# Multivariate Statistics for Wildlife and Ecology Research / Edition 1

Multivariate Statistics for Wildlife and Ecology Research gives the re ader a solid conceptual understanding of the role of multivariate stat istics in ecological applications and the relationships among various techniques, while avoiding detailed mathematics and underlying theory. More important, the reader will gain insight into the type of researc h questions

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## Overview

Multivariate Statistics for Wildlife and Ecology Research gives the re ader a solid conceptual understanding of the role of multivariate stat istics in ecological applications and the relationships among various techniques, while avoiding detailed mathematics and underlying theory. More important, the reader will gain insight into the type of researc h questions best handled by each technique and the important considera tions in applying each one. Whether used as a textbook for specialized courses or as a supplement to general statistics texts, the book emph asizes those techniques that students of ecology and natural resources most need to understand and employ in their research. Detailed exampl es use real wildlife data sets analyzed using the SAS statistical soft ware program.

## Product Details

ISBN-13:
9780387986425
Publisher:
Springer New York
Publication date:
06/16/2000
Edition description:
1st ed. 2000. Corr. 2nd printing 2002
Pages:
283
Product dimensions:
6.10(w) x 9.10(h) x 0.70(d)

## Table of Contents

1 Introduction and Overview.- 1.1 Objectives.- 1.2 Multivariate Statistics: An Ecological Perspective.- 1.3 Multivariate Description and Inference.- 1.4 Multivariate Confusion!.- 1.5 Types of Multivariate Techniques.- 1.5.1 Ordination.- 1.5.2 Cluster Analysis.- 1.5.3 Discriminant Analysis.- 1.5.4 Canonical Correlation Analysis.- 2 Ordination: Principal Components Analysis.- 2.1 Objectives.- 2.2 Conceptual Overview.- 2.2.1 Ordination.- 2.2.2 Principal Components Analysis (PCA).- 2.3 Geometric Overview.- 2.4 The Data Set.- 2.5 Assumptions.- 2.5.1 Multivariate Normality.- 2.5.2 Independent Random Sample and the Effects of Outliers.- 2.5.3 Linearity.- 2.6 Sample Size Requirements.- 2.6.1 General Rules.- 2.6.2 Specific Rules.- 2.7 Deriving the Principal Components.- 2.7.1 The Use of Correlation and Covariance Matrices.- 2.7.2 Eigenvalues and Associated Statistics.- 2.7.3 Eigenvectors and Scoring Coefficients.- 2.8 Assessing the Importance of the Principal Components.- 2.8.1 Latent Root Criterion.- 2.8.2 Scree Plot Criterion.- 2.8.3 Broken Stick Criterion.- 2.8.4 Relative Percent Variance Criterion.- 2.8.5 Significance Tests.- 2.9 Interpreting the Principal Components.- 2.9.1 Principal Component Structure.- 2.9.2 Significance of Principal Component Loadings.- 2.9.3 Interpreting the Principal Component Structure.- 2.9.4 Communality.- 2.9.5 Principal Component Scores and Associated Plots.- 2.10 Rotating the Principal Components.- 2.11 Limitations of Principal Components Analysis.- 2.12 R-Factor Versus Q-Factor Ordination.- 2.13 Other Ordination Techniques.- 2.13.1 Polar Ordination.- 2.13.2 Factor Analysis.- 2.13.3 Nonmetric Multidimensional Scaling.- 2.13.4 Reciprocal Averaging.- 2.13.5 Detrended Correspondence Analysis.- 2.13.6 Canonical Correspondence Analysis.- Appendix 2.1.- 3 Cluster Analysis.- 3.1 Objectives.- 3.2 Conceptual Overview.- 3.3 The Definition of Cluster.- 3.4 The Data Set.- 3.5 Clustering Techniques.- 3.6 Nonhierarchical Clustering.