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Multivariate Statistical Methods: A Primer
288![Multivariate Statistical Methods: A Primer](http://img.images-bn.com/static/redesign/srcs/images/grey-box.png?v11.8.5)
Multivariate Statistical Methods: A Primer
288Paperback(5th ed.)
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Overview
For those looking to become proficient in multivariate statistical methods, but who might not be deeply versed in the language of mathematics, provides conceptual intros to methods, practical suggestions, new references, and a more extensive collection of R functions and code that will deepen toolkit of multivariate statistical methods.
Product Details
ISBN-13: | 9781032591971 |
---|---|
Publisher: | CRC Press |
Publication date: | 10/04/2024 |
Edition description: | 5th ed. |
Pages: | 288 |
Product dimensions: | 6.12(w) x 9.19(h) x (d) |
About the Author
Bryan Manly, PhD, was born in London, UK on May 27, 1944, and he is practically retired from academic work. His areas of interest are in statistical ecology, environmental statistics, computer intensive statistics, and general applied statistics. He is the author of over two hundred papers and seven books that have been both fundamental statistical research, and applications to several related disciplines. Bryan's academic career began in 1966 as a statistician and one of the first computer programmers, at the British multinational manufacturer Fisons, marking the start of a brilliant career as a researcher and statistical consultant in several countries around the world: University of Salford (UK), University of Papua New Guinea, University of Otago (New Zealand), Louisiana State University, University of Wyoming, and WEST, Inc. (USA). Among other distinctions, he is an Elected Fellow of the Royal Society of New Zealand, and he was awarded as Distinguished Statistical Ecologist in the International Ecology Congress, held in Manchester, 1994. Bryan is an excellent connoisseur of home brewing and homemade wine; everybody praises his good hand in making peerless wine!
Jorge A. Navarro Alberto, PhD, is a professor emeritus at the Autonomous University of Yucatán, México, where he specialized in ecological and environmental statistics research. Dr. Navarro Alberto earned his PhD degree in Statistics at the University of Otago, New Zealand. His academic career spanned more than 36 years teaching statistics for biologists, marine biologists, and natural resource managers in Mexico, and as a visiting professor at the University of Wyoming, with a vast experience in teaching multivariate analysis courses for life scientists. He is the co-author of the last edition of the book Randomization, Bootstrap and Monte Carlo Methods in Biology, and the co-editor of Introduction to Ecological Sampling, published by CRC Press. After retirement, Jorge is still active in the professional and academic arenas, working as a (more relaxed) part-time statistical consultant, and as one of the associate editors of the international journal, Environmental and Ecological Statistics. He also member of the Mexican representation at the International Statistical Literacy Project, Finland.
Ken Gerow, PhD, recently retired from the University of Wyoming, where, as a professor of statistics for over thirty years, he taught statistics to quantitative scientists from many disciplines. Dr. Gerow earned his PhD degree in Statistics at Cornell University. He is the author or a coauthor of over ninety research articles, books, and book chapters, in topics ranging from the molecular and cellular world to the visible world around us (plant, animal, and human systems). Ken considers himself to be a parasitic biologist because he only publishes with other people's data.
Table of Contents
Chapter 1 | The material of multivariate analysis | 1 |
1.1 | Examples of multivariate data | 1 |
1.2 | Preview of multivariate methods | 12 |
1.3 | The multivariate normal distribution | 14 |
1.4 | Computer programs | 15 |
1.5 | Graphical methods | 15 |
1.6 | Chapter summary | 16 |
References | 16 | |
Chapter 2 | Matrix algebra | 17 |
2.1 | The need for matrix algebra | 17 |
2.2 | Matrices and vectors | 17 |
2.3 | Operations on matrices | 19 |
2.4 | Matrix inversion | 21 |
2.5 | Quadratic forms | 22 |
2.6 | Eigenvalues and eigenvectors | 22 |
2.7 | Vectors of means and covariance matrices | 23 |
2.8 | Further reading | 25 |
2.9 | Chapter summary | 25 |
References | 26 | |
Chapter 3 | Displaying multivariate data | 27 |
3.1 | The problem of displaying many variables in two dimensions | 27 |
3.2 | Plotting index variables | 27 |
