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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