Environmental Data Analysis: An Introduction with Examples in R

Preface
	References
The Technical Side: Selecting a Statistical Software
	Downloading and Installing R
	A Short Test in R
	Editors and Environments for R
	Tutorial
	References
Contents
1 Samples, Random Variables—Histograms, Density Distribution
	1.1 Sample Statistics
		1.1.1 Measures of Centrality
		1.1.2 Measures of Spread
		1.1.3 Sample Statistics: An Example
	1.2 Frequency, Density and Distribution
	References
2 Samples, Random Variables—Histograms and Density Distribution in R
	2.1 Data Collection
	2.2 Data Entry
	2.3 Importing Data to R
		2.3.1 Entering Small Data Sets Manually
		2.3.2 Read in Larger Data Sets from a File
	2.4 Simple, Descriptive Statistics and Graphic Representation
		2.4.1 Graphic Representation of Sample Statistics with R
		2.4.2 Descriptive Statistics with R
		2.4.3 Density Histogram and Empirical Density
	2.5 Exercises
	References
3 Distributions, Parameters and Estimators
	3.1 Distribution
		3.1.1 Central Limit Theorem
	3.2 Parameters of a Distribution
	3.3 Estimators (for Distribution Parameters)
		3.3.1 The Likelihood
		3.3.2 Maximizing the Likelihood
		3.3.3 Maximum Likelihood—Analytical
		3.3.4 Maximum Likelihood—Numerical
		3.3.5 Maximum Likelihood—High Praise
	3.4 Some Important Distributions
		3.4.1 Normal (= Gaussian) Distribution
		3.4.2 Bernoulli Distribution
		3.4.3 Binomial Distribution
		3.4.4 Poisson Distribution
		3.4.5 Negative Binomial Distribution
		3.4.6 Log-Normal Distribution
		3.4.7 Uniform Distribution
		3.4.8 β-distribution
		3.4.9 γ-distribution
		3.4.10 Truncated Distributions
	3.5 Selecting a Distribution
		3.5.1 Comparing Two Distributions: The Kolmogorov-Smirnov Test
		3.5.2 Comparing Fits: Likelihood and the Akaike Information Criterion
	References
4 Distributions, Parameters and Estimators in R
	4.1 Displaying Distributions
		4.1.1 Continuous Distributions
		4.1.2 Discrete Distributions
	4.2 Calculating the Likelihood of a Data Set
	4.3 Empirical Cumulative Distribution Function and the Kolmogorov-Smirnov Test
	4.4 Test for Normal Distribution
	4.5 Exercises
	References
5 Correlation and Association
	5.1 Correlation
		5.1.1 Non-parametric Correlation
		5.1.2 Correlation with and between Discrete Variables
		5.1.3 Multiple Correlations
	5.2 Test for Association—The χ2-test
	References
6 Correlation and Association in R
	6.1 Non-parametric Correlation
	6.2 Multiple Correlations and the Correlation Matrix
	6.3 Point-Biserial and Point-Polyserial Correlation
	6.4 The χ2-test with R
	6.5 Exercises
	Reference
7 Regression—Part I
	7.1 Regression
		7.1.1 Regression: A Distribution Parameter Varies  with the Predictor
		7.1.2 Regression and Maximum Likelihood
		7.1.3 The Other Scale and the Link Function
	7.2 Categorical Predictors
		7.2.1 A Categorical Predictor with Two Levels
		7.2.2 A Categorical Predictor with More that Two Levels
	7.3 A Couple of Examples
		7.3.1 Height and Sex—A GLM Without The G
		7.3.2 Smokers and Sex—The χ2-test as a Binomial GLM
	Reference
8 Regression in R—Part I
	8.1 Regression Using GLM
	8.2 Regression: Maximum Likelihood by Hand
		8.2.1 Poisson Model by Hand
		8.2.2 Non-linear Regression by Hand
	8.3 GLM with VGAM
