9780471468158

Applied MANOVA and Discriminant Analysis

by ;
  • ISBN13:

    9780471468158

  • ISBN10:

    0471468150

  • Edition: 2nd
  • Format: Hardcover
  • Copyright: 2006-05-05
  • Publisher: Wiley-Interscience
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Summary

A complete introduction to discriminant analysis--extensively revised, expanded, and updated This Second Edition of the classic book, Applied Discriminant Analysis, reflects and references current usage with its new title, Applied MANOVA and Discriminant Analysis. Thoroughly updated and revised, this book continues to be essential for any researcher or student needing to learn to speak, read, and write about discriminant analysis as well as develop a philosophy of empirical research and data analysis. Its thorough introduction to the application of discriminant analysis is unparalleled. Offering the most up-to-date computer applications, references, terms, and real-life research examples, the Second Edition also includes new discussions of MANOVA, descriptive discriminant analysis, and predictive discriminant analysis. Newer SAS macros are included, and graphical software with data sets and programs are provided on the book's related Web site. The book features: Detailed discussions of multivariate analysis of variance and covariance An increased number of chapter exercises along with selected answers Analyses of data obtained via a repeated measures design A new chapter on analyses related to predictive discriminant analysis Basic SPSS(r) and SAS(r) computer syntax and output integrated throughout the book Applied MANOVA and Discriminant Analysis enables the reader to become aware of various types of research questions using MANOVA and discriminant analysis; to learn the meaning of this field's concepts and terms; and to be able to design a study that uses discriminant analysis through topics such as one-factor MANOVA/DDA, assessing and describing MANOVA effects, and deleting and ordering variables.

Author Biography

CARL J. HUBERTY, PhD, is Professor Emeritus in the Department of Educational Psychology and Instructional Technology at The University of Georgia. He received his PhD in statistical methods from The University of Iowa and has written chapters in many books throughout his career. </p> <p>STEPHEN OLEJNIK, PhD, is Professor in the Department of Educational Psychology and Instructional Technology at The University of Georgia. He received his PhD in educational psychology, applied statistics, and research design from Michigan State University.

