| |

| |

Preface | |

| |

| |

| |

Introduction | |

| |

| |

| |

Who Should Read This Book | |

| |

| |

| |

How This Book is Organized | |

| |

| |

| |

How to Read This Book and Learn from It | |

| |

| |

| |

Note for Instructors | |

| |

| |

| |

Book Web Site | |

| |

| |

| |

Fundamentals of Statistics | |

| |

| |

| |

Statistical Thinking | |

| |

| |

| |

Data Format | |

| |

| |

| |

Descriptive Statistics | |

| |

| |

| |

Measures of Location | |

| |

| |

| |

Measures of Variability | |

| |

| |

| |

Data Visualization | |

| |

| |

| |

Dot Plots | |

| |

| |

| |

Histograms | |

| |

| |

| |

Box Plots | |

| |

| |

| |

Scatter Plots | |

| |

| |

| |

Probability and Probability Distributions | |

| |

| |

| |

Probability and Its Properties | |

| |

| |

| |

Probability Distributions | |

| |

| |

| |

Expected Value and Moments | |

| |

| |

| |

Joint Distributions and Independence | |

| |

| |

| |

Covariance and Correlation | |

| |

| |

| |

Rules of Two and Three Sigma | |

| |

| |

| |

Sampling Distributions and the Laws of Large Numbers | |

| |

| |

| |

Skewness and Kurtosis | |

| |

| |

| |

Statistical Inference | |

| |

| |

| |

Introduction | |

| |

| |

| |

Point Estimation of Parameters | |

| |

| |

| |

Definition and Properties of Estimators | |

| |

| |

| |

The Method of the Moments and Plug-In Principle | |

| |

| |

| |

The Maximum Likelihood Estimation | |

| |

| |

| |

Interval Estimation | |

| |

| |

| |

Hypothesis Testing | |

| |

| |

| |

Samples From Two Populations | |

| |

| |

| |

Probability Plots and Testing for Population Distributions | |

| |

| |

| |

Probability Plots | |

| |

| |

| |

Kolmogorov-Smirnov Statistic | |

| |

| |

| |

Chi-Squared Test | |

| |

| |

| |

Ryan-Joiner Test for Normality | |

| |

| |

| |

Outlier Detection | |

| |

| |

| |

Monte Carlo Simulations | |

| |

| |

| |

Bootstrap | |

| |

| |

| |

Statistical Models | |

| |

| |

| |

Introduction | |

| |

| |

| |

Regression Models | |

| |

| |

| |

Simple Linear Regression Model | |

| |

| |

| |

Residual Analysis | |

| |

| |

| |

Multiple Linear Regression and Matrix Notation | |

| |

| |

| |

Geometric Interpretation in an n-Dimensional Space | |

| |

| |

| |

Statistical Inference in Multiple Linear Regression | |

| |

| |

| |

Prediction of the Response and Estimation of the Mean Response | |

| |

| |

| |

More on Checking the Model Assumptions | |

| |

| |

| |

Other Topics in Regression | |

| |

| |

| |

Experimental Design and Analysis | |

| |

| |

| |

Analysis of Designs with Qualitative Factors | |

| |

| |

| |

Other Topics in Experimental Design | |

| |

| |

Supplement 4A. Vector and Matrix Algebra | |

| |

| |

Vectors | |

| |

| |

Matrices | |

| |

| |

Eigenvalues and Eigenvectors of Matrices | |

| |

| |

Spectral Decomposition of Matrices | |

| |

| |

Positive Definite Matrices | |

| |

| |

A Square Root Matrix | |

| |

| |

Supplement 4B. Random Vectors and Matrices | |

| |

| |

Sphering | |

| |

| |

| |

Fundamentals of Multivariate Statistics | |

| |

| |

| |

Introduction | |

| |

| |

| |

The Multivariate Random Sample | |

| |

| |

| |

Multivariate Data Visualization | |

| |

| |

| |

The Geometry of the Sample | |

| |

| |

| |

The Geometric Interpretation of the Sample Mean | |

| |

| |

| |

The Geometric Interpretation of the Sample Standard Deviation | |

| |

| |

| |

The Geometric Interpretation of the Sample Correlation Coefficient | |

| |

| |

| |

The Generalized Variance | |

