Applied Statistics for Environmental Science With R

Front Matter
Copyright
Dedication
Preface
Multivariate Data
	Learning Objectives
	The Concept of Environmental Statistics
	The Concept of Multivariate Analysis
	Configuration of Multivariate Data
	Examples of Multivariate Data
	Multivariate Normal Distribution
		Univariate Normal Distribution
		Multivariate Normal Distribution
	Further Reading
R Statistical Software
	Learning Objectives
	Introduction
	Installing R
		R Material
		R Packages
	The R Console
	Expression and Assignment in R
	Variables and Vectors in R
		Matrix in R
	Basic Definitions
	Plots in R
	RStudio
		Navigating RStudio
	Importing Data
	Further Reading
Statistical Notions
	Learning Objectives
	Introduction
	The Concept of Statistics
	Common Concepts
		Qualitative Variables
		Quantitative Variables
			Discrete Variable
			Continuous Variable
	Data Gathering
		Approaches for Gathering Data
	Sampling Methods
		Simple Random Sampling
		Systematic Sampling
		Stratified Sampling
		Cluster Sampling
	Further Reading
Measures of Center and Variation
	Learning Objectives
	Introduction
	Measures of Center and Dispersion in R
	Measures of Center
		The Arithmetic Mean for a Single Variable
		The Mean Vector (Multivariate)
	Measure of Variation
		Variance and Standard Deviation for a Single Variable
	The Concept of Covariance
		Covariance Matrices (Multivariate)
	Correlation Analysis
		Correlation Matrices
	Scatter Diagram
		The Scatter Diagram Matrix
	Euclidean Distance
	Further Reading
Statistical Hypothesis Testing
	Learning Objectives
	Introduction
	Statistical Hypothesis Testing in R
	Common Steps for Hypothesis Testing
		The Concept of Null and Alternative Hypotheses
		Basic Concepts
	Hypothesis Testing for a Mean Value
		Hypothesis Testing for One Population Mean
		Hypothesis Testing for a Mean Vector for one Sample
	Hypothesis Testing for Two Population Means
		Hypothesis Testing for Two Population Means
		Hypothesis Testing for Mean Vectors for Two Populations
	Further Reading
Multivariate Analysis of Variance
	Learning Objectives
	Introduction
	Analysis of Variance in R
	The Concept of Analysis of Variance
		One-Way Analysis of Variance
			Hypothesis Testing for a One-Way Analysis of Variance
			Explanation of the Analysis of Variance Results
		Two-Way Analysis of Variance
			Hypothesis Testing for a Two-way Analysis of Variance
	The Concept of Multivariate Analysis of Variance
		One-Way Multivariate Analysis of Variance
			Hypothesis Testing for One-Way MANOVA
		Two-Way Multivariate Analysis of Variance
	Further Reading
Regression Analysis
	Learning Objectives
	The Concept of Regression Analysis
	Regression Models in R
	The Concept of Simple Linear Regression Model
		Hypothesis Testing for Regression Models
		Explanation of Regression Model
		Prediction Using a Regression Equation
		Extreme Values and Influential Observations
		Residuals
		Explained and Unexplained Variation
		Coefficient of Determination
	Multiple Linear Regression Model
	Hypothesis Testing for Multiple Linear Regression
		Hypothesis Testing for Overall Significance of the Regression Model
		Hypothesis Testing on Individual Regression Coefficients
		Hypothesis Testing on a Subset of the Regression Coefficients
	Adjusted Coefficient of Determination
	Multivariate Multiple Linear Regression Model
	Further Readings
Principal Components
	Learning Objectives
	Introduction
	Principal Components Analysis in R
	Describing Principal Components
	Common Procedure for Computing Principal Components
	Extract Principal Components from Correlation Matrix
	Standardization
	Selecting the Number of Components
	Further Reading
Factor Analysis
	Learning Objectives
	Introduction
	Factor Analysis in R
	General Model for Factor Analysis
	Common Steps for Factor Analysis
		Principal Component Method
	Further Reading
Discriminant Analysis
	Learning Objectives
	Introduction
	Discriminant Analysis in R
	Configuration of Discriminant Analysis Data
	The Concept of Discriminant Function
		Common Steps for Computing the Discriminant Function
	Allocation
	Further Reading
Clustering Approaches
	Learning Objectives
	What is Cluster Analysis?
	Cluster Analysis in R
	Measures of Distance
	Clustering Procedures
		Hierarchical Clustering Procedure
			Agglomerative Method
			Divisive Method
		Non-Hierarchical Clustering Procedure
	Further Reading
Appendix
	Chapter 1
		Standard Normal Curve
	Chapter 2
		Example 2.17
		Example 2.18
	Chapter 4
		Example 4.1
		Example 4.2
		Example 4.3
		Example 4.4
		Example 4.5
		Example 4.6
		Example 4.7
		Example 4.8
		Example 4.9
		Figure 4.2
			#Figure4_2a
			#Figure4_2b
		Example 4.10
		Example 4.11
		Example 4.12
	Chapter 5
		#Example 5.2 (a)
		#Example 5.2 (b)
		#Example 5.2 (c)
		Example 5.3
		Example 5.4
		T graph
		Example 5.5
		Example 5.6
		Example 5.7
		Example 5.8
		Example 5.9
		Example 5.10
		Example 5.11
		#Brief data _ Input information
		Example 5.12
		Example 5.13
	Chapter 6
		Example 6.1
		Example 6.2
		Example 6.3
		Example 6.4
		Example 6.5
		Example 6.6
		Example 6.7
		Example 6.8
	Chapter 7
		Example 7.1
		Example 7.2
		Example 7.3
		Example 7.4
		Example 7.5
	Chapter 8
		Example 8.1
		#Figure 8.1
		#Figure 8.2
		Example 8.2
		#Figure 8.4
		#Figure 8.5
	Chapter 9
		Example 9.1
		#Figure 9.1
		#Figure 9.2
		#Figure 9.3
		#Figure 9.4
		#Figure 9.5
		# Figure 9.6
		Example 9.2
		#Figure 9.7
		#Figure 9.8
		#Figure 9.9
		#Figure 9.10
	Chapter 10
		Example 10.1
		#Figure 10.1
		Example 10.2
		Example 10.3
		#Figure 10.3
		#Figure 10.4
		Example 10.4
	Chapter 11
		Example 11.1
		Example 11.2
Index
	A
	B
	C
	D
	E
	F
	G
	H
	I
	J
	K
	L
	M
	N
	O
	P
	Q
	R
	S
	T
	U
	V
	W
	Z