Table of Contents

List of Figures
xix
List of Tables
xxi
Preface to Second Edition xxv
Acknowledgments xxvii
Preface to First Edition xxix
Notation xxxi
I. INTRODUCTION
1(32)
Discriminant Analysis in Research
3(12)
A Little History
3(2)
Overview
5(1)
Descriptive Discriminant Analysis
5(2)
Predictive Discriminant Analysis
7(2)
Design in Discriminant Analysis
9(6)
Grouping Variables
9(1)
Response Variables
9(4)
Exercises
13(2)
Preliminaries
15(18)
Introduction
15(1)
Research Context
15(1)
Data, Analysis Units, Variables, and Constructs
16(2)
Summarizing Data
18(3)
Matrix Operations
21(5)
SSCP Matrix
22(1)
Determinant
23(1)
Inverse
24(1)
Eigenanalysis
25(1)
Distance
26(2)
Linear Composite
28(1)
Probability
28(1)
Statistical Testing
29(1)
Judgment in Data Analysis
30(1)
Summary
31(2)
Further Reading
31(1)
Exercises
32(1)
II. ONE-FACTOR MANOVA/DDA
33(96)
Group Separation
35(26)
Introduction
35(1)
Two-Group Analyses
35(6)
Univariate Analysis
35(4)
Multivariate Analysis
39(2)
Test for Covariance Matrix Equality
41(2)
Yao Test
43(1)
Multiple-Group Analyses---Single Factor
44(8)
Univariate Analysis
44(3)
Multivariate Analysis
47(5)
Computer Application
52(4)
Summary
56(5)
Exercises
57(4)
Assessing Manova Effects
61(20)
Introduction
61(1)
Strength of Association
62(4)
Univariate
62(1)
Multivariate
62(3)
Bias
65(1)
Computer Application I
66(1)
Group Contrasts
67(5)
Univariate
67(1)
Multivariate
68(4)
Computer Application II
72(2)
Covariance Matrix Heterogeneity
74(1)
Sample Size
74(1)
Summary
75(6)
Technical Notes
76(1)
Exercises
77(4)
Describing Manova Effects
81(22)
Introduction
81(1)
Omnibus Effects
82(3)
An Eigenanalysis
82(1)
Linear Discriminant Functions
83(2)
Computer Application I
85(2)
Standardized LDF Weights
87(1)
LDF Space Dimension
88(5)
Statistical Tests
89(2)
Proportion of Variance
91(1)
LDF Plots
91(2)
Computer Application II
93(1)
Computer Application III
94(2)
Contrast Effects
96(1)
Computer Application IV
96(2)
Summary
98(5)
Technical Note
99(1)
Further Reading
100(1)
Exercises
100(3)
Deleting and Ordering Variables
103(14)
Introduction
103(1)
Variable Deletion
103(3)
Purposes of Deletion
103(1)
McCabe Analysis
104(1)
Computer Application
105(1)
Variable Ordering
106(4)
Meaning of Importance
106(2)
Computer Application I
108(2)
Variable Ranking
110(1)
Contrast Analyses
110(1)
Computer Application II
111(2)
Comments
113(4)
Further Reading
114(1)
Exercises
115(2)
Reporting DDA Results
117(12)
Introduction
117(1)
Example of Reporting DDA Results
117(5)
Computer Package Information
122(1)
Reporting Terms
123(1)
Manova/DDA Applications
124(1)
Concerns
124(2)
Overview
126(3)
Further Reading
127(1)
Exercises
127(2)
III. FACTORIAL MANOVA, MANCOVA, AND REPEATED MEASURES
129(124)
Factorial Manova
131(32)
Introduction
131(1)
Research Context
131(3)
Univariate Analysis
134(2)
Multivariate Analysis
136(3)
Omnibus Tests
136(2)
Distribution Assumptions
138(1)
Computer Application I
139(7)
Computer Application II
146(4)
Nonorthogonal Design
150(1)
Outcome Variable Ordering and Deletion
151(1)
Summary
152(11)
Technical Notes
152(7)
Exercises
159(4)
Analysis of Covariance
163(30)
Introduction
163(1)
Research Context
164(2)
Univariate ANCOVA
166(4)
Testing for Equality of Regression Slopes
166(2)
Omnibus Test of Adjusted Means
168(2)
Multivariate Ancova (Mancova)
170(3)
Matrix Calculations
170(1)
Testing for Equal Slopes
171(2)
Computer Application I
173(1)
Comparing Adjusted Means---Omnibus Test
174(1)
Computer Application II
175(5)
Contrast Analysis
180(1)
Computer Application III
180(4)
Summary
184(9)
Technical Note
184(6)
Exercises
190(3)
Repeated-Measures Analysis
193(34)
Introduction
193(2)
Research Context
195(1)
Univariate Analyses
196(3)
Omnibus Test
196(1)
Contrast Analysis
197(2)
Multivariate Analysis
199(3)
Computer Application I
202(2)
Univariate and Multivariate Analyses
204(3)
Testing for Sphericity
207(3)
Computer Application II
210(2)
Contrast Analysis
212(2)
Computer Application III
214(2)
Summary
216(11)
Technical Notes
217(6)
Exercises
223(4)
Mixed-Model Analysis
227(26)
Introduction
227(1)
Research Context
228(1)
Univariate Analysis
229(2)
Multivariate Analysis
231(6)
Group-by-Time Interaction
232(3)
Repeated-Measures Variable Main Effect
235(2)
Computer Application I
237(3)
Contrast Analysis
240(3)
Computer Application II
243(3)
Summary
246(7)
Technical Note
247(2)
Exercises
249(4)
IV. GROUP MEMBERSHIP PREDICTION
253(138)
Classification Basics
255(14)
Introduction
255(1)
Notion of Distance
256(3)
Distance and Classification
259(1)
Classification Rules in General
260(4)
Maximum Likelihood
260(1)
Typicality Probability
261(1)
Posterior Probability
