Applied Multivariate Statistical Analysis

by Johnson, Richard Arnold; Wichern, Dean W.

• ISBN13: 9780138341947
• ISBN10: 013834194X
• Edition: 4th
• Format: Hardcover
• Copyright: 1998-02-01
• Publisher: Prentice Hall

Summary

This market leading text is appropriate for courses that teach statistical methods for describing and analyzing multivariate data in depts. of statistics, math, marketing, and in the biological, physical, and social sciences. The 4th edition makes more extensive use of SAS and SPSS output with an emphasis on interpretation. Features include additional exercises, data sets, and graphics to illustrate points. Various techniques such as MANOVA and Discriminate Analysis, Correspondence Analysis, and Biplots are integrated more thoroughly.

Table of Contents

PREFACE	xiii
PART I Getting Started	1	(223)
1 ASPECTS OF MULTIVARIATE ANALYSIS	1	(48)
1.1 Introduction	1	(2)
1.2 Applications of Multivariate Techniques	3	(2)
1.3 The Organization of Data	5	(14)
1.4 Data Displays and Pictorial Representations	19	(9)
1.5 Distance	28	(8)
1.6 Final Comments	36	(1)
Exercises	36	(11)
References	47	(2)
2 MATRIX ALGEBRA AND RANDOM VECTORS	49	(67)
2.1 Introduction	49	(1)
2.2 Some Basics of Matrix and Vector Algebra	49	(12)
2.3 Positive Definite Matrices	61	(6)
2.4 A Square-Root Matrix	67	(1)
2.5 Random Vectors and Matrices	68	(1)
2.6 Mean Vectors and Covariance Matrices	69	(12)
2.7 Matrix Inequalities and Maximization	81	(5)
Supplement 2A Vectors and Matrices: Basic Concepts	86	(21)
Exercises	107	(8)
References	115	(1)
3 SAMPLE GEOMETRY AND RANDOM SAMPLING	116	(41)
3.1 Introduction	116	(1)
3.2 The Geometry of the Sample	117	(7)
3.3 Random Samples and the Expected Values of the Sample Mean and Covariance Matrix	124	(5)
3.4 Generalized Variance	129	(16)
3.5 Sample Mean, Covariance, and Correlation as Matrix Operations	145	(3)
3.6 Sample Values of Linear Combinations of Variables	148	(5)
Exercises	153	(3)
References	156	(1)
4 THE MULTIVARIATE NORMAL DISTRIBUTION	157	(67)
4.1 Introduction	157	(1)
4.2 The Multivariate Normal Density and Its Properties	158	(19)
4.3 Sampling from a Multivariate Normal Distribution and Maximum Likelihood Estimation	177	(7)
4.4 The Sampling Distribution of X and S	184	(1)
4.5 Large-Sample Behavior of X and S	185	(3)
4.6 Assessing the Assumption of Normality	188	(12)
4.7 Detecting Outliers and Data Cleaning	200	(4)
4.8 Transformations to Near Normality	204	(10)
Exercises	214	(8)
References	222	(2)
PART II Inferences About Multivariate Means and Linear Models	224	(234)
5 INFERENCES ABOUT A MEAN VECTOR	224	(66)
5.1 Introduction	224	(1)
5.2 The Plausibility of XXX(0) as a Value for a Normal Population Mean	224	(7)
5.3 Hotelling's T(2) and Likelihood Ratio Tests	231	(4)
5.4 Confidence Regions and Simultaneous Comparisons of Component Means	235	(17)
5.5 Large Sample Inferences about a Population Mean Vector	252	(5)
5.6 Multivariate Quality Control Charts	257	(11)
5.7 Inferences about Mean Vectors When Some Observations Are Missing	268	(5)
5.8 Difficulties Due To Time Dependence in Multivariate Observations	273	(3)
Supplement 5A Simultaneous Confidence Intervals and Ellipses as Shadows of the p-Dimensional Ellipsoids	276	(3)
Exercises	279	(9)
References	288	(2)
6 COMPARISONS OF SEVERAL MULTIVARIATE MEANS	290	(87)
6.1 Introduction	290	(1)
6.2 Paired Comparisons and a Repeated Measures Design	291	(11)
6.3 Comparing Mean Vectors from Two Populations	302	(12)
6.4 Comparing Several Multivariate Population Means (One-Way MANOVA)	314	(15)
6.5 Simultaneous Confidence Intervals for Treatment Effects	329	(2)
6.6 Two-Way Multivariate Analysis of Variance	331	(12)