- 3.6.1 Polythetic Agglomerative Nonhierarchical Clustering.- 3.6.2 Polythetic Divisive Nonhierarchical Clustering.- 3.7 Hierarchical Clustering.- 3.7.1 Polythetic Agglomerative Hierarchical Clustering.- 3.7.2 Polythetic Divisive Hierarchical Clustering.- 3.8 Evaluating the Stability of the Cluster Solution.- 3.9 Complementary Use of Ordination and Cluster Analysis.- 3.10 Limitations of Cluster Analysis.- Appendix 3.1.- 4 Discriminant Analysis.- 4.1 Objectives.- 4.2 Conceptual Overview.- 4.2.1 Overview of Canonical Analysis of Discriminance.- 4.2.2 Overview of Classification.- 4.2.3 Analogy with Multiple Regression Analysis and Multivariate Analysis of Variance.- 4.3 Geometric Overview.- 4.4 The Data Set.- 4.5 Assumptions.- 4.5.1 Equality of Variance-Covariance Matrices.- 4.5.2 Multivariate Normality.- 4.5.3 Singularities and Multicollinearity.- 4.5.4 Independent Random Sample and the Effects of Outliers.- 4.5.5 Prior Probabilities Are Identifiable.- 4.5.6 Linearity 153.- 4.6 Sample Size Requirements.- 4.6.1 General Rules.- 4.6.2 Specific Rules.- 4.7 Deriving the Canonical Functions.- 4.7.1 Stepwise Selection of Variables.- 4.7.2 Eigenvalues and Associated Statistics.- 4.7.3 Eigenvectors and Canonical Coefficients.- 4.8 Assessing the Importance of the Canonical Functions.- 4.8.1 Relative Percent Variance Criterion.- 4.8.2 Canonical Correlation Criterion.- 4.8.3 Classification Accuracy.- 4.8.4 Significance Tests.- 4.8.5 Canonical Scores and Associated Plots.- 4.9 Interpreting the Canonical Functions.- 4.9.1 Standardized Canonical Coefficients.- 4.9.2 Total Structure Coefficients.- 4.9.3 Covariance-Controlled Partial F-Ratios.- 4.9.4 Significance Tests Based on Resampling Procedures.- 4.9.5 Potency Index.- 4.10 Validating the Canonical Functions.- 4.10.1 Split-Sample Validation.- 4.10.2 Validation Using Resampling Procedures.- 4.11 Limitations of Discriminant Analysis.- Appendix 4.1.- 5 Canonical Correlation Analysis.- 5.1 Objectives.- 5.2 Conceptual Overview.- 5.3 Geometric Overview.- 5.4 The Data Set.- 5.5 Assumptions.- 5.5.1 Multivariate Normality.- 5.5.2 Singularities and Multicollinearity.- 5.5.3 Independent Random Sample and the Effects of Outliers.- 5.5.4 Linearity.- 5.6 Sample Size Requirements.- 5.6.1 General Rules.- 5.6.2 Specific Rules.- 5.7 Deriving the Canonical Variates.- 5.7.1 The Use of Covariance and Correlation Matrices.- 5.7.2 Eigenvalues and Associated Statistics.- 5.7.3 Eigenvectors and Canonical Coefficients.- 5.8 Assessing the Importance of the Canonical Variates.- 5.8.1 Canonical Correlation Criterion.- 5.8.2 Canonical Redundancy Criterion.- 5.8.3 Significance Tests.- 5.8.4 Canonical Scores and Associated Plots.- 5.9 Interpreting the Canonical Variates.- 5.9.1 Standardized Canonical Coefficients.- 5.9.2 Structure Coefficients.- 5.9.3 Canonical Cross-Loadings.- 5.9.4 Significance Tests Based on Resampling Procedures.- 5.10 Validating the Canonical Variates.- 5.10.1 Split-Sample Validation.- 5.10.2 Validation Using Resampling Procedures.- 5.11 Limitations of Canonical Correlation Analysis.- Appendix 5.1.- 6 Summary and Comparison.- 6.1 Objectives.- 6.2 Relationship Among Techniques.- 6.2.1 Purpose and Source of Variation Emphasized.- 6.2.2 Statistical Procedure.- 6.2.3 Type of Statistical Technique and Variable Set Characteristics.- 6.2.4 Data Structure.- 6.2.5 Sampling Design.- 6.3 Complementary Use of Techniques.- Appendix: Acronyms Used in This Book.

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