Applied Multivariate Statistical Analysis 6th Edition

【实例简介】
Applied Multivariate Statistical Analysis 6th Edition Pearson New International Edition Author: Richard A. Johnson 文字版
Pearson education limited Edinburgh Gate Harlow Essex cm20 2JE England and Associated Companies throughout the world Visitusontheworldwidewebat:www.pearsoned.co.uk C Pearson Education Limited 2014 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise without either the prior written permission of the publisher or a licence permitting restricted copying in the United Kingdom issued by the Copyright Licensing Agency Ltd, Saffron House, 6-10 Kirby Street, London ECIN 8TS All trademarks used herein are the property of their respective owners. The use of any trademark in this text does not vest in the author or publisher any trademark ownership rights in such trademarks, nor does the use of such trademarks imply any affiliation with or endorsement of this book by such owners. PEARSON ISBN10:1-292-02494-1 IsBN13:978-1-292-02494-3 British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the british Library Printed in the united states of america PEARSO N CU O M LBRAR Y Table of contents Chapter I Aspects of Multivariate Analysis Richard A Johnson/Dean W. Wichern Chapter 3 Sample Geometry and Random Sampling Richard A. ohnson/Dean W. Wichern 49 Chapter 2 Matrix Algebra and random vectors Richard A Johnson/Dean W. wichern 87 Chapter 4. The multivariate Normal Distribution Richard A. ohnson/Dean W. Wichern 149 Chapter 5 Inferences about a mean vector Richard A Johnson/Dean W. Wichern 210 Chapter 6. Comparisons of Several Multivariate Means Richard A Johnson/Dean w. wichern 273 Chapter 7. Multivariate Linear Regression Models Richard a. ohnson/ Dean W. Wichern 360 Chapter 8. Principal Components Richard A Johnson/Dean W. Wichern 430 Chapter 9. Factor Analysis and Inference for Structured Covariance Matrices Richard A Johnson/Dean W. Wichern l81 Chapter 10. Canonical Correlation Analysis Richard A Johnson/Dean W. Wichern 539 Chapter I. Discrimination and classification Richard A Johnson/Dean W. Wichern 575 Chapter 12 Clustering, Distance Methods and Ordination Richard A Johnson/Dean W. Wichern 671 Appendix Richard A. ohnson/Dean w. wichern 757 765 This page intentionally lefi blank Chapter ASPECTS OF MULTIVARIATE ANALYSis 1. Introduction Scientific inquiry is an iterative learning process Objectives pertaining to the expla nation of a social or physical phenomenon must be spccificd and then tested b gathering and analyzing data. In turn, an analysis of the data gathered by experi mentation or observation will usually suggest a modified explanation of the phe nomenon. Throughout this iterative learning process, variables are often added or deleted from the study. Thus, the complexities of most phenomena require an inves tigator to collect observations on many different variables Th is book is concerned with statistical methods designed to elicit information from these kinds of data sets Because the data include simultaneous measurements on many variables, this body of methodology is called multivariate analysis The need to understand the relationships between many variables makes multi variate analysis an inherently difficult subject. Often, the human mind is over- whelmed by the sheer bulk of the data. additionally, more mathematics is required to derive multivariate statistical techniques for making inferences than in a univari ate setting, We have chosen to provide explanations based upon algebraic concepts and to avoid the derivations of statistical results that require the calculus of many variables. Our objective is to introduce several useful multivariate techniques in a clear manner, making heavy use of illustrative examples and a minimum of mathe matics. Nonetheless, some mathematical sophistication and a desire to think quanti tatively will be required Most of our emphasis will be on the analysis of measurements obtained with- out actively controlling or manipulating any of the variables on which the mea surements are made. Only in Chapters 6 and 7 shall we treat a fcw cxpcrimental plans(designs for generating data that prescribe the active manipulation of im portant variables. Although the experimental design is ordinarily the most impor- tant part of a scientific investigation, it is frequently impossible to control the From Chapter 1 of Applied Multivariate Statistical Analysis, Sixth Edition. Richard A. Johnson Dean W.Wichern. Copyright o 2007 by Pearson Education, Inc. All rights reserved 2 Chapter 1 Aspects of Multivariate Analysis generation of appropriate data in certain disciplines. (This is true, for example, in business, economics, ecology, geology, and sociology. You should consult [6 and [7] for detailed accounts of design principles that, fortunately, also apply to multi variate situalions It will become increasingly clear that many multivariate methods are based upon an underlying probability model known as the multivariate normal distribution Other