Applied MANOVA and Discriminant Analysis

by Huberty, Carl J.; Olejnik, Stephen

• ISBN13: 9780471468158
• ISBN10: 0471468150
• Edition: 2nd
• Format: Hardcover
• Copyright: 2006-05-05
• Publisher: Wiley-Interscience

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