Tests of Individual Roots 234
4.5.4 Simplified Coefficients as a Solution to the Robustness Problem 237
4.5.5 Finite Intersection Tests 238
Contents xv
4.6 Simple Cases of Manova 240
4.7 Higher Order Anova: Interactions 243
4.8 Higher Order Manova 245
Example 4.2 Eyeball to Eyeball in a Prisoner s Dilemma 248
Table 4.5 Proportion of Mutually Cooperative Choices as f(Contact, Communic n) 248
Table 4.6 Mean Proportion of Total Responses Accounted for by
Each Outcome 249
Table 4.7 Summary Table for Anova on Discriminant Function from One Way
Manova 251
4.9 Within Subject Univariate Anova Versus Manova 252
Example 4.3 Stress, Endorphins, and Pain 256
4.10 Computerized Manova 257
4.10.1 Generic Setup for SPSS MANOVA 257
4.10.2 Supplementary Computations 259
4.10.3 Pointing and Clicking to a Manova on SPSS PC 259
4.10.4 Generic Setup for S AS PROC GLM 260
Demonstration Problems 262
Answers 264
5 Canonical Correlation: Relationships Between
Two Sets of Variables
5.1 Formulae for Computing Canonical Rs 268
5.1.1 Heuristic Justification of Canonical Formulae 270
5.1.2. Simple Cases of Canonical Correlations 272
5.1.3. Example of a Canonical Analysis 274
Table 5.1 Correlations of Background Variables with Marijuana
Questions 275
Table 5.2 Canonical Analysis of Background Variables versus Marijuana
Questions 276
5.2 Relationships to Other Statistical Techniques 277
5.3 Likelihood Ratio Tests of Relationships between Sets of Variables 279
5.4 Generalization and Specialization of Canonical Analysis 280
5.4.1 Testing the Independence of m Sets of Variables 281
Example 5.2 Consistency of Behavior across Different Experimental Games 282
Table 5.3 Correlation Matrix for Game OutcomeVariables, Flint (1970) 283
5.4.2 Repeated Battery Canona 284
5.4.3 Rotation of Canonical Variates 288
Example 5.3 A Canonical Cautionary 290
Figure 5.1 Naturally Occurring versus Canona based Pairings of Beefy Breasted
Bowery Birds (BBBBs) 291
5.4.4 The Redundancy Coefficient 293
5.4.5 What s Missing from Canonical Analysis? 295
xvi Contents
5.5 Computerized Canonical Correlation 297
5.5.1 Matrix Manipulation Systems 297
5.5.1.1 MATLAB 297
5.5.1.2 SAS PROC MATRIX and SPSS Matrix/End Matrix 299
5.5.2 SAS PROC CANCORR 301
5.5.3. Canona via SPSS MANOVA 304
5.5.4 SPSS Canona From Correlation Matrix : Be Careful 305
Demonstration Problems and Some Real Data Employing Canonical
Correlation 307
Answers 309
6 Principal Component Analysis:
Relationships Within a Single Set of Variables
6.1 Definition of Principal Components 319
6.1.1 Terminology and Notation in PCA and FA 320
6.1.2 Scalar Formulae for Simple Cases of PCA 322
6.1.3 Computerized PCA 325
6.1.4 Additional Unique Properties (AUPs) of PCs 326
6.2 Interpretation of Principal Components 327
Example 6.1 Known generating variables 332
6.3 Uses of Principal Components 333
6.3.1 Uncorrelated Contributions 333
6.3.2 Computational Convenience 334
6.3.3 Principal Component Analysis as a Means of Handling Linear
Dependence 335
6.3.4 Examples of PCA 338
Example 6.2 Components of the WISC R 338
Example 6.3 Attitudes toward cheating 343
Table 6.1 PCA on Questions 12 23 of Cheating Questionnaire 344
Example 6.4 Fat, four eyed, and female again 344
Table 6.2 Manova Test of Obesity Main Effect 345
Table 6.3 PCA Based Manova of Obesity Main Effect 347
6.3.5 Quantifying Goodness of Interpretation of Components 348
6.4 Significance Tests for Principal Components 351
6.4.1 Sampling Properties of Covariance Based PCs 353
6.4.2 Sampling Properties of Correlation Based PCs 354
6.5 Rotation of Principal Components 356
Example 6.1 revisited 356
6.5.1 Basic Formulae for Rotation 358
Figure 6.1 Factor structures, example 6.1 358
Figure 6.2 Rotation, general case 358
6.5.2 Objective Criteria for Rotation 360
Contents xvii
Table 6.4 Quadrant within which 4^ Must Fall as Function of Signs of
Numerator and Denominator of Expression (6.9) 364
6.5.3 Examples of Rotated PCs 365
Table 6.5 Intermediate Calculations for Quartimax and Varimax Rotation 365
Table 6.6 Varimax Rotation of PC, PC4, Cheating Questionnaire 367
