Data Analysis and Statistics for Geography, Environmental Science, and Engineering
Features
- Provides an integrated practical guide to data analysis and statistics using free open-source R software
- Presents a broad focus geared towards sustainability science and engineering
- Reviews the necessary mathematics and theoretical fundamentals
- Includes practical exercises using free open-source R software and written with a tutorial style
- Helps readers acquire skills to implement and conduct analysis and analyze results
- Includes more than 300 figures to aid in comprehension
Pedagogical Features
- Solved examples
- Homework problems
- Guided computer exercises
A solutions manual and PowerPoint® slides with figures and equations are available with qualifying course adoption
Summary
Providing a solid foundation for twenty-first-century scientists and engineers, Data Analysis and Statistics for Geography, Environmental Science, and Engineering guides readers in learning quantitative methodology, including how to implement data analysis methods using open-source software. Given the importance of interdisciplinary work in sustainability, the book brings together principles of statistics and probability, multivariate analysis, and spatial analysis methods applicable across a variety of science and engineering disciplines.
Learn How to Use a Variety of Data Analysis and Statistics Methods
Based on the author’s many years of teaching graduate and undergraduate students, this textbook emphasizes hands-on learning. Organized into two parts, it allows greater flexibility using the material in various countries and types of curricula. The first part covers probability, random variables and inferential statistics, applications of regression, time series analysis, and analysis of spatial point patterns. The second part uses matrix algebra to address multidimensional problems. After a review of matrices, it delves into multiple regression, dependent random processes and autoregressive time series, spatial analysis using geostatistics and spatial regression, discriminant analysis, and a variety of multivariate analyses based on eigenvector methods.
Build from Fundamental Concepts to Effective Problem Solving
Each chapter starts with conceptual and theoretical material to give a firm foundation in how the methods work. Examples and exercises illustrate the applications and demonstrate how to go from concepts to problem solving. Hands-on computer sessions allow students to grasp the practical implications and learn by doing. Throughout, the computer examples and exercises use seeg and RcmdrPlugin.seeg, open-source R packages developed by the author, which help students acquire the skills to implement and conduct analysis and to analyze the results.
This self-contained book offers a unified presentation of data analysis methods for more effective problem solving. With clear, easy-to-follow explanations, the book helps students to develop a solid understanding of basic statistical analysis and prepares them for learning the more advanced and specialized methods they will need in their work.
Table of Contents
PART I Introduction to Probability, Statistics, Time Series, and Spatial Analysis
Introduction
Brief History of Statistical and Probabilistic Analysis
Computers
Applications
Types of Variables
Probability Theory and Random Variables
Methodology
Descriptive Statistics
Inferential Statistics
Predictors, Models, and Regression
Time Series
Spatial Data Analysis
Matrices and Multiple Dimensions
Other Approaches: Process-Based Models
Baby Steps: Calculations and Graphs
Exercises
Computer Session: Introduction to R
Supplementary Reading
Probability Theory
Events and Probabilities
Algebra of Events
Combinations
Probability Trees
Conditional Probability
Testing Water Quality: False Negative and False Positive
Bayes’ Theorem
Generalization of Bayes’ Rule to Many Events
Bio-Sensing
Decision Making
Exercises
Computer Session: Introduction to Rcmdr, Programming, and Multiple Plots
Supplementary Reading
Random Variables, Distributions, Moments, and Statistics
Random Variables
Distributions
Moments
Some Important RV and Distributions
Application Examples: Species Diversity
Central Limit Theorem
Random Number Generation
Exercises
Computer Session: Probability and Descriptive Statistics
Example Binomial
Supplementary Reading
Exploratory Analysis and Introduction to Inferential Statistics
Exploratory Data Analysis (EDA)
Relationships: Covariance and Correlation
Statistical Inference
Statistical Methods
Parametric Methods
Nonparametric Methods
Exercises
Computer Session: Exploratory Analysis and Inferential Statistics
Supplementary Reading
More on Inferential Statistics: Goodness of Fit, Contingency Analysis, and Analysis of Variance
Goodness of Fit (GOF)
Counts and Proportions
Contingency Tables and Cross-Tabulation
Analysis of Variance
Exercises
Computer Session: More on Inferential Statistics
Supplementary Reading
Regression
Simple Linear Least Squares Regression
ANOVA as Predictive Tool
Nonlinear Regression
Computer Session: Simple Regression
Supplementary Reading
Stochastic or Random Processes and Time Series
Stochastic Processes and Time Series: Basics
Gaussian
Autocovariance and Autocorrelation
Periodic Series, Filtering, and Spectral Analysis
Poisson Process
Marked Poisson Process
Simulation
Exercises
Computer Session: Random Processes and Time Series
Supplementary Reading
Spatial Point Patterns
Types of Spatially Explicit Data
Types of Spatial Point Patterns
Spatial Distribution
Testing Spatial Patterns: Cell Count Methods
Nearest-Neighbor Analysis
Marked Point Patterns
Geostatistics: Regionalized Variables
Variograms: Covariance and Semivariance
Directions
Variogram Models
Exercises
Computer Session: Spatial Analysis
Supplementary Reading
PART II Matrices, Tempral and Spatial Autoregressive Processes, and Multivariate Analysis
Matrices and Linear Algebra
Matrices
Dimension of a Matrix
Vectors
Square Matrices
Matrix Operations
Solving Systems of Linear Equations
Linear Algebra Solution of the Regression Problem
Alternative Matrix Approach to Linear Regression
Exercises
Computer Session: Matrices and Linear Algebra
Supplementary Reading
Multivariate Models
Multiple Linear Regression
Multivariate Regression
Two-Group Discriminant Analysis
Multiple Analysis of Variance (MANOVA)
Exercises
Computer Session: Multivariate Models
Supplementary Reading
Dependent Stochastic Processes and Time Series
Markov
Semi-Markov Processes
Autoregressive (AR) Process
ARMA and ARIMA Models
Exercises
Computer Session: Markov Processes and Autoregressive Time Series
Supplementary Reading
Geostatistics: Kriging
Kriging
Ordinary Kriging
Universal Kriging
Data Transformations
Exercises
Computer Session: Geostatistics, Kriging
Supplementary Reading
Spatial Auto-Correlation and Auto-Regression
Lattice Data: Spatial Auto-Correlation and Auto-Regression
Spatial Structure and Variance Inflation
Neighborhood Structure
Spatial Auto-Correlation
Spatial Auto-Regression
Exercises
Computer Session: Spatial Correlation and Regression
Supplementary Reading
Multivariate Analysis I: Reducing Dimensionality
Multivariate Analysis: Eigen-Decomposition
Vectors and Linear Transformation
Eigenvalues and Eigenvectors
Eigen-Decomposition of a Covariance Matrix
Principal Components Analysis (PCA)
Singular Value Decomposition and Biplots
Factor Analysis
Correspondence Analysis
Exercises
Computer Session: Multivariate Analysis, PCA
Supplementary Reading
Multivariate Analysis II: Identifying and Developing Relationships among Observations and Variables
Introduction
Multigroup Discriminant Analysis (MDA)
Canonical Correlation
Constrained (or Canonical) Correspondence Analysis (CCA)
Cluster Analysis
Multidimensional Scaling (MDS)
Exercises
Computer Session: Multivariate Analysis II
Supplementary Reading
Bibliography
Index
