Front Cover -- Advanced Statistics from an Elementary Point of View -- Copyright Page -- Dedication -- Table of Contents -- Preface -- Chapter 1. Introduction -- 1.1 Statistics Defined -- 1.2 Types of Statistics -- 1.3 Levels of Discourse: Sample vs. Population -- 1.4 Levels of Discourse: Target vs. Sampled Population -- 1.5 Measurement Scales -- 1.6 Sampling and Sampling Errors -- 1.7 Exercises -- Chapter 2. Elementary Descriptive Statistical Techniques -- 2.1 Summarizing Sets of Data Measured on a Ratio or Interval Scale -- 2.2 Tabular Methods -- 2.3 Quantitative Summary Characteristics -- 2.4 Correlation between Variables X and Y -- 2.5 Rank Correlation between Variables X and Y -- 2.6 Exercises -- Chapter 3. Probability Theory -- 3.1 Mathematical Foundations: Sets, Set Relations, and Functions -- 3.2 The Random Experiment, Events, Sample Space, and the Random Variable -- 3.3 Axiomatic Development of Probability Theory -- 3.4 The Occurrence and Probability of an Event -- 3.5 General Addition Rule for Probabilities -- 3.6 Joint, Marginal, and Conditional Probability -- 3.7 Classification of Events -- 3.8 Sources of Probabilities -- 3.9 Bayes' Rule -- 3.10 Exercises -- Chapter 4. Random Variables and Probability Distributions -- 4.1 Random Variables -- 4.2 Discrete Probability Distributions -- 4.3 Continuous Probability Distributions -- 4.4 Mean and Variance of a Random Variable -- 4.5 Chebyshev's Theorem for Random Variables -- 4.6 Moments of a Random Variable -- 4.7 Quantiles of a Probability Distribution -- 4.8 Moment-Generating Function -- 4.9 Probability-Generating Function -- 4.10 Exercises -- Chapter 5. Bivariate Probability Distributions -- 5.1 Bivariate Random Variables -- 5.2 Discrete Bivariate Probability Distributions -- 5.3 Continuous Bivariate Probability Distributions.

5.4 Expectations and Moments of Bivariate Probability Distributions -- 5.5 Chebyshev's Theorem for Bivariate Probability Distributions -- 5.6 Joint Moment-Generating Function -- 5.7 Exercises -- Chapter 6. Discrete Parametric Probability Distributions -- 6.1 Introduction -- 6.2 Counting Rules -- 6.3 Discrete Uniform Distribution -- 6.4 The Bernoulli Distribution -- 6.5 The Binomial Distribution -- 6.6 The Multinomial Distribution -- 6.7 The Geometric Distribution -- 6.8 The Negative Binomial Distribution -- 6.9 The Poisson Distribution -- 6.10 The Hypergeometric Distribution -- 6.11 The Generalized Hypergeometric Distribution -- 6.12 Exercises -- Chapter 7. Continuous Parametric Probability Distributions -- 7.1 Introduction -- 7.2 The Uniform Distribution -- 7.3 The Normal Distribution -- 7.4 The Normal Approximation to Binomial Probabilities -- 7.5 The Normal Approximation to Poisson Probabilities -- 7.6 The Exponential Distribution -- 7.7 Gamma and Beta Functions -- 7.8 The Gamma Distribution -- 7.9 The Beta Distribution -- 7.10 Other Useful Continuous Distributions -- 7.11 Exercises -- Chapter 8. Sampling and the Sampling Distribution of a Statistic -- 8.1 The Purpose of Random Sampling -- 8.2 Sampling Scenarios -- 8.3 The Arithmetic of Random Sampling -- 8.4 The Sampling Distribution of a Statistic -- 8.5 The Sampling Distribution of the Mean -- 8.6 A Weak Law of Large Numbers -- 8.7 Convergence Concepts -- 8.8 A Central Limit Theorem -- 8.9 The Sampling Distribution of a Proportion -- 8.10 The Sampling Distribution of the Variance -- 8.11 A Note on Sample Moments -- 8.12 Exercises -- Chapter 9. The Chi-Square, Student's t, and Snedecor's F Distributions -- 9.1 Derived Continuous Parametric Distributions -- 9.2 The Chi-Square Distribution -- 9.3 The Sampling Distribution of the Variance When Sampling from a Normal Population.

