The Elements of Statistics with Applications to Economics and the Social Sciences
1. Statistics as Science. What You Will Learn in this Chapter. Introduction. Statistics: A Framework for Decision Making. Statistics and the Methodology of Science. Statistics as Science Itself. Summary. Case Study: Was There Age Discrimination in a Public Utility. Addendum for the Reader. Exercises. 2. Types of Variables, Measurements, and Explanation. What You Will Learn in this Chapter. Introduction. Types of Variables. Random and Deterministic Variables. Summary. Case Study: Was There Age Discrimination in a Public Utility. Figures. Exercises. 3. How to Describe and Summarize Random Data by Graphical Procedures. What You Will Learn in this Chapter. Introduction. Describing Data by Box and Whisker Plots. Plotting Relative Frequencies. Cumulative Frequencies. Histogram. Summary. Case Study: Was There Age Discrimination in a Public Utility. Figures. Exercises. 4. Moments and the Shape of Histograms. What You Will Learn in this Chapter. Introduction. The Mean, a Measure of Location. The Second Moment as a Measure of Spread. General Definition of Moments. Standardized Moments. Standardization of Variables. Summary. Case Study: Was There Age Discrimination in a Public Utility. Figures. Exercises. 5. The Description of Bivariate Data. What You Will Learn From this Chapter. Introduction. Three Dimensional Histograms. Scatter Plots. Standardization for Pairs of Random Variables. Covariation and m11, The First Cross Product Moment. Linear Statistical Relationships and the Correlation Coefficient. The Correlation Coefficient and "Slope". Rank Correlation. Bivariate Categorical Data. Summary. Case Study: Was There Age Discrimination in a Public Utility. Figures. Exercises. 6. The Theory of Statistics: An Introduction. What You Will Learn in this Chapter. Introduction. The Theory: First Steps. Conditional Probability. Random Variables: Intuition Made Formal. Statistical Independence. Summary. Case Study: Was There Age Discrimination in a Public Utility. Figures. Exercises. 7. The Generation and Description of Discrete Probability Distribution. What You Will Learn in this Chapter. Introduction. Combinations and Permutation. Generating Binomial Probabilities. Expectation. The Cumulative Distribution Function. Summary. Case Was There Age Discrimination in a Public Utility Study: Was There Age Discrimination in a Public Utility. Figures. Exercises. 8. The Generation of Some Continuous Probability Distributions. What You Will Learn in this Chapter. Introduction. How to Express Probability in Terms of Continuous Random Variables. Theoretical Moments and Density Functions. The Uniform Distribution. The Normal, or Gaussian, Density Function and the Central Limit Theorem. Summary. Case Study: Was There Age Discrimination in a Public Utility. Figures. Exercises. 9. Elementary Sampling Theory. What You Will Learn in This Chapter. Introduction. An Illustrative Example. An Introduction to the Theory of Simple Random Sampling. Stratified Random Sampling. Summary. Case Study: Was There Age Discrimination in a Public Utility. Figures. Exercises. 10. Estimation of Theoretical Moments and the Parametes of Probability Distributions. What You Will Learn in this Chapter. Introduction. The Estimation of Theoretical Moments: Large Sample Results. The Estimation of Moments and Parameters: Confidence Intervals and Small Sample Results. Maximum Likelihood Estimators. Summary. Case Study: Was There Age Discrimination in a Public Utility. Figures. Exercises. 11. Hypothesis Testing: Or How to Discriminate Between Two Alternatives. What You Will Learn in this Chapter. Introduction. The Basic Idea of Hypothesis Tests. Simple and Composite Hypothesis Test. Two Sided Hypothesis Tests. Test of Proportions. Hypothesis Tests When the Variance Is Unknown. Some Practical Examples. Summary. Case Study: What There Age Discrimination in a Public Utility. Figures. Exercises. 12. The Generation of Bivariate and Conditional Probability Distributions. What You Will Learn in this Chapter. Introduction. Some Pragmatic Examples. The Generation of Bivariate Discrete Distribution. The Generation of Bivariate Continuous Distribution. Bivariate and Conditional Distributions Obtained by Sampling. Summary. Case Study: Was There Age Discrimination in a Public Utility. Exercises. 13. The Theory and Practice of Regression Analysis. What You Will Learn in this Chapter. Introduction. The Regression Model. Estimation and Inference: The Basics. Estimation and Inference: Confidence Intervals and Hypothesis Tests. The Regression in Regression Analysis. Summary. Case Study: Was There Age Discrimination in a Public Utility. Figures. Exercises. 14. Comparing Populations Through the Analysis of Variance. What You Will Learn in this Chapter. Introduction. An Introduction to One Way Analysis of Variance. Summary. Case Study: Was There Age Discrimination in a Public Utility. Figures. Exercises. 15. Retrospective. What You Will Learn in this Chapter. Introduction. A Schematic Review of What You Have Learned. The Role of Statistics in Everyday Life. Case Study: Was There Discrimination in a Public Utility. The Relationship Between Sciences and Statistics. What You Might Learn Next in Statistics. Exercises. A. Mathematical Appendix: Review of Concepts and Conventions. Notational Conventions. Indexing. Sigma Notation. Elementary Set Theory. Elements of Calculus. Exercises. B. Directions for Using the Student Version of S-Plus 4.5 in this Text. C. Directions for Using Microsoft Excel in this Text.