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- Product code: 19435
- ISBN: 0131219731,
ISBN13: 9780131219731,
834 pages, CD-Rom + pb
Published by Prentice Hall on 2003
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Description of Applied Multivariate Statistical Analysis |
Appropriate for experimental scientists in a variety of disciplines, this market-leading text offers a readable introduction to the statistical analysis of multivariate observations. Its overarching goal is to provide readers with the knowledge necessary to make proper interpretations and select appropriate techniques for analyzing multivariate data. It is suitable for junior/senior or graduate level course that explores the statistical methods for describing and analyzing multivariate data.
Features and Benefits:
NEW - Enhanced discussions of Multivariate Quality Control and Correspondence Analysis - Provides the student with a greater understanding of these essential topics.
NEW - Eight new data sets- Includes bear data, lizard data, Egyptian skulls, welding data and more - Provides greater variety of data sets for instructors to assign.
An abundance of examples and exercises based on real data - Over 50 real data sets are included on an enclosed computer disk - Provides students with the opportunity to duplicate the authors analyses, carry out the analyses, or analyze the data using suggested methods.
Important results and formulas are highlighted and boxed - Directs students attention toward key concepts.
Applications of multivariate methods are emphasized - Makes the mathematics as accessible as possible for the student.
A clear and insightful explanation of multivariate techniques - Assists students as they navigate difficult topics.
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Contents of Applied Multivariate Statistical Analysis |
(NOTE: Each chapter begins with an Introduction, and concludes with Exercises and References.)
I. GETTING STARTED
1. Aspects of Multivariate Analysis
Applications of Multivariate Techniques
The Organization of Data
Data Displays and Pictorial Representations
Distance
Final Comments
2. Matrix Algebra and Random Vectors
Some Basics of Matrix and Vector Algebra
Positive Definite Matrices
A Square-Root Matrix
Random Vectors and Matrices
Mean Vectors and Covariance Matrices
Matrix Inequalities and Maximization
Supplement 2A Vectors and Matrices - Basic Concepts
3. Sample Geometry and Random Sampling
The Geometry of the Sample. Random Samples and the Expected Values of the Sample Mean and Covariance Matrix
Generalized Variance
Sample Mean, Covariance, and Correlation as Matrix Operations
Sample Values of Linear Combinations of Variables
4. The Multivariate Normal Distribution
The Multivariate Normal Density and Its Properties
Sampling from a Multivariate Normal Distribution and Maximum Likelihood Estimation
The Sampling Distribution of X and S
Large-Sample Behavior of X and S
Assessing the Assumption of Normality
Detecting Outliners and Data Cleaning
Transformations to Near Normality
II. INFERENCES ABOUT MULTIVARIATE MEANS AND LINEAR MODELS
5. Inferences About a Mean Vector
The Plausibility of …m0 as a Value for a Normal Population Mean
Hotellings T2 and Likelihood Ratio Tests
Confidence Regions and Simultaneous Comparisons of Component Means
Large Sample Inferences about a Population Mean Vector
Multivariate Quality Control Charts
Inferences about Mean Vectors When Some Observations Are Missing
Difficulties Due To Time Dependence in Multivariate Observations
Supplement 5A Simultaneous Confidence Intervals and Ellipses as Shadows of the p-Dimensional Ellipsoids
6. Comparisons of Several Multivariate Means.
Paired Comparisons and a Repeated Measures Design. Comparing Mean Vectors from Two Populations. Comparison of Several Multivariate Population Means (One-Way MANOVA). Simultaneous Confidence Intervals for Treatment Effects. Two-Way Multivariate Analysis of Variance. Profile Analysis. Repealed Measures, Designs, and Growth Curves. Perspectives and a Strategy for Analyzing Multivariate Models.
7. Multivariate Linear Regression Models.
The Classical Linear Regression Model. Least Squares Estimation. Inferences About the Regression Model. Inferences from the Estimated Regression Function. Model Checking and Other Aspects of Regression. Multivariate Multiple Regression. The Concept of Linear Regression. Comparing the Two Formulations of the Regression Model. Multiple Regression Models with Time Dependant Errors. Supplement 7A The Distribution of the Likelihood Ratio for the Multivariate Regression Model.
III. ANALYSIS OF A COVARIANCE STRUCTURE
8. Principal Components.
Population Principal Components. Summarizing Sample Variation by Principal Components. Graphing the Principal Components. Large-Sample Inferences. Monitoring Quality with Principal Components. Supplement 8A The Geometry of the Sample Principal Component Approximation.
9. Factor Analysis and Inference for Structured Covariance Matrices.
The Orthogonal Factor Model. Methods of Estimation. Factor Rotation. Factor Scores. Perspectives and a Strategy for Factor Analysis. Structural Equation Models. Supplement 9A Some Computational Details for Maximum Likelihood Estimation.
10. Canonical Correlation Analysis
Canonical Variates and Canonical Correlations. Interpreting the Population Canonical Variables. The Sample Canonical Variates and Sample Canonical Correlations. Additional Sample Descriptive Measures. Large Sample Inferences.
IV. CLASSIFICATION AND GROUPING TECHNIQUES
11. Discrimination and Classification.
Separation and Classification for Two Populations. Classifications with Two Multivariate Normal Populations. Evaluating Classification Functions. Fishers Discriminant Function…¤Separation of Populations. Classification with Several Populations. Fishers Method for Discriminating among Several Populations. Final Comments.
12. Clustering, Distance Methods and Ordination.
Similarity Measures. Hierarchical Clustering Methods. Nonhierarchical Clustering Methods. Multidimensional Scaling. Correspondence Analysis. Biplots for Viewing Sample Units and Variables. Procustes Analysis- A Method for Comparing Configurations.
Appendix
Standard Normal Probabilities. Students t-Distribution Percentage Points. …2 Distribution Percentage Points. F-Distribution Percentage Points. F-Distribution Percentage Points (…a = .10). F-Distribution Percentage Points (…a = .05). F-Distribution Percentage Points (…a = .01).
Data Index
Subject Index
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