| |

| |

| |

Distances in the p-Dimensional Space | |

| |

| |

| |

The Multivariate Normal (Gaussian) Distribution | |

| |

| |

| |

The Definition and Properties of the Multivariate Normal Distribution | |

| |

| |

| |

Properties of the Mahalanobis Distance | |

| |

| |

| |

Multivariate Statistical Inference | |

| |

| |

| |

Introduction | |

| |

| |

| |

Inferences About a Mean Vector | |

| |

| |

| |

Testing the Multivariate Population Mean | |

| |

| |

| |

Interval Estimation for the Multivariate Population Mean | |

| |

| |

| |

Confidence Regions | |

| |

| |

| |

Comparing Mean Vectors from Two Populations | |

| |

| |

| |

Equal Covariance Matrices | |

| |

| |

| |

Unequal Covariance Matrices and Large Samples | |

| |

| |

| |

Unequal Covariance Matrices and Samples Sizes Not So Large | |

| |

| |

| |

Inferences About a Variance-Covariance Matrix | |

| |

| |

| |

How to Check Multivariate Normality | |

| |

| |

| |

Principal Component Analysis | |

| |

| |

| |

Introduction | |

| |

| |

| |

Definition and Properties of Principal Components | |

| |

| |

| |

Definition of Principal Components | |

| |

| |

| |

Finding Principal Components | |

| |

| |

| |

Interpretation of Principal Component Loadings | |

| |

| |

| |

Scaling of Variables | |

| |

| |

| |

Stopping Rules for Principal Component Analysis | |

| |

| |

| |

Fair-Share Stopping Rules | |

| |

| |

| |

Large-Gap Stopping Rules | |

| |

| |

| |

Principal Component Scores | |

| |

| |

| |

Residual Analysis | |

| |

| |

| |

Statistical Inference in Principal Component Analysis | |

| |

| |

| |

Independent and Identically Distributed Observations | |

| |

| |

| |

Imaging Related Sampling Schemes | |

| |

| |

| |

Further Reading | |

| |

| |

| |

Canonical Correlation Analysis | |

| |

| |

| |

Introduction | |

| |

| |

| |

Mathematical Formulation | |

| |

| |

| |

Practical Application | |

| |

| |

| |

Calculating Variability Explained by Canonical Variables | |

| |

| |

| |

Canonical Correlation Regression | |

| |

| |

| |

Further Reading | |

| |

| |

| |

Cross-Validation | |

| |

| |

| |

Discrimination and Classification - Supervised Learning | |

| |

| |

| |

Introduction | |

| |

| |

| |

Classification for Two Populations | |

| |

| |

| |

Classification Rules for Multivariate Normal Distributions | |

| |

| |

| |

Cross-Validation of Classification Rules | |

| |

| |

| |

Fisher's Discriminant Function | |

| |

| |

| |

Classification for Several Populations | |

| |

| |

| |

Gaussian Rules | |

| |

| |

| |

Fisher's Method | |

| |

| |

| |

Spatial Smoothing for Classification | |

| |

| |

| |

Further Reading | |

| |

| |

| |

Clustering - Unsupervised Learning | |

| |

| |

| |

Introduction | |

| |

| |

| |

Similarity and Dissimilarity Measures | |

| |

| |

| |

Similarity and Dissimilarity Measures for Observations | |

| |

| |

| |

Similarity and Dissimilarity Measures for Variables and Other Objects | |

| |

| |

| |

Hierarchical Clustering Methods | |

| |

| |

| |

Single Linkage Algorithm | |

| |

| |

| |

Complete Linkage Algorithm | |

| |

| |

| |

Average Linkage Algorithm | |

| |

| |

| |

Ward Method | |

| |

| |

| |

Nonhierarchical Clustering Methods | |

| |

| |

| |

K-Means Method | |

| |

| |

| |

Clustering Variables | |

| |

| |

| |

Further Reading | |

| |

| |

| |

Probability Distributions | |

| |

| |

| |

Data Sets | |

| |

| |

| |

Miscellanea | |

| |

| |

References | |

| |

| |

Index | |