	8.4 Modelling Distribution Parameters (Other Than Just the Mean)
	8.5 Exercises
	References
9 Regression—Part II
	9.1 Model Diagnostics
		9.1.1 Analysis of the Predictors
		9.1.2 Analysis of Influential Points
		9.1.3 Analysis of the Dispersion
		9.1.4 Analysis of the Residuals
		9.1.5 Analysis of the Functional Relationship Between y and x
	References
10 Regression in R—Part II
	10.1 Model Diagnostics
		10.1.1 Analysis of the Predictors
		10.1.2 Analysis of Influential Points
		10.1.3 Analysis of the Dispersion
		10.1.4 Analysis of the Residuals
		10.1.5 Analysis of the Functional Relationship Between y and x
	10.2 Regression Diagnostics for a Linear Model (LM)
	10.3 Exercises
	References
11 The Linear Model: t-test and ANOVA
	11.1 The t-test
		11.1.1 One Sample t-test
		11.1.2 Paired Sample t-test
		11.1.3 Two Sample Test
	11.2 Analysis of Variance (ANOVA): Analysing for Significant Differences
		11.2.1 ANOVA with a Continuous Predictor: An Example
		11.2.2 Assumptions of an ANOVA
		11.2.3 Making Non-normally Distributed Data Work with ANOVA
		11.2.4 ANOVA for More Than 2 Levels
		11.2.5 Post-Hoc Comparisons
	11.3 From Regression to ANOVA
		11.3.1 ANOVA and Regression: Comparing Results
		11.3.2 Degrees of Freedom from ANOVA and Explaining Them Through Regression
	11.4 ANOVAs for GLMs
	References
12 The Linear Model: t-test and ANOVA in R
	12.1 t-test and Its Variants in R
	12.2 ANOVA in R
		12.2.1 Test for Homogeneity of Variance
		12.2.2 Calculate Significance from F-values
		12.2.3 Post-Hoc Comparisons with R
	12.3 ANOVA to Regression and Back
	12.4 ANOVAs for GLM
	12.5 Exercises
13 Hypotheses and Tests
	13.1 Scientific Method: Observations …
	13.2 Testing Hypotheses
		13.2.1 Recipe for Testing Hypotheses
		13.2.2 Error Types
	13.3 Tests
		13.3.1 Further Test Related Terminology
		13.3.2 Final Comments on Tests
	13.4 Exercises
	References
14 Experimental Design
	14.1 Design Principles
		14.1.1 Principle 1: Representativity
		14.1.2 Principle 2: Independence
		14.1.3 Principle 3: Control Group
	14.2 Important Designs for Manipulative Experiments
		14.2.1 Fully Randomised Block Design
		14.2.2 Split-Plot Design
		14.2.3 Nested Design
	14.3 Survey Design
		14.3.1 Simple Random Sampling
		14.3.2 Multi-level Sampling Methods
	References
15 Multiple Regression: Regression with Multiple Predictors
	15.1 Visualising Multiple Predictors
		15.1.1 Visualising Two Categorical Predictors
		15.1.2 Visualising a Categorical and a Continuous Predictor
	15.2 Interactions Between Predictors
	15.3 Collinearity
		15.3.1 Principal Component Analysis
		15.3.2 Cluster Analysis
	15.4 Model Selection
		15.4.1 Two-Way ANOVA by Hand
	15.5 For the Math Curious: The Math Behind the Linear Model
	References
16 Multiple Regression in R
	16.1 Visualising and Fitting Interactions
		16.1.1 Two Categorical Predictors: Regression and ANOVA
		16.1.2 One Continuous and One Categorical Predictor
		16.1.3 Multiple Regression with Two Continuous Variables
	16.2 Collinearity
		16.2.1 Principal Component Analysis in R
		16.2.2 Cluster-Analysis in R
	16.3 Model Selection
		16.3.1 Model Selection by Hand
		16.3.2 Automated Model Selection
		16.3.3 Best-Subset Regression
	16.4 Exercises
	References
17 Outlook
	References
Index