Reasoning with Data

An Introduction to Traditional and Bayesian Statistics Using R


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Jeffrey M. Stanton
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Introduction Getting Started 1. Statistical Vocabulary Descriptive Statistics Measures of Central Tendency Measures of Dispersion Distributions and Their Shapes Conclusion Exercises 2. Reasoning with Probability Outcome Tables Contingency Tables Conclusion Exercises 3. Probabilities in the Long Run Sampling Repetitious Sampling with R Using Sampling Distributions and Quantiles to Think about Probabilities Conclusion Exercises 4. Introducing the Logic of Inference Using Confidence Intervals Exploring the Variability of Sample Means with Repetitious Sampling Our First Inferential Test: The Confidence Interval Conclusion Exercises 5. Bayesian and Traditional Hypothesis Testing The Null Hypothesis Significance Test Replication and the NHST Conclusion Exercises 6. Comparing Groups and Analyzing Experiments Frequentist Approach to ANOVA Bayesian Approach to ANOVA Finding an Effect Conclusion Exercises 7. Associations between Variables Inferential Reasoning about Correlation Null Hypothesis Testing on the Correlation Bayesian Tests on the Correlation Coefficient Categorical Associations Exploring the Chi-Square Distribution with a Simulation The Chi-Square Test with Real Data Bayesian Approach to Chi-Square Test Conclusion Exercises 8. Linear Multiple Regression Bayesian Approach to Linear Regression A Linear Regression Model with Real Data Conclusion Exercises 9. Interactions in ANOVA and Regression Interactions in ANOVA Interactions in Multiple Regression Bayesian Analysis of Regression Interactions Conclusion Exercises 10. Logistic Regression A Logistic Regression Model with Real Data Bayesian Estimation of Logistic Regression Conclusion Exercises 11. Analyzing Change over Time Repeated Measures Analysis Time-Series Analysis Exploring a Time Series with Real Data Finding Change Points in Time Series Probabilities in Change-Point Analysis Conclusion Exercises 12. Dealing with Too Many Variables Internal Consistency Reliability Rotation Conclusion Exercises 13. All Together Now The Big Picture Appendix A. Getting Started with R Running R and Typing Commands Installing Packages Quitting, Saving, and Restoring Conclusion Appendix B. Working with Data Sets in R Data Frames in R Reading Data Frames from External Files Appendix C. Using dplyr with Data Frames References Index

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