Table 6.7 Varimax Rotation of All Twelve PCs, Cheating Questionnaire 368
Table 6.8 Large Loadings for Cheating Questionnaire 369
6.5.4 Individual Scores on Rotated PCs 369
Example 6.5 A factor fable 373
Figure 6.3 Architectural dimensions of houses 373
Figure 6.4 Schematic representation of 27 houses 374
Table 6.9 Scores on Observed and Derived Variables for27 Houses 375
Figure 6.5 Same 27 houses sorted on basis of loadings based interpretation of
Factor 1 377
6.5.5 Uncorrelated Components Versus Orthogonal Profiles Rotation 379
Demonstration Problems 381
Answers 383
Figure 6.6 Rotation of factor structure for problem 1 386
7 Factor Analysis: The Search for Structure
7.1 The Model 394
7.2 Communalities 397
7.2.1 Theoretical Solution 398
7.2.2 Empirical Approximations 400
7.2.3 Iterative Procedure 401
7.2.4 Is the Squared Multiple Correlation the True CommunaHty? 401
7.3 Factor Analysis Procedures Requiring CommunaHty Estimates 404
7.3.1 Principal Factor Analysis 404
7.3.2 Triangular (Choleski) Decomposition 405
7.3.3 Centroid Analysis 406
7.4 Methods Requiring Estimate of Number of Factors 406
7.5 Other Approaches to Factor Analysis 409
7.6 Factor Loadings versus Factor Scores 410
7.6.1 Factor Score Indeterminacy 411
7.6.2 Relative Validities of Loadings Derived versus Scoring Coefficient Derived
Factor Interpretations 412
Table 7.1 Mean Validity, Univocality, and Orthogonality of Regression and
Loading Estimates for Three Levels of Complexity 413
7.6.3 Regression Based Interpretation of Factors is Still a Hard Sell 414
7.7 Relative Merits of Principal Component Analysis versus Factor Analysis 416
7.7.1 Similarity of Factor Scoring Coefficients 416
Table 7.2 Comparison of Factor Structures for PCA versus Two PFAs of
Same Data 417
xviii Contents
Table 7.3 Comparison of Kaiser Normalized Factor Structures 418
Table 7.4 Comparison of Factor Score Coefficients 418
7.7.2 Bias in Estimates of Factor Loadings 420
7.8 Computerized Exploratory Factor Analysis 421
Example 7.1 WISC R Revisited 423
7.9 Confirmatory Factor Analysis 433
7.9.1 SASPROCCALIS
Example 7.1 Revisited: Model Comparisons Galore 434
8 The Forest Revisited
8.1 Scales of Measurement and Multivariate Statistics 444
Table 8.1 Representative Critical Values for Measures of Association 446
8.2 Effects of Violations of Distributional Assumptions in Multivariate
Analysis 450
8.3 Nonlinear Relationships in Multivariate Statistics 453
8.4 The Multivariate General Linear Hypothesis 456
Example 8.1 Unbalanced Manova via the multivariate general linear model 460
8.5 Structural Equation Modeling 464
8.5.1 General Approach and Examples 464
Example 8.2 Path Analysis ofScarr (1985) via SEM 464
Example 8.3 All Three Colleges in the Faculty Salary Example 468
Example 8.4 Increment to Canonical R2via CALIS LinEqs? 470
8.5.2 SEM Is Not a General Model for Multivariate Statistics 473
Example 8.5 Higher Order Confirmatory Factor Analysis via SEM: WISC R One
More Time 413
8.5.3 Other User Friendly SEM Programs 478
8.6 Where to Go from Here 479
8.7 Summing Up 480
Digression 1
Finding Maxima and Minima of Polynomials
Dl. 1 Derivatives and Slopes 482
Dl .2 Optimization Subject to Constraints 485
Digression 2
Matrix Algebra
D2.1 Basic Notation 487
D2.2 Linear Combinations of Matrices 489
D2.3 Multiplication of Matrices 489
Contents xix
D2.4 Permissible Manipulations 493
D2.5 Inverses 493
D2.6 Determinants 496
D2.7 Some Handy Formulae for Inverses and Determinants in Simple Cases 500
D2.8 Rank 501
D2.9 Matrix Calculus 502
D2.10 Partitioned Matrices 503
D2.11 Characteristic Roots and Vectors 506
D2.12 Solution of Homogeneous Systems of Equations 512
Digression 3
Solution of Cubic Equations 514
Appendix A
Statistical Tables
A.I A.4 (Why omitted from this edition) 517
A.5 Greatest Characteristic Root Distribution 518
Appendix B
Computer Programs Available from the Author
B.I cvinter. p values and Critical Values for Univariate Statistics 532
B.2 gcrinter. Critical Values for the Greatest Characteristic Root (g.c.r.)
