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Full Description
This text grew out of the author's notes for a course that he has taught for many years to a diverse group of undergraduates. The early introduction to the major concepts engages students immediately, which helps them see the big picture, and sets an appropriate tone for the course. In subsequent chapters, these topics are revisited, developed, and formalized, but the early introduction helps students build a true understanding of the concepts. The text utilizes the statistical software R, which is both widely used and freely available (thanks to the Free Software Foundation). However, in contrast with other books for the intended audience, this book by Akritas emphasizes not only the interpretation of software output, but also the generation of this output. Applications are diverse and relevant, and come from a variety of fields.
Contents
1. Basic Statistical Concepts 1.1 Why Statistics?1.2 Populations and Samples 1.2.1 Exercises 1.3 Some Sampling Concepts1.3.1 Representative Samples 1.3.2 Simple Random Sampling, and Stratied Sampling 1.3.3 Sampling With and Without Replacement 1.3.4 Non-representative Sampling 1.3.5 Exercises 1.4 Random Variables and Statistical Populations 1.4.1 Exercises 1.5 Basic Graphics for Data Visualization 1.5.1 Histograms and Stem and Leaf Plots 1.5.2 Scatterplots 1.5.3 Pie Charts and Bar Graphs 1.5.4 Exercises 1.6 Proportions, Averages and Variances 1.6.1 Population Proportion and Sample Proportion 1.6.2 Population Average and Sample Average 1.6.3 Population Variance and Sample Variance 1.6.4 Exercises 1.7 Medians, Percentiles and Box Plots 1.7.1 Exercises 1.8 Comparative Studies 1.8.1 Basic Concepts and Comparative Graphics 1.8.2 Lurking Variables and Simpson's Paradox 1.8.3 Causation: Experiments and Observational Studies 1.8.4 Factorial Experiments: Main Eects and Interactions 1.8.5 Exercises 1.9 The Role of Probability 1.10 Approaches to Statistical Inference 2. Introduction to Probability 2.1 Overview 2.2 Sample Spaces, Events and Set Operations 2.2.1 Exercises 2.3 Experiments with Equally Likely Outcomes 2.3.1 Denition and Interpretation of Probability 2.3.2 Counting Techniques 2.3.3 Probability Mass Functions and Simulations 2.3.4 Exercises 2.4 Axioms and Properties of Probabilities 2.4.1 Exercises 2.5 Conditional Probability 2.5.1 The Multiplication Rule and Tree Diagrams 2.5.2 Law of Total Probability and Bayes Theorem 2.5.3 Exercises 2.6 Independent Events 2.6.1 Applications to System Reliability 2.6.2 Exercises3. Random Variables and Their Distributions 3.1 Introduction.3.2 Describing a Probability Distribution. 3.2.1 Random Variables, Revisited 3.2.2 The Cumulative Distribution Function 3.2.3 The Density Function of a Continuous Distribution 3.2.4 Exercises3.3 Parameters of Probability Distributions 3.3.1 Expected Value 3.3.2 Variance and Standard Deviation 3.3.3 Population Percentiles 3.3.4 Exercises 3.4 Models for Discrete Random Variables 3.4.1 The Bernoulli and Binomial Distributions 3.4.2 The Hypergeometric Distribution. 3.4.3 The Geometric and Negative Binomial Distributions 3.4.4 The Poisson Distribution 3.4.5 Exercises 3.5 Models for Continuous Random Variables 3.5.1 The Exponential Distribution 3.5.2 The Normal Distribution 3.5.3 The Q-Q Plot 3.5.4 Exercises4. Jointly Distributed Random Variables 4.1 Introduction. 4.2 Describing Joint Probability Distributions 4.2.1 The Joint and Marginal PMF 4.2.2 The Joint and Marginal PDF 4.2.3 Exercises 4.3 Conditional Distributions 4.3.1 Conditional Probability Mass Functions 4.3.2 Conditional Probability Density Functions 4.3.3 The Regression Function 4.3.4 Independence 4.3.5 Exercises 4.4 Mean Value of Functions of Random Variables 4.4.1 The Basic Result 4.4.2 Expected Value of Sums 4.4.3 The Covariance and the Variance of Sums 4.4.4 Exercises 4.5 Quantifying Dependence 4.5.1 Positive and Negative Dependence 4.5.2 Pearson's (or Linear) Correlation Coefficient 4.5.3 Exercises 4.6 Models for Joint Distributions. 4.6.1 Hierarchical Models 4.6.2 Regression Models 4.6.3 The Bivariate Normal Distribution 4.6.4 The Multinomial Distribution 4.6.5 Exercises 5. Some Approximation Results 5.1 Introduction 5.2 The LLN and the Consistency of Averages 5.2.1 Exercises 5.3 Convolutions 5.3.1 What They Are and How They Are Used 5.3.2 The Distribution of[X bar]in The Normal Case 5.3.3 Exercises 5.4 The Central Limit Theorem 5.4.1 The DeMoivre-Laplace Theorem 5.4.2 Exercises 6. Fitting Models to Data 6.1 Introduction. 