Statistics with R

Chapter 1: Introduction and R Instructions Basic Terminology Data: Qualitative or Quantitative Data: Cross-Sectional or Longitudinal Descriptive Statistics Probability Statistics: Estimation and Inference Chapter 2: Descriptive Statistics: Tabular and Graphical Methods Methods of Summarizing and Displaying Qualitative Data Methods of Summarizing and Displaying Quantitative Data Cross Tabulations and Scatter Plots Chapter 3: Descriptive Statistics: Numerical Methods Measures of Central Tendency Measures of Location Exploratory Data Analysis: The Box Plot Display Measures of Variability The z-Score: A Measure of Relative Location Measures of Association: The Bivariate Case The Geometric Mean Chapter 4: Introduction to Probability Some Important Definitions Counting Rules Assigning Probabilities Events and Probabilities Probabilities of Unions and Intersections of Events Conditional Probability Bayes' Theorem and Events Chapter 5: Discrete Probability Distributions The Discrete Uniform Probability Distribution The Expected Value and Standard Deviation of a Discrete Random Variable The Binomial Probability Distribution The Poisson Probability Distribution The Hypergeometric Probability Distribution The Hypergeometric Probability Distribution: The General Case Bayes' Theorem and Discrete Random Variables Chapter 6: Continuous Probability Distributions Continuous Uniform Probability Distribution Normal Probability Distribution Exponential Probability Distribution Optional Material: Derivation of the Cumulative Exponential Probability Func- tion Bayes' Theorem and Continuous Random Variables Chapter 7: Point Estimation and Sampling Distributions Populations and Samples The Simple Random Sample The Sample Statistic: x, s, and p The Sampling Distribution of x The Sampling Distribution of p Some Other Commonly Used Sampling Methods Bayes' Theorem: Approximate Bayesian Computation Chapter 8: Confidence Interval Estimation Interval Estimate of ? When ? Is Known Interval Estimate of ? When ? Is Unknown Sample Size Determination in the Case of ? Interval Estimate of p Sample Size Determination in the Case of p Bayes' Theorem: Confidence Intervals or Credible Intervals Chapter 9: Hypothesis Tests: Introduction, Basic Concepts, and an Example Chapter 10: Hypothesis Tests about Means and Proportions: Applications The Lower-Tail Hypothesis Test about ?: ? Is Known The Two-Tail Hypothesis Test about ?: ? Is Known The Upper-Tail Hypothesis Test about ?: ? Is Unknown The Two-Tail Hypothesis Test about ?: ? is Unknown Hypothesis Tests about p Calculating the Probability of a Type II Error: ? Adjusting the Sample Size to Control the Size of ? Bayes' Theorem and an Inferential Approach to p Chapter 11: Comparisons of Means and Proportions The Difference between ?1 and ?2: Independent Samples The Difference between ?1 and ?2: Paired Samples The Difference between p1 and p2: Independent Samples Bayes' Theorem and the Difference between p1 and p2 Chapter 12: Simple Linear Regression Simple Linear Regression: The Model The Estimated Regression Equation Goodness of Fit: The Coefficient of Determination, r2 The Hypothesis Test about ?1 Alternative Approaches to Testing Significance So Far, We Have Tested Only b1. Will We Also Test b0? Assumptions: What Are They? Assumptions: How Are They Validated? Optional Material: Derivation of the Expressions for the Least-Squares Estimates of ?0 and ?1 Bayes' Theorem: Using Stan to Estimate the Relationship between Two Variables Chapter 13: Multiple Regression Simple Linear Regression: A Reprise Multiple Regression: The Model Multiple Regression: The Multiple Regression Equation The Estimated Multiple Regression Equation Multiple Regression: The 2 Independent Variable Case Assumptions: What Are They? Can We Validate Them? Tests of Significance: The Overall Regression Model Tests of Signicance: The Independent Variables There Must Be An Easier Way Than This, Right? Using the Estimated Regression Equation for Prediction Independent Variable Selection: The Best-Subsets Method Logistic Regression: The Zero-One Dependent Variable Bayes' Theorem: Stan and Multiple Regression Analysis