Description
Engaging and accessible, this book teaches readers how to use inferential statistical thinking to check their assumptions, assess evidence about their beliefs, and avoid overinterpreting results that may look more promising than they really are. It provides step-by-step guidance for using both classical (frequentist) and Bayesian approaches to inference. Statistical techniques covered side by side from both frequentist and Bayesian approaches include hypothesis testing, replication, analysis of variance, calculation of effect sizes, regression, time series analysis, and more. Students also get a complete introduction to the open-source R programming language and its key packages. Throughout the text, simple commands in R demonstrate essential data analysis skills using real-data examples. The companion website provides annotated R code for the book's examples, in-class exercises, supplemental reading lists, and links to online videos, interactive materials, and other resources.
Pedagogical Features
*Playful, conversational style and gradual approach; suitable for students without strong math backgrounds.
*End-of-chapter exercises based on real data supplied in the free R package.
*Technical explanation and equation/output boxes.
*Appendices on how to install R and work with the sample datasets.
Chapter
1. Statistical Vocabulary
Measures of Central Tendency
BOX. Mean and Standard Deviation Formulas
Distributions and Their Shapes
2. Reasoning with Probability
BOX. Make Your Own Tables with R
3. Probabilities in the Long Run
Repetitious Sampling with R
Using Sampling Distributions and Quantiles to Think about Probabilities
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
BOX. Formulas for the Confidence Interval
5. Bayesian and Traditional Hypothesis Testing
BOX. Notation, Formula, and Notes on Bayes’ Theorem
BOX. Markov-Chain Monte Carlo Overview
BOX. Detailed Output from BESTmcmc()
The Null Hypothesis Significance Test
BOX. The Calculation of t
6. Comparing Groups and Analyzing Experiments
Frequentist Approach to ANOVA
BOX. More Information about Degrees of Freedom
The Bayesian Approach to ANOVA
BOX. Giving Some Thought to Priors
BOX. Interpreting Bayes Factors
7. Associations between Variables
BOX. Formula for Pearson's Correlation
Inferential Reasoning about Correlation
BOX. Reading a Correlation Matrix
Null Hypothesis Testing on the Correlation
Bayesian Tests on the Correlation Coefficient
Exploring the Chi-Square Distribution with a Simulation
The Chi-Square Test with Real Data
The Bayesian Approach to the Chi-Square Test
8. Linear Multiple Regression
BOX. Making Sense of Adjusted R-Squared
The Bayesian Approach to Linear Regression
A Linear Regression Model with Real Data
9. Interactions in ANOVA and Regression
BOX. Degrees of Freedom for Interactions
BOX. A Word about Standard Error
Interactions in Multiple Regression
BOX. Diagnosing Residuals and Trying Alternative Models
Bayesian Analysis of Regression Interactions
A Logistic Regression Model with Real Data
BOX. Multinomial Logistic Regression
Bayesian Estimation of Logistic Regression
11. Analyzing Change over Time
Repeated-Measures Analysis
Exploring a Time Series with Real Data
Finding Change Points in Time Series
Probabilities in Change-Point Analysis
12. Dealing with Too Many Variables
BOX. Mean Composites versus Factor Scores
Internal Consistency Reliability
Appendix A. Getting Started with R
Running R and Typing Commands
Quitting, Saving, and Restoring
Appendix B. Working with Data Sets in R
Reading into Data Frames from External Files
Appendix C. Using dplyr with Data Frames
Reasoning with Data
：An Introduction to Traditional and Bayesian Statistics Using R
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