6.2 Some Estimation Concepts 6.2.1 Unbiased Estimation 6.2.2 Model-Freevs Model-Based Estimation 6.2.3 Exercises 6.3 Methods for Fitting Models to Data 6.3.1 The Method of Moments 6.3.2 The Method of Maximum Likelihood 6.3.3 The Method of Least Squares 6.3.4 Exercises 6.4 Comparing Estimators: The MSE Criterion 6.4.1 Exercises7. Condence and Prediction Intervals 7.1 Introduction to Condence Intervals 7.1.1 Construction of Condence Intervals 7.1.2 Z Condence Intervals 7.1.3 The T Distribution and T Condence Intervals 7.1.4 Outline of the Chapter 7.2 CI Semantics: The Meaning of "Condence" 7.3 Types of Condence Intervals 7.3.1 T CIs for the Mean. 7.3.2 Z CIs for Proportions 7.3.3 T CIs for the Regression Parameters 7.3.4 The Sign CI for the Median 7.3.5 Chi-Square CIs for the Normal Variance and Standard Deviation 7.3.6 Exercises 7.4 The Issue of Precision 7.4.1 Exercises 7.5 Prediction Intervals 7.5.1 Basic Concepts 7.5.2 Prediction of a Normal Random Variable 7.5.3 Prediction in Normal Simple Linear Regression 7.5.4 Exercises8. Testing of Hypotheses 8.1 Introduction. 8.2 Setting up a Test Procedure 8.2.1 The Null and Alternative Hypotheses 8.2.2 Test Statistics and Rejection Rules 8.2.3 Z Tests and T Tests 8.2.4 P -Values 8.2.5 Exercises 8.3 Types of Tests 8.3.1 T Tests for the Mean 8.3.2 Z Tests for Proportions 8.3.3 T Tests about the Regression Parameters 8.3.4 The ANOVA F Test in Regression 8.3.5 The Sign Test for the Median 8.3.6 Chi-SquareTests for a Normal Variance 8.3.7 Exercises 8.4 Precision in Hypothesis Testing 8.4.1 Type I and Type II Errors 8.4.2 Power and Sample Size Calculations 8.4.3 Exercises 9. Comparing Two Populations 9.1 Introduction. 9.2 Two-Sample Tests and CIs for Means 9.2.1 Some Basic Results 9.2.2 Condence Intervals 9.2.3 Hypothesis Testing 9.2.4 Exercises 9.3 The Rank-Sum Test Procedure 9.3.1 Exercises 9.4 Comparing Two Variances 9.4.1 Levene's Test 9.4.2 The F Test under Normality 9.4.3 Exercises 9.5 Paired Data 9.5.1 Denition and Examples of Paired Data 9.5.2 The Paired Data T Test 9.5.3 The Paired T Test for Proportions 9.5.4 The Wilcox on Signed-Rank Test 9.5.5 Exercises 10. Comparing k(> 2) Populations10.1 Introduction 10.2 Types of k-Sample Tests 10.2.1 The ANOVA F Test for Means 10.2.2 The Kruskal-Wallis Test 10.2.3 The Chi-Square Test for Proportions 10.2.4 Exercises 10.3 Simultaneous CIs and Multiple Comparisons 10.3.1 Bonferroni Multiple Comparisons and Simultaneous CIs 10.3.2 Tukey's Multiple Comparisons and Simultaneous CIs 10.3.3 Tukey's Multiple Comparisons on the Ranks 10.3.4 Exercises 10.4 Randomized Block Designs 10.4.1 The Statistical Model and Hypothesis 10.4.2 The ANOVA F Test 10.4.3 Friedman's Test and F Test on the Ranks 10.4.4 Multiple Comparisons 10.4.5 Exercises 11. Multifactor Experiments 11.1 Introduction. 11.2 Two-Factor Designs 11.2.1 F Tests for Main Effects and Interactions 11.2.2 Testing the Validity of Assumptions 11.2.3 One Observation per Cell 11.2.4 Exercises11.3 Three-Factor Designs 11.3.1 Exercises 11.4 2r Factorial Experiments 11.4.1 Blocking and Confounding 11.4.2 Fractional Factorial Designs 11.4.3 Exercises12. Polynomial and Multiple Regression 12.1 Introduction. 12.2 The Multiple Linear Regression Model 12.2.1 Exercises 12.3 Estimation Testing and Prediction 12.3.1 The Least Squares Estimators 12.3.2 Model Utility Test 12.3.3 Testing the Significance of Regression Coefficients 12.3.4 Condence Intervals and Prediction 12.3.5 Exercises12.4 Additional Topics 12.4.1 Weighted Least Squares 12.4.2 Applications to Factorial Designs 12.4.3 Variable Selection 12.4.4 Inuential Observations 12.4.5 Multicolinearity 12.4.6 Logistic Regression 12.4.7 Exercises 13. Statistical Process Control 13.1 Introduction and Overview 13.2 The [X bar] Chart 13.2.1 [X bar] Chart with Known Target Values 13.2.2 [X bar] Chart with Estimated Target Values 13.2.3 The [X bar] Chart 13.2.4 Average Run Length, and Supplemental Rules13.2.5 Exercises 13.3 The S and R Charts 13.3.1 Exercises 13.4 The p and c Charts 13.4.1 The p Chart 13.4.2 The c Chart 13.4.3 Exercises 13.5 CUSUM and EWMA Charts 13.5.1 The CUSUM Chart 13.5.2 The EWMA Chart 13.5.3 Exercises A. Tables B. Answers To Selected Exercises