methods are ad hoc in nature and are justified by logical or commonsense arguments. Regardless of their origin, multivariate techniques must, invariably be implemented on a computer. Recent advances in computer technology have been accompanied by the development of rather sophisticated statistical software packages, making the implementation step easier Multivariate analysis is a"mixed bag It is difficult to establish a classification scheme for multivariate techniques that is both widely accepted and indicates the appropriateness of the techniqucs Onc classification distinguishes techniques de- signed to study interdependent relationships from those designed to study depen dent relationships. Another classifies techniques according to the number of populations and the number of sets of variables being studied. Chapters in this text are divided into sections according to inference about treatment means, inference about covariance structure, and techniques for sorting or grouping This should not however, be considered an attempt to place each method into a slot. Rather, the choice of methods and the types of analyses employed are largely determined by the objectives of the investigation. In Section 1. 2, we list a smaller number of practical problems designed to illustrate the connection between the choice of a sta- tistical method and the objectives of the study. These problems, plus the examples in the lext, should provide you with an appreciation of the applicability of multivariate techniques across different fields The objectives of scientific investigations to which multivariate methods most naturally lend themselves include the following: 1. Data reduction or structural simplification. The phenomenon being studied is represented as simply as possible without sacrificing valuable information. It is hoped that this will make interpretation easier 2. Sorting and grouping. Groups of"similar"objects or variables are created, based upon measured characterisLics. Alternatively, rules for classifying objects into well-defined groups may be required 3. Investigation of the dependence among variables. The nature of the relation ships among variables is of interest. Are all the variables mutually independent or are one or more variables dependent on the others? If so how 4. Prediction. Relationships between variables must be determined for the pur pose of predicting the values of one or more variables on the basis of observa- tions on the other variables 5. Hypothesis construction and testing. Specific statistical hypotheses, formulated in terms of the parameters of multivariate populations are tested. This may be done to validate assumptions or to reinforce prior convictions We conclude this brief overview of multivariate analysis with a quotation from F.H. C. Marriott [19], page 89. The statement was made in a discussion of cluster analysis, but we feel it is appropriate for a broader range of methods. You should keep it in mind whenever you attempt or read about a data analysis. It allows one to Applications of Multivariate Techniques 3 maintain a proper perspective and not be overwhelmed by the elegance of some of the theol If the results disagree with informed opinion, do not admit a simple logical interpreta tion, and do not show up clearly in a graphical presentation, they are probably wrong There is no magic about numerical methods, and many ways in which they can break down. They are a valuable aid to the interpretation of data, not sausage machines automatically transforming bodies of numbers into packets of scientific fact. .2 Applications of multivariate Techniques The published applications of multivariate methods have increased tremendously in recent years. It is now difficult to cover the variety of real-world applications of these methods with brief discussions as we did in earlier editions of this book how ever, in order to give some indication of the usefulness of multivariate techniques, we offer the following short descriptions of the results of studies from several disci plines. These descriptions are organized according to the categories of objectives given in the previous scction. Of course, many of our examples are multifaceted and could be placed in more than one category Data reduction or simplification Using data on several variables related to cancer patient responses to radio- therapy, a simple measure of patient response to radiotherapy was constructed (See Exercise 1.15.) Track records from many nations were used to develop an index of perfor- for both male and female athletes. (See[8] and 22].) Multispectral image data collected by a high-altitude scanner were reduced to a form that could be viewed as images(pictures)of a shoreline in two dimensions (See[23].) Data on several variables relating to yield and protein content were used to cre ate an index to select parents of subsequent generations of improved bean ts(See[13]. A matrix of tactic similarities was developed from aggregate data derived from professional mediators. From this matrix the number of dimensions by which professional mediators judge the tactics they use in resolving disputes was determined. (See [21) Sorting and grouping Data on several variables related to computer use were employed to create clusters of categories of computer jobs that allow a better determination of existing(or planned) computer utilization. (See [2]) Measurements of several physiological variables were used to develop a screen ing proccdure that discriminates alcoholics from nonalcoholics. (Scc [26] Data related to responses to visual stimuli were used to develop a rule for sepa- rating people suffering from a multiple-sclerosis-caused visual pathology from those not suffering from the disease. (See Exercise 1. 