262(1)
Prior Probability
263(1)
Comments
264(5)
Technical Note
265(1)
Further Reading
265(1)
Exercises
266(3)
Multivariate Normal Rules
269(16)
Introduction
269(1)
Normal Density Functions
269(2)
Classification Rules Based on Normality
271(2)
Classification Functions
273(4)
Quadratic Functions
273(1)
Linear Functions
274(1)
Distance-Based Classification
275(2)
Summary of Classification Statistics
277(1)
Choice of Rule Form
278(3)
Normal-Based Rule
278(1)
Covariance Matrix Equality
279(1)
Rule Choice
280(1)
Priors
281(1)
Comments
281(4)
Technical Notes
283(1)
Further Reading
283(1)
Exercises
284(1)
Classification Results
285(10)
Introduction
285(1)
Research Context
285(1)
Computer Application
286(1)
Individual Unit Results
287(3)
In-Doubt Units
288(1)
Outliers
289(1)
Group Results
290(1)
Comments
291(4)
Technical Note
291(1)
Exercises
292(3)
Hit Rate Estimation
295(20)
Introduction
295(1)
True Hit Rates
296(1)
Hit Rate Estimators
297(7)
Formula Estimators
297(2)
Internal Analysis
299(1)
External Analysis
300(2)
Maximum-Posterior-Probability Method
302(2)
Computer Application
304(2)
Choice of Hit Rate Estimator
306(1)
Outliers and In-Doubt Units
306(3)
Outliers
307(1)
In-Doubt Units
307(2)
Sample Size
309(1)
Comments
310(5)
Further Reading
311(1)
Exercises
312(3)
Effectiveness of Classification Rules
315(20)
Introduction
315(1)
Proportional Chance Criterion
316(3)
Definition
316(1)
Statistical Test
317(2)
Maximum-Chance Criterion
319(1)
Improvement over Chance
320(1)
Comparison of Rules
320(1)
Computer Application I
321(2)
Effect of Unequal Priors
323(2)
PDA Validity/Reliability
325(1)
Applying a Classification Rule to New Units
325(5)
Computer Application II
326(1)
Computer Application III
327(3)
Comments
330(5)
Technical Notes
330(1)
Further Reading
331(1)
Exercises
332(3)
Deleting and Ordering Predictors
335(14)
Introduction
335(1)
Predictor Deletion
336(1)
Purposes of Deletion
336(1)
Deletion Methods
336(1)
Package Analyses
337(1)
All Possible Subsets
337(1)
Computer Application
337(3)
Predictor Ordering
340(3)
Meaning of Importance
340(1)
Variable Ranking
340(3)
Reanalysis
343(1)
Comments
343(2)
Side Note
345(4)
Further Reading
346(1)
Exercises
347(2)
Two-Group Classification
349(12)
Introduction
349(1)
Two-Group Rule
349(2)
Regression Analogy
351(2)
MRA--PDA Relationship
353(2)
Necessary Sample Size
355(1)
Univariate Classification
356(5)
Further Reading
357(2)
Exercises
359(2)
Nonnormal Rules
361(14)
Introduction
361(1)
Continuous Variables
362(4)
Rank Transformation Analysis
362(1)
Nearest-Neighbor Analyses
363(3)
Another Density Estimation Analysis
366(1)
Other Analyses
366(1)
Categorical Variables
366(3)
Direct Probability Estimation Analysis
367(1)
Dummy Variable Analysis
367(1)
Overall--Woodward Analysis
368(1)
Fisher--Lancaster Analysis
368(1)
Other Analyses
369(1)
Predictor Mixtures
369(1)
Comments
370(5)
Further Reading
371(2)
Exercises
373(2)
Reporting PDA Results
375(10)
Introduction
375(1)
Example of Reporting PDA Results
375(3)
Some Additional Specific PDA Information
378(1)
Computer Package Information
379(1)
Reporting Terms
379(2)
Sources of PDA Applications
381(1)
Concerns
381(1)
Overview
382(3)
Further Reading
383(1)
Exercises
383(2)
PDA-Related Analyses
385(6)
Introduction
385(1)
Nonlinear Methods
385(1)
Classification and Regression Trees (CART)
385(1)
Logistic Regression
385(1)
Neural Networks
386(1)
Other Methods
386(5)
Cluster Analysis
386(1)
Image Analysis
387(1)
Optimal Allocation
387(1)
Pattern Recognition
387(1)
Further Reading
388(3)
V. ISSUES AND PROBLEMS
391(20)
Issues in PDA and DDA
393(8)
Introduction
393(1)
Five Choices in PDA
393(2)
Linear Versus Quadratic Rules
393(1)
Nonnormal Classification Rules
394(1)
Prior Probabilities
394(1)
Misclassification Costs
394(1)
Hit-Rate Estimation
395(1)
Stepwise Analyses
395(1)
Standardized Weights Versus Structure r's
396(2)
Data-Based Structure
398(3)
Further Reading
400(1)
Problems in PDA and DDA
401(10)
Introduction
401(1)
Missing Data
401(4)
Data Inspection
401(1)
Data Imputation
402(2)
Missing G Values
404(1)
Ad Hoc Strategy
404(1)
Outliers and Influential Observations
405(1)
Outlier Identification
405(1)
Influential Observations
406(1)
Initial Group Misclassification
406(1)
Misclassification Costs
407(1)
Statistical Versus Clinical Prediction
407(2)
Other Problems
409(2)
Further Reading
409(2)
Appendix A Data Set Descriptions 411(4)
Appendix B Some DA-Related Originators 415(4)
Appendix C List of Computer Syntax 419(2)
Appendix D Contents of Wiley Website 421(4)
References 425(24)
Answers to Exercises 449(32)
Index 481

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