Distribution 532
Appendix C
Derivations
Derivation 1.1 Per Experiment and Experimentwise Error Rates for Bonferroni Adjusted
Tests 533
Derivation 2.1 Scalar Formulae for MRA with One, Two, and Three Predictors 536
Derivation 2.2 Coefficients That Minimize Error Also Maximize Correlation 539
Derivation 2.3 Maximizing r via Matrix Algebra 541
Derivation 2.4 Independence of Irrelevant Parameters 542
Derivation 2.5 Variances of bs and of Linear Combinations Thereof 542
Derivation 2.6 Drop in R2 = /(l #2;.oth) 543
Derivation 2.7 MRA on Group Membership Variables Yields Same F As Anova 544
n
Derivation 2.8 Unweighted Means and Least Squares Anova Are Identical in the 2
Design 545
xx Contents
Derivation 3.1 T2 and Associated Discriminant Function 546
Single Sampled 546
Two Sampled 548
Derivation 3.2 Relationship between T2 and MRA 549
Two Sample t Versus Pearson r With Group Membership Variables 549
Single Sample t Test versus Raw Score rn. 550
^Versus MRA 551
Derivation 4.1 Maximizing F(a) in Manova 552
Derivation 5.1 Canonical Correlation and Canonical Variates 554
Derivation 5.2 Canonical Correlation as Mutual Regression Analysis 556
Derivation 5.3 Relationship between Canonical Analysis and Manova 557
Derivation 6.1 Principal Components 560
Derivation 6.2 PC Coefficients Define Both Components in Terms of Xs and
Xs in Terms of PCs 562
Derivation 6.3 What Does Rotation of Loadings Do to Coefficients? 564
Derivation 7.1 Near Equivalence of PCA and Equal Communalities PFA 566
References 567
Index 584
|
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| publisher | Erlbaum |
| record_format | marc |
| spelling | Harris, Richard J. Verfasser aut A primer of multivariate statistics Richard J. Harris 3. ed. Mahwah [u.a.] Erlbaum 2001 XX, 609 S. txt rdacontent n rdamedia nc rdacarrier Hier auch später erschienene Nachdrucke Multivariate analysis Multivariate Analyse (DE-588)4040708-1 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Multivariate Analyse (DE-588)4040708-1 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010329551&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Harris, Richard J. A primer of multivariate statistics Multivariate analysis Multivariate Analyse (DE-588)4040708-1 gnd |
| subject_GND | (DE-588)4040708-1 (DE-588)4151278-9 |
| title | A primer of multivariate statistics |
| title_auth | A primer of multivariate statistics |
| title_exact_search | A primer of multivariate statistics |
| title_full | A primer of multivariate statistics Richard J. Harris |
| title_fullStr | A primer of multivariate statistics Richard J. Harris |
| title_full_unstemmed | A primer of multivariate statistics Richard J. Harris |
| title_short | A primer of multivariate statistics |
| title_sort | a primer of multivariate statistics |
| topic | Multivariate analysis Multivariate Analyse (DE-588)4040708-1 gnd |
| topic_facet | Multivariate analysis Multivariate Analyse Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010329551&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT harrisrichardj aprimerofmultivariatestatistics |