9.4 Student's t Distribution -- 9.5 Snedecor's F Distribution -- 9.6 Exercises -- Chapter 10. Point Estimation and Properties of Point Estimators -- 10.1 Statistics as Point Estimators -- 10.2 Desirable Properties of Estimators as Statistical Properties -- 10.3 Small Sample Properties of Point Estimators -- 10.4 Large Sample Properties of Point Estimators -- 10.5 Techniques for Finding Good Point Estimators -- 10.6 Exercises -- Chapter 11. Interval Estimation and Confidence Interval Estimates -- 11.1 Interval Estimators -- 11.2 Central Confidence Intervals -- 11.3 The Pivotal Quantity Method -- 11.4 A Confidence Interval for µ Under Random Sampling from a Normal Population with Known Variance -- 11.5 A Confidence Interval for µ Under Random Sampling from a Normal Population with Unknown Variance -- 11.6 A Confidence Interval for σ2 Under Random Sampling from a Normal Population with Unknown Mean -- 11.7 A Confidence Interval for p Under Random Sampling from a Binomial Population -- 11.8 Joint Estimation of a Family of Population Parameters -- 11.9 Confidence Intervals for the Difference of Means When Sampling from Two Independent Normal Populations -- 11.10 Confidence Intervals for the Difference of Means When Sampling from Two Dependent Populations: Paired Comparisons -- 11.11 Confidence Intervals for the Difference of Proportions When Sampling from Two Independent Binomial Populations -- 11.12 Confidence Interval for the Ratio of Two Variances When Sampling from Two Independent Normal Populations -- 11.13 Exercises -- Chapter 12. Tests of Parametric Statistical Hypotheses -- 12.1 Statistical Inference Revisited -- 12.2 Fundamental Concepts for Testing Statistical Hypotheses -- 12.3 What Is the Research Question? -- 12.4 Decision Outcomes -- 12.5 Devising a Test for a Statistical Hypothesis.

12.6 The Classical Approach to Statistical Hypothesis Testing -- 12.7 Types of Tests or Critical Regions -- 12.8 The Essentials of Conducting a Hypothesis Test -- 12.9 Hypothesis Test for µ Under Random Sampling from a Normal Population with Known Variance -- 12.10 Reporting Hypothesis Test Results -- 12.11 Determining the Probability of a Type II Error β -- 12.12 Hypothesis Tests for µ Under Random Sampling from a Normal Population with Unknown Variance -- 12.13 Hypothesis Tests for p Under Random Sampling from a Binomial Population -- 12.14 Hypothesis Tests for σ2 Under Random Sampling from a Normal Population -- 12.15 The Operating Characteristic and Power Functions of a Test -- 12.16 Determining the Best Test for a Statistical Hypothesis -- 12.17 Generalized Likelihood Ratio Tests -- 12.18 Hypothesis Tests for the Difference of Means When Sampling from Two Independent Normal Populations -- 12.19 Hypothesis Tests for the Difference of Means When Sampling from Two Dependent Populations: Paired Comparisons -- 12.20 Hypothesis Tests for the Difference of Proportions When Sampling from Two Independent Binomial Populations -- 12.21 Hypothesis Tests for the Difference of Variances When Sampling from Two Independent Normal Populations -- 12.22 Hypothesis Tests for Spearman's Rank Correlation Coefficient ρS -- 12.23 Exercises -- Chapter 13. Nonparametric Statistical Techniques -- 13.1 Parametric vs. Nonparametric Methods -- 13.2 Tests for the Randomness of a Single Sample -- 13.3 Single-Sample Sign Test Under Random Sampling -- 13.4 Wilcoxon Signed Rank Test of a Median -- 13.5 Runs Test for Two Independent Samples -- 13.6 Mann-Whitney (Rank-Sum) Test for Two Independent Samples -- 13.7 The Sign Test When Sampling from Two Dependent Populations: Paired Comparisons.

13.8 Wilcoxon Signed Rank Test When Sampling from Two Dependent Populations: Paired Comparisons -- 13.9 Exercises -- Chapter 14. Testing Goodness of Fit -- 14.1 Distributional Hypotheses -- 14.2 The Multinomial Chi-Square Statistic: Complete Specification of H0 -- 14.3 The Multinomial Chi-Square Statistic: Incomplete Specification of H0 -- 14.4 The Kolmogorov-Smirnov Test for Goodness of Fit -- 14.5 The Lilliefors Goodness-of-Fit Test for Normality -- 14.6 The Shapiro-Wilk Goodness-of-Fit Test for Normality -- 14.7 The Kolmogorov-Smirnov Test for Goodness of Fit: Two Independent Samples -- 14.8 Assessing Normality via Sample Moments -- 14.9 Exercises -- Chapter 15. Testing Goodness of Fit: Contingency Tables -- 15.1 An Extension of the Multinomial Chi-Square Statistic -- 15.2 Testing Independence -- 15.3 Testing k Proportions -- 15.4 Testing for Homogeneity -- 15.5 Measuring Strength of Association in Contingency Tables -- 15.6 Testing Goodness of Fit with Nominal-Scale Data: Paired Samples -- 15.7 Exercises -- Chapter 16. Bivariate Linear Regression and Correlation -- 16.1 The Regression Model -- 16.2 The Strong Classical Linear Regression Model -- 16.3 Estimating the Slope and Intercept of the Population Regression Line -- 16.4 Mean, Variance, and Sampling Distribution of the Least Squares Estimators β0 and β1 -- 16.5 Precision of the Least Squares Estimators β0, β1: Confidence Intervals -- 16.6 Testing Hypotheses Concerning β0, β1 -- 16.7 The Precision of the Entire Least Squares Regression Equation: A Confidence Band -- 16.8 The Prediction of a Particular Value of Y Given X -- 16.9 Decomposition of the Sample Variation of Y -- 16.10 The Correlation Model -- 16.11 Estimating the Population Correlation Coefficient ρ -- 16.12 Inferences about the Population Correlation Coefficient ρ -- 16.13 Exercises -- Appendix A -- Table A.1 Standard Normal Areas.

Table A.2 Cumulative Distribution Function Values for the Standard Normal Distribution.