Multivariate Statistical Methods

Multivariate Statistical Methods

by Donald F. Morrison

Hardcover(2d ed)

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Product Details

ISBN-13: 9780070431867
Publisher: McGraw-Hill Companies, The
Publication date: 01/01/1976
Series: Mcgraw-Hill Series in Probability and Statistics
Edition description: 2d ed
Pages: 415

Table of Contents

1Samples from the Multivariate Normal Population1
Introduction1
Why Do We Need Multivariate Methods?1
Multidimensional Random Variables3
The Multivariate Normal Distribution8
Conditional and Marginal Distributions of Multinormal Variates14
Samples from the Multinormal Population20
Correlation and Regression25
Simultaneous Inferences about Regression Coefficients34
Inferences about the Correlation Matrix38
Samples with Incomplete Observations43
Exercises46
2Tests of Hypotheses on Means55
Introduction55
Tests on Means and the T[superscript 2] Statistic55
Simultaneous Inferences for Means62
The Case of Two Samples64
The Analysis of Repeated-Measurements68
Groups of Repeated Measurements: The Paired T[superscript 2] Test84
Profile Analysis for Two Independent Groups87
The Power of Tests on Mean Vectors93
Some Tests with Known Covariance Matrices97
Tests for Outlying Observations99
Testing the Normality Assumption103
Exercises108
3The Multivariate Analysis of Variance131
Introduction131
The Multivariate General Linear Model131
The Multivariate Analysis of Variance140
The Multivariate Analysis of Covariance156
Multiple Comparisons in the Multivariate Analysis of Variance164
Profile Analysis172
Curve Fitting for Repeated Measurements183
Other Test Criteria190
Exercises192
4Classification by Discriminant Functions209
Introduction209
The Linear Discriminant Function for Two Groups210
Classification with Known Parameters213
The Case of Unequal Covariance Matrices215
Estimation of the Misclassification Probabilities218
Classification for Several Groups221
Linear Discrimination with a Singular Covariance Matrix226
Classification by Logistic Regression230
Some Further Aspects of Classification232
Exercises234
5Inferences from Covariance Matrices242
Introduction242
Hypothesis Tests for a Single Covariance Matrix242
Tests for Two Special Patterns245
Testing the Equality of Several Covariance Matrices247
Testing the Independence of Sets of Variates249
Canonical Correlation255
Exercises260
6The Structure of Multivariate Observations: I. Principal Components264
Introduction264
The Principal Components of Multivariate Observations265
The Geometrical Meaning of Principal Components274
The Interpretation of Principal Components278
Some Patterned Matrices and Their Principal Components282
The Sampling Properties of Principal Components285
Some Further Topics293
Exercises298
7The Structure of Multivariate Observations: II. Factor Analysis317
Introduction317
The Mathematical Model for Factor Analysis318
Estimation of the Factor Loadings322
Testing the Goodness of Fit of the Factor Model327
Examples of Factor Analyses329
Factor Rotation334
An Alternative Model for Factor Analysis340
The Evaluation of Factors342
Models for the Dependence Structure of Ordered Responses345
Clustering Sampling Units351
Multidimensional Scaling357
Exercises364
References371
Appendix ATables and Charts400
Table 1Upper Critical Values of the Standard Normal Distribution400
Table 2Upper Critical Values of the Chi-squared Distribution401
Table 3Upper Percentage Points of the t Distribution402
Table 4Upper Percentage Points of the F Distribution403
Table 5The Fisher z Transformation405
Table 6Minimum Sample Sizes for a Single-Sample Repeated Measures Design406
Charts 1-8: Power Functions of the F Test410
Charts 9-16 and Table 7-15: Upper percentage points of the largest characteristic root418
Appendix BData Sets443
Wechsler Adult Intelligence Scale subtest scores443
Iris Species Petal and Sepal Measurements445
Obesity Study Biochemical Levels447
Financial Ratios of Solvent and Financially Distressed Property Liability Insurers449
Financial Ratios of Bankrupt and Solvent Companies452
Dimensions and Characteristics of Winged Aphids (Alate adelges)454
Exchangeable Cations in Forest Soil455
Average Instructor and Course Evaluations for Business School Faculty Members457
Name Index461
Subject Index465

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