3.3 | The draftsman's plot | 29 |
3.4 | The representation of individual data points | 30 |
3.5 | Profiles of variables | 32 |
3.6 | Discussion and further reading | 33 |
3.7 | Chapter summary | 34 |
References | 34 | |
Chapter 4 | Tests of significance with multivariate data | 35 |
4.1 | Simultaneous tests on several variables | 35 |
4.2 | Comparison of mean values for two samples: the single variable case | 35 |
4.3 | Comparison of mean values for two samples: the multivariate case | 37 |
4.4 | Multivariate versus univariate tests | 41 |
4.5 | Comparison of variation for two samples: the single-variable case | 42 |
4.6 | Comparison of variation for two samples: the multivariate case | 42 |
4.7 | Comparison of means for several samples | 46 |
4.8 | Comparison of variation for several samples | 49 |
4.9 | Computer programs | 54 |
4.10 | Chapter summary | 54 |
Exercise | 55 | |
References | 57 | |
Chapter 5 | Measuring and testing multivariate distances | 59 |
5.1 | Multivariate distances | 59 |
5.2 | Distances between individual observations | 59 |
5.3 | Distances between populations and samples | 62 |
5.4 | Distances based on proportions | 67 |
5.5 | Presence-absence data | 68 |
5.6 | The Mantel randomization test | 69 |
5.7 | Computer programs | 72 |
5.8 | Discussion and further reading | 72 |
5.9 | Chapter summary | 73 |
Exercise | 74 | |
References | 74 | |
Chapter 6 | Principal components analysis | 75 |
6.1 | Definition of principal components | 75 |
6.2 | Procedure for a principal components analysis | 76 |
6.3 | Computer programs | 84 |
6.4 | Further reading | 85 |
6.5 | Chapter summary | 85 |
Exercises | 87 | |
References | 90 | |
Chapter 7 | Factor analysis | 91 |
7.1 | The factor analysis model | 91 |
7.2 | Procedure for a factor analysis | 93 |
7.3 | Principal components factor analysis | 95 |
7.4 | Using a factor analysis program to do principal components analysis | 97 |
7.5 | Options in analyses | 100 |
7.6 | The value of factor analysis | 101 |
7.7 | Computer programs | 101 |
7.8 | Discussion and further reading | 102 |
7.9 | Chapter summary | 102 |
Exercise | 103 | |
References | 103 | |
Chapter 8 | Discriminant function analysis | 105 |
8.1 | The problem of separating groups | 105 |
8.2 | Discrimination using Mahalanobis distances | 105 |
8.3 | Canonical discriminant functions | 107 |
8.4 | Tests of significance | 108 |
8.5 | Assumptions | 109 |
8.6 | Allowing for prior probabilities of group membership | 114 |
8.7 | Stepwise discriminant function analysis | 114 |
8.8 | Jackknife classification of individuals | 116 |
8.9 | Assigning of ungrouped individuals to groups | 116 |
8.10 | Logistic regression | 117 |
8.11 | Computer programs | 122 |
8.12 | Discussion and further reading | 122 |
8.13 | Chapter summary | 123 |
Exercises | 124 | |
References | 124 | |
Chapter 9 | Cluster analysis | 125 |
9.1 | Uses of cluster analysis | 125 |
9.2 | Types of cluster analysis | 125 |
9.3 | Hierarchic methods | 127 |
9.4 | Problems of cluster analysis | 129 |
9.5 | Measures of distance | 129 |
9.6 | Principal components analysis with cluster analysis | 130 |
9.7 | Computer programs | 134 |
9.8 | Discussion and further reading | 135 |
9.9 | Chapter summary | 136 |
Exercises | 137 | |
References | 141 | |
Chapter 10 | Canonical correlation analysis | 143 |
10.1 | Generalizing a multiple regression analysis | 143 |
10.2 | Procedure for a canonical correlation analysis | 145 |
10.3 | Tests of significance | 146 |
10.4 | Interpreting canonical variates | 148 |
10.5 | Computer programs | 158 |
10.6 | Further reading | 158 |
10.7 | Chapter summary | 159 |
Exercise | 159 | |
References | 161 | |
Chapter 11 | Multidimensional scaling | 163 |
11.1 | Constructing a map from a distance matrix | 163 |
11.2 | Procedure for multidimensional scaling | 165 |
11.3 | Computer programs | 172 |
11.4 | Further reading | 174 |
11.5 | Chapter summary | 174 |
Exercise | 175 | |
References | 175 | |
Chapter 12 | Ordination | 177 |
12.1 | The ordination problem | 177 |
12.2 | Principal components analysis | 178 |
12.3 | Principal coordinates analysis | 181 |
12.4 | Multidimensional scaling | 189 |
12.5 | Correspondence analysis | 191 |
12.6 | Comparison of ordination methods | 196 |
12.7 | Computer programs | 197 |
12.8 | Further reading | 197 |
12.9 | Chapter summary | 198 |
Exercise | 198 | |
References | 198 | |
Chapter 13 | Epilogue | 201 |
13.1 | The next step | 201 |
13.2 | Some general reminders | 201 |
13.3 | Missing values | 202 |
References | 203 | |
Appendix | Computer packages for multivariate analyses | 205 |
References | 207 | |
Author Index | 209 | |
Subject Index | 211 |