14. 4 Chapter 1 Aspects of Multivariate analysis The u.s. internal revenue service uses data collected from tax returns to sort taxpayers into two groups: those that will be audited and those that will not (See[31) Investigation of the dependence among variables Data on several variables were used to identify factors that were responsible for client success in hiring external consultants (Scc[12] .) Measurements of variables related to innovation on the one hand and vari ables related to the business environment and business organization on the other hand, were used to discover why some firms are product innovators and some firms are not. (See [3.) Measurements of pulp fiber characteristics and subsequent measurements of characteristics of the paper made from them are used to examine the relations between pulp fiber properties and the resulting paper properties. The goal is to determine those fibers that lead to higher quality paper. (See [17) The associations between measures of risk-taking propensity and measures of socioeconomic characteristics for top-level business executives were used to assess the relation between risk-taking behavior and performance. (See [18-) Prediction The associations between test scores, and several high school performance vari ables, and several college performance variables were used to develop predic tors of success in college. (Scc[10].) Data on several variables related to the size distribution of sediments were used to develop rules for predicting different depositional environments. (See [7] and 20].) Measurements on sevcral accounting and financial variables were uscd to de velop a method for identifying potentially insolvent property-liability insurers (See281.) CDNA microarray experiments(gene expression data)are increasingly used to study the molecular variations among cancer tumors. a reliable classification of tumors is cssential for successful diagnosis and trcatmcnt of cancer.(Scc[].) Hyp potheses testin Several pollution-related variables were measured to determine whether levels for a large metropolitan area were roughly constant throughout the week, or whether there was a noticeable difference between weekdays and weekends (See Exercise 1.6 Experimental data on several variables were used to see whether the nature of the instructions makes any difference in perceived risks, as quantified by test scores(See[27. Data on many variables were used to investigate the differences in structure of American occupations to dctcrminc the support for one of two competing soci- ological theories (See [16] and [25].) Data on several variables were used to determine whether different types of firms in newly industrialized countries exhibited different patterns of innova tion.(See [15)) The Organization of Data 5 lh The preceding descriptions offer glimpses into the use of multivariate methods widely diverse fields 1.3 The Organization of data Throughout this text, we are going to be concerned with analyzing measurements made on several variables or charactcristics. These mcasurcments(commonly called data must frequently be arranged and displayed in various ways. For example, graphs and tabular arrangements are important aids in data analysis Summary num bers, which quantitatively portray certain features of the data, are also necessary to any description We now introduce the preliminary concepts underlying these first steps of data organization Arrays Multivariate data arise whenever an investigator, seeking to understand a social or physical phenomenon, selects a number p= 1 of variables or characters to record The values of these variables are all recorded for each distinct item, individual. or experimental unit. We will use the notation xi k to indicate the particular value of the kth variable that is observed on the jth item, or trial. That is xik measurement of the kth variable on the ith item Consequently, n measurements on p variables can be displayed as follows Variable 1 variable 2 Variable k variable p Item 1 11 Item 2. C Item户 x jk x Item n: Or we can display these data as a rectangular array, called X, of n rows and p columns lk xj1 xj2 ik enl xn2 k Xnp The array X, then, contains the data consisting of all of the observations on all of the variables 【实例截图】
【核心代码】