Applied Multivariate Statistics for the Social Sciences, Fifth Edition

by Stevens, James

• ISBN13: 9780805837766
• ISBN10: 0805837760
• Edition: 4th
• Format: Hardcover
• Copyright: 2001-08-01
• Publisher: Lawrence Erlbau

Summary

This best-selling text is written for those who use, rather than develop, advanced statistical methods. Dr. Stevens focuses on a conceptual understanding of the material rather than proving results. Helpful narrative and numerous examples enhance understanding, and a chapter on matrix algebra serves as a review. Printouts from SPSS and SAS with annotations indicate what the numbers mean and encourage interpretation of the results. In addition to demonstrating how to use the packages effectively, the author stresses the importance of checking the data, assessing the assumptions, and ensuring adequate sample size (by providing guidelines) so that the results can be generalized. The new edition features a CD-ROM with the data sets and many new exercises. Ideal for courses on advanced or multivariate statistics found in psychology, education, and business departments, the book also appeals to practicing researchers with little or no training in multivariate methods. Prerequisites include a course on factorial analysis of variance. It does not assume a working knowledge of matrix algebra.

Table of Contents

Preface	p. xiii
Introduction
Introduction	p. 1
Type I Error, Type II Error, and Power	p. 3
Multiple Statistical Tests and the Probability of Spurious Results	p. 6
Statistical Significance Versus Practical Significance	p. 9
Outliers	p. 12
Research Examples for Some Analyses Considered in This Text	p. 17
The SAS and SPSS Statistical Packages	p. 24
SPSS for Windows--Releases 9.0 and 10.0	p. 34
Data Files	p. 36
Data Editing	p. 40
SPSS Output Navigator	p. 45
Some Issues Unique to Multivariate Analysis	p. 48
Data Collection and Integrity	p. 49
Defining a Measure of Statistical Distance	p. 50
Milk Data	p. 52
Exercises	p. 53
Matrix Algebra
Introduction	p. 56
Addition, Subtraction, and Multiplication of a Matrix by a Scalar	p. 59
Obtaining the Matrix of Variances and Covariances	p. 62
Determinant of a Matrix	p. 64
Inverse of a Matrix	p. 70
Eigenvalues	p. 73
SPSS Matrix Procedure	p. 75
SAS IML Procedure	p. 76
Exercises	p. 77
Multiple Regression
Introduction	p. 80
Simple Regression	p. 82
Multiple Regression for Two Predictors--Matrix Formulation	p. 86
Mathematical Maximization Nature of Least Squares Regression	p. 88
Breakdown of Sum of Squares in Regression and F Test for Multiple Correlation	p. 89
Relationship of Simple Correlations to Multiple Correlation	p. 91
Multicollinearity	p. 91
Model Selection	p. 93
Two Computer Examples	p. 98
Checking Assumptions for the Regression Model	p. 110
Model Validation	p. 113
Importance of the Order of the Predictors in Regression Analysis	p. 119
Other Important Issues	p. 121
Outliers and Influential Data Points	p. 125
Further Discussion of the Two Computer Examples	p. 138
Sample Size Determination for a Reliable Prediction Equation	p. 143
Logistic Regression	p. 146
Other Types of Regression Analysis	p. 155
Multivariate Regression	p. 155
Summary of Important Points	p. 159
Exercises	p. 161
Two-Group Multivariate Analysis Of Variance
Introduction	p. 173
Four Statistical Reasons for Preferring a Multivariate Analysis	p. 174
The Multivariate Test Statistic as a Generalization of Univariate t	p. 175
Numerical Calculations for a Two-Group Problem	p. 177
Three Post Hoc Procedures	p. 181
SAS and SPSS Control Lines for Sample Problem and Selected Printout	p. 183
Multivariate Significance but No Univariate Significance	p. 184
Multivariate Regression Analysis for the Sample Problem	p. 188
Power Analysis	p. 192
Ways of Improving Power	p. 195
Power Estimation on SPSS MANOVA	p. 197
Multivariate Estimation of Power	p. 197
Summary	p. 202
Exercises	p. 203
K-Group Manova: A Priori And Post Hoc Procedures
Introduction	p. 208
Multivariate Regression Analysis for a Sample Problem	p. 209
Traditional Multivariate Analysis of Variance	p. 210
Multivariate Analysis of Variance for Sample Data	p. 212
Post Hoc Procedures	p. 217
The Tukey Procedure	p. 222
Planned Comparisons	p. 225
Test Statistics for Planned Comparisons	p. 228
Multivariate Planned Comparisons on SPSS MANOVA	p. 231
Correlated Contrasts	p. 235
Studies Using Multivariate Planned Comparisons	p. 241
Stepdown Analysis	p. 243
Other Multivariate Test Statistics	p. 243
How Many Dependent Variables for a MANOVA?	p. 245
Power Analysis--A Priori Determination of Sample Size	p. 245
Summary	p. 247
Novince (1977) Data for Multivariate Analysis of Variance Presented in Tables 5.3 and 5.4	p. 249
Exercises	p. 250
Assumptions In Manova
Introduction	p. 256
ANOVA and MANOVA Assumptions	p. 257
Independence Assumption	p. 258
What Should Be Done With Correlated Observations?	p. 260
Normality Assumption	p. 261
Multivariate Normality	p. 262
Assessing Univariate Normality	p. 263
Homogeneity of Variance Assumption	p. 268
Homogeneity of the Covariance Matrices	p. 269
