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| Preface | |
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| Introduction | |
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| Who Should Read This Book | |
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| How This Book is Organized | |
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| How to Read This Book and Learn from It | |
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| Note for Instructors | |
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| Book Web Site | |
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| Fundamentals of Statistics | |
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| Statistical Thinking | |
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| Data Format | |
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| Descriptive Statistics | |
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| Measures of Location | |
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| Measures of Variability | |
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| Data Visualization | |
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| Dot Plots | |
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| Histograms | |
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| Box Plots | |
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| Scatter Plots | |
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| Probability and Probability Distributions | |
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| Probability and Its Properties | |
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| Probability Distributions | |
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| Expected Value and Moments | |
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| Joint Distributions and Independence | |
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| Covariance and Correlation | |
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| Rules of Two and Three Sigma | |
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| Sampling Distributions and the Laws of Large Numbers | |
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| Skewness and Kurtosis | |
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| Statistical Inference | |
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| Introduction | |
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| Point Estimation of Parameters | |
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| Definition and Properties of Estimators | |
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| The Method of the Moments and Plug-In Principle | |
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| The Maximum Likelihood Estimation | |
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| Interval Estimation | |
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| Hypothesis Testing | |
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| Samples From Two Populations | |
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| Probability Plots and Testing for Population Distributions | |
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| Probability Plots | |
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| Kolmogorov-Smirnov Statistic | |
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| Chi-Squared Test | |
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| Ryan-Joiner Test for Normality | |
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| Outlier Detection | |
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| Monte Carlo Simulations | |
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| Bootstrap | |
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| Statistical Models | |
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| Introduction | |
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| Regression Models | |
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| Simple Linear Regression Model | |
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| Residual Analysis | |
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| Multiple Linear Regression and Matrix Notation | |
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| Geometric Interpretation in an n-Dimensional Space | |
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| Statistical Inference in Multiple Linear Regression | |
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| Prediction of the Response and Estimation of the Mean Response | |
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| More on Checking the Model Assumptions | |
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| Other Topics in Regression | |
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| Experimental Design and Analysis | |
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| Analysis of Designs with Qualitative Factors | |
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| Other Topics in Experimental Design | |
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| Supplement 4A. Vector and Matrix Algebra | |
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| Vectors | |
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| Matrices | |
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| Eigenvalues and Eigenvectors of Matrices | |
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| Spectral Decomposition of Matrices | |
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| Positive Definite Matrices | |
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| A Square Root Matrix | |
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| Supplement 4B. Random Vectors and Matrices | |
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| Sphering | |
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| Fundamentals of Multivariate Statistics | |
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| Introduction | |
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| The Multivariate Random Sample | |
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| Multivariate Data Visualization | |
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| The Geometry of the Sample | |
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| The Geometric Interpretation of the Sample Mean | |
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| The Geometric Interpretation of the Sample Standard Deviation | |
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| The Geometric Interpretation of the Sample Correlation Coefficient | |
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| The Generalized Variance | |
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| Distances in the p-Dimensional Space | |
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| The Multivariate Normal (Gaussian) Distribution | |
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| The Definition and Properties of the Multivariate Normal Distribution | |
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| Properties of the Mahalanobis Distance | |
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| Multivariate Statistical Inference | |
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| Introduction | |
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| Inferences About a Mean Vector | |
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| Testing the Multivariate Population Mean | |
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| Interval Estimation for the Multivariate Population Mean | |
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| Confidence Regions | |
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| Comparing Mean Vectors from Two Populations | |
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| Equal Covariance Matrices | |
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| Unequal Covariance Matrices and Large Samples | |
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| Unequal Covariance Matrices and Samples Sizes Not So Large | |
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| Inferences About a Variance-Covariance Matrix | |
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| How to Check Multivariate Normality | |
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| Principal Component Analysis | |
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| Introduction | |
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| Definition and Properties of Principal Components | |
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| Definition of Principal Components | |
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| Finding Principal Components | |
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| Interpretation of Principal Component Loadings | |
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| Scaling of Variables | |
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| Stopping Rules for Principal Component Analysis | |
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| Fair-Share Stopping Rules | |
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| Large-Gap Stopping Rules | |
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| Principal Component Scores | |
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| Residual Analysis | |
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| Statistical Inference in Principal Component Analysis | |
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| Independent and Identically Distributed Observations | |
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| Imaging Related Sampling Schemes | |
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| Further Reading | |
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| Canonical Correlation Analysis | |
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| Introduction | |
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| Mathematical Formulation | |
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| Practical Application | |
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| Calculating Variability Explained by Canonical Variables | |
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| Canonical Correlation Regression | |
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| Further Reading | |
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| Cross-Validation | |
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| Discrimination and Classification - Supervised Learning | |
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| Introduction | |
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| Classification for Two Populations | |
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| Classification Rules for Multivariate Normal Distributions | |
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| Cross-Validation of Classification Rules | |
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| Fisher's Discriminant Function | |
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| Classification for Several Populations | |
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| Gaussian Rules | |
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| Fisher's Method | |
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| Spatial Smoothing for Classification | |
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| Further Reading | |
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| Clustering - Unsupervised Learning | |
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| Introduction | |
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| Similarity and Dissimilarity Measures | |
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| Similarity and Dissimilarity Measures for Observations | |
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| Similarity and Dissimilarity Measures for Variables and Other Objects | |
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| Hierarchical Clustering Methods | |
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| Single Linkage Algorithm | |
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| Complete Linkage Algorithm | |
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| Average Linkage Algorithm | |
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| Ward Method | |
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| Nonhierarchical Clustering Methods | |
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| K-Means Method | |
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| Clustering Variables | |
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| Further Reading | |
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| Probability Distributions | |
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| Data Sets | |
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| Miscellanea | |
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| References | |
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| Index | |