6.7 Profile Analysis	343	(7)
6.8 Repeated Measures Designs and Growth Curves	350	(5)
6.9 Perspectives and a Strategy for Analyzing Multivariate Models	355	(3)
Exercises	358	(17)
References	375	(2)
7 MULTIVARIATE LINEAR REGRESSION MODELS	377	(81)
7.1 Introduction	377	(1)
7.2 The Classical Linear Regression Model	377	(4)
7.3 Least Squares Estimation	381	(9)
7.4 Inferences About the Regression Model	390	(10)
7.5 Inferences from the Estimated Regression Function	400	(4)
7.6 Model Checking and Other Aspects of Regression	404	(6)
7.7 Multivariate Multiple Regression	410	(17)
7.8 The Concept of Linear Regression	427	(11)
7.9 Comparing the Two Formulations of the Regression Model	438	(3)
7.10 Multiple Regression Models with Time Dependent Errors	441	(5)
Supplement 7A The Distribution of the Likelihood Ratio for the Multivariate Multiple Regression Model	446	(2)
Exercises	448	(8)
References	456	(2)
PART III Analysis of Covariance Structure	458	(171)
8 PRINCIPAL COMPONENTS	458	(56)
8.1 Introduction	458	(1)
8.2 Population Principal Components	458	(13)
8.3 Summarizing Sample Variation by Principal Components	471	(13)
8.4 Graphing the Principal Components	484	(3)
8.5 Large Sample Inferences	487	(3)
8.6 Monitoring Quality with Principal Components	490	(8)
Supplement 8A The Geometry of the Sample Principal Component Approximation	498	(5)
Exercises	503	(9)
References	512	(2)
9 FACTOR ANALYSIS AND INFERENCE FOR STRUCTURED COVARIANCE MATRICES	514	(73)
9.1 Introduction	514	(1)
9.2 The Orthogonal Factor Model	515	(6)
9.3 Methods of Estimation	521	(19)
9.4 Factor Rotation	540	(10)
9.5 Factor Scores	550	(7)
9.6 Perspectives and a Strategy for Factor Analysis	557	(8)
9.7 Structural Equation Models	565	(7)
Supplement 9A Some Computational Details for Maximum Likelihood Estimation	572	(3)
Exercises	575	(10)
References	585	(2)
10 CANONICAL CORRELATION ANALYSIS	587	(42)
10.1 Introduction	587	(1)
10.2 Canonical Variates and Canonical Correlations	587	(8)
10.3 Interpreting the Population Canonical Variables	595	(6)
10.4 The Sample Canonical Variates and Sample Canonical Correlations	601	(9)
10.5 Additional Sample Descriptive Measures	610	(5)
10.6 Large Sample Inferences	615	(4)
Exercises	619	(8)
References	627	(2)
PART IV Classification and Grouping Techniques	629	(171)
11 DISCRIMINATION AND CLASSIFICATION	629	(97)
11.1 Introduction	629	(1)
11.2 Separation and Classification for Two Populations	630	(9)
11.3 Classification with Two Multivariate Normal Populations	639	(10)
11.4 Evaluating Classification Functions	649	(12)
11.5 Fisher's Discriminant Function--Separation of Populations	661	(4)
11.6 Classification with Several Populations	665	(18)
11.7 Fisher's Method for Discriminating among Several Populations	683	(14)
11.8 Final Comments	697	(6)
Exercises	703	(20)
References	723	(3)
12 CLUSTERING, DISTANCE METHODS AND ORDINATION	726	(74)
12.1 Introduction	726	(2)
12.2 Similarity Measures	728	(10)
12.3 Hierarchical Clustering Methods	738	(16)
12.4 Nonhierarchical Clustering Methods	754	(6)
12.5 Multidimensional Scaling	760	(10)
12.6 Correspondence Analysis	770	(9)
12.7 Biplots for Viewing Sampling Units and Variables	779	(3)
12.8 Procrustes Analysis: A Method for Comparing Configurations	782	(8)
Exercises	790	(8)
References	798	(2)
APPENDIX	800	(11)
Table 1 Standard Normal Probabilities	801	(1)
Table 2 Student's t-Distribution Percentage Points	802	(1)
Table 3 Alpha(2) Distribution Percentage Points	803	(1)
Table 4 F-Distribution Percentage Points (Alpha = .10)	804	(2)
Table 5 F-Distribution Percentage Points (Alpha = .05)	806	(2)
Table 6 F-Distribution Percentage Points (Alpha = .01)	808	(3)
DATA INDEX	811	(1)
SUBJECT INDEX	812