General Procedure for Assessing Violations in MANOVA	p. 276
Multivariate Test Statistics for Unequal Covariance Matrices	p. 279
Exercises	p. 280
Discriminant Analysis
Introduction	p. 285
Descriptive Discriminant Analysis	p. 286
Significance Tests	p. 287
Interpreting the Discriminant Functions	p. 288
Graphing the Groups in the Discriminant Plane	p. 289
Rotation of the Discriminant Functions	p. 296
Stepwise Discriminant Analysis	p. 296
Two Other Studies That Used Discriminant Analysis	p. 297
The Classification Problem	p. 301
Linear vs. Quadratic Classification Rule	p. 316
Characteristics of a Good Classification Procedure	p. 316
Summary of Major Points	p. 317
Exercises	p. 318
Factorial Analysis Of Variance
Introduction	p. 321
Advantages of a Two-Way Design	p. 322
Univariate Factorial Analysis	p. 324
Factorial Multivariate Analysis of Variance	p. 331
Weighting of the Cell Means	p. 332
Three-Way MANOVA	p. 335
Exercises	p. 336
Analysis Of Covariance
Introduction	p. 339
Purposes of Covariance	p. 340
Adjustment of Posttest Means and Reduction of Error Variance	p. 342
Choice of Covariates	p. 345
Assumptions in Analysis of Covariance	p. 347
Use of ANCOVA With Intact Groups	p. 350
Alternative Analyses for Pretest-Posttest Designs	p. 351
Error Reduction and Adjustment of Posttest Means for Several Covariates	p. 353
MANCOVA--Several Dependent Variables and Several Covariates	p. 354
Testing the Assumption of Homogeneous Regression Hyperplanes on SPSS	p. 355
Two Computer Examples	p. 356
Bryant-Paulson Simultaneous Test Procedure	p. 361
Summary of Major Points	p. 366
Exercises	p. 367
Stepdown Analysis
Introduction	p. 374
Four Appropriate Situations for Stepdown Analysis	p. 375
Controlling on Overall Type I Error	p. 376
Stepdown F's for Two Groups	p. 377
Comparison of Interpretation of Stepdown F's vs. Univariate F's	p. 379
Stepdown F's for k Groups--Effect of Within and Between Correlations	p. 381
Summary	p. 383
Confirmatory And Exploratory Factor Analysis
Introduction	p. 385
The Nature of Principal Components	p. 386
Three Uses for Components as a Variable Reducing Scheme	p. 388
Criteria for Deciding on How Many Components to Retain	p. 389
Increasing Interpretability of Factors by Rotation	p. 391
What Loadings Should Be Used for Interpretation?	p. 393
Sample Size and Reliable Factors	p. 395
Four Computer Examples	p. 395
The Communality Issue	p. 409
A Few Concluding Comments	p. 410
Exploratory and Confirmatory Factor Analysis	p. 411
PRELIS	p. 415
A LISREL Example Comparing Two A Priori Models	p. 419
Identification	p. 427
Estimation	p. 429
Assessment of Model Fit	p. 430
Model Modification	p. 435
LISREL 8 Example	p. 437
EQS Example	p. 445
Some Caveats Regarding Structural Equation Modeling	p. 449
Exercises	p. 454
Canonical Correlation
Introduction	p. 471
The Nature of Canonical Correlation	p. 472
Significance Tests	p. 473
Interpreting the Canonical Variates	p. 475
Computer Example Using SAS CANCORR	p. 476
A Study That Used Canonical Correlation: Relationship Between Student Needs and Teacher Ratings	p. 479
Using SAS for Canonical Correlation on Two Sets of Factor Scores	p. 481
The Redundancy Index of Stewart and Love	p. 483
Rotation of Canonical Variates	p. 485
Obtaining More Reliable Canonical Variates	p. 485
Summary	p. 486
Exercises	p. 487
Repeated Measures Analysis
Introduction	p. 492
Single-Group Repeated Measures	p. 496
The Multivariate Test Statistic for Repeated Measures	p. 497
Assumptions in Repeated Measures Analysis	p. 500
Computer Analysis of the Drug Data	p. 502
Post Hoc Procedures in Repeated Measures Analysis	p. 506
Should We Use the Univariate or Multivariate Approach?	p. 509
Sample Size for Power = .80 in Single-Sample Case	p. 510
Multivariate Matched Pairs Analysis	p. 512
One Between and One Within Factor--A Trend Analysis	p. 512
Post Hoc Procedures for the One Between and One Within Design	p. 519
One Between and Two Within Factors	p. 521
Two Between and One Within Factors	p. 526
Two Between and Two Within Factors	p. 532
Totally Within Designs	p. 532
Planned Comparisons in Repeated Measures Designs	p. 534
Profile Analysis	p. 536
Doubly Multivariate Repeated Measures Designs	p. 538
Summary of Major Points	p. 544
Exercises	p. 552
Categorical Data Analysis: The Log Linear Model
Introduction	p. 558
Sampling Distributions: Binomial and Multinomial	p. 561
Two Way Chi Square--Log Linear Formulation	p. 564
Three-Way Tables	p. 567
Model Selection	p. 576
Collapsibility	p. 578
The Odds (Cross-Product) Ratio	p. 582
Normed Fit Index and Residual Analysis	p. 583
Residual Analysis	p. 584
Cross-Validation	p. 585
Higher Dimensional Tables--Model Selection
Contrasts for the Log Linear Model	p. 586
Log Linear Analysis for Ordinal Data	p. 590
Sampling and Structural (Fixed) Zeros	p. 595
Exercises	p. 596
References	p. 603
Statistical Tables	p. 614
Data Sets	p. 634
Obtaining Nonorthogonal Contrasts in Repeated Measures Designs	p. 653
Answer Section	p. 661
Author Index	p. 689
Subject Index	p. 693
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