Multivariate Statistics for the Environmental Sciences

by Peter J. A. Shaw

• ISBN13: 9780340807637
• ISBN10: 0340807636
• Edition: 1st
• Format: Paperback
• Copyright: 2003-05-08
• Publisher: Hodder Education Publishers

Summary

This book introduces the most commonly used techniques for dealing with multivariate data; the sort of multi-species multi-chemical data sets that are routinely encountered in environmental investigations. It assumes prior knowledge of multivariate analyses and requires no mathematics beyond simple linear equations. The topics covered include diversity indices, multiple regression, cluster analysis, and the commoner ordination techniques (principal components analysis, detreded correspondance analysis and canonical correspondence analysis). Other less used ordinations (Bray-Curtis, Correspondence Analysis) are where this helps understanding of the most commonly used techniques. Where suitable, the author shows how to construct biplots and triplots, and how to run Monte-Carlo testing. Each technique is illustrated by worked examples using simple, familiar data sets, and the key features of the output from standard software packages is explained. Pitfalls for the unwary are highlighted wherever they occur. Appendices list and explain the acronyms that can make some published research impenetrable. The availablity of each multivariate techlnique in all major software packages is listed, to help users choose the software suitable for them. The overall aim of the book is to introduce inexperienced users gently to the multivariate analytical tools available to them.

Author Biography

Peter Shaw is a Senior Lecturer in the School of Life Sciences, University of Surrey Roehampton, UK.

Table of Contents

Preface	vii
Introduction	1	(29)
What is meant by multivariate statistics?	1	(4)
The scope of this book	5	(1)
When multivariate statistics might be used	6	(1)
Minimum computing requirements	7	(1)
Preparing the data	7	(14)
The sample datasets	21	(9)
Measurements of ecological diversity	30	(15)
The concept of diversity	30	(2)
The Simpson index	32	(2)
The Shannon index	34	(1)
Jack-knifing	35	(1)
Examples	35	(9)
Further diversity indices	44	(1)
Linear regression: simple and multiple	45	(28)
Introduction	45	(1)
The data space	46	(1)
Bivariate linear regression	47	(11)
Additional independent variables	58	(4)
Pitfalls for the unwary	62	(1)
Worked examples	62	(11)
Basic concepts in ordination	73	(10)
Introduction to ordination	73	(8)
A historical overview of ordination	81	(2)
Bray--Curtis ordination	83	(9)
History of Bray--Curtis ordination	83	(1)
Theory of Bray--Curtis ordination	84	(6)
Limitations of Bray--Curtis ordination	90	(2)
Principal components analysis	92	(33)
A brief overview of principal components analysis	92	(1)
What does PCA achieve?	93	(7)
Deeper into the mechanics of PCA	100	(7)
Preliminary interpretation of a PCA	107	(9)
Other worked examples of PCA	116	(9)
Correspondence analysis, simple and detrended	125	(24)
General introduction	125	(1)
Correspondence analysis	126	(8)
Detrended correspondence analysis	134	(8)
Worked examples	142	(7)
Classification: cluster analysis and related techniques	149	(30)
Introduction to classification	149	(1)
A taxonomy of classification techniques	150	(6)
Cluster analysis	156	(15)
Divisive classification techniques	171	(8)
Canonical correspondence analysis (CCA)	179	(19)
Introduction	179	(2)
The mechanics of canonical correspondence analysis	181	(2)
Worked example: CCA on the Wimbledon Common dataset	183	(8)
Alaskan streams dataset	191	(2)
Drained mires in Finland	193	(5)
A brief review of other multivariate techniques	198	(8)
Appendix 1: Synonyms and acronyms of multivariate techniques	206	(2)
Appendix 2: A general approach to linear regression using linear algebra	208	(5)
Appendix 3: Multivariate software for the environmental researcher	213	(2)
Appendix 4: Suggested further reading	215	(2)
Glossary	217	(5)
Bibliography	222	(7)
Index	229