Statistical Thinking for the 21st Century

by Russell A. Poldrack

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Statistical thinking is a way of understanding a complex world by describing it in relatively simple terms that nonetheless capture essential aspects of its structure, and that also provide us some idea of how uncertain we are about our knowledge. The foundations of statistical thinking come primarily from mathematics and statistics, but also from computer science, psychology, and other fields of study.

Description from LibreTexts.

Publisher
Stanford University
Subjects
Statistics, Introductory Statistics
Licence
CC BY-NC 4.0, as LibreTexts states it. Non-commercial use only.
Who can read
Tweens profiles and older, judged from its title and subjects

Contents

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  1. Front Matter
  2. 1.1: Why does this book exist?
  3. TitlePage
  4. InfoPage
  5. TitlePage
  6. 1.2: Why R?
  7. Table of Contents
  8. InfoPage
  9. Licensing
  10. 1.3: The golden age of data
  11. Table of Contents
  12. 1.4: An open source book
  13. 1.5: Acknowledgements
  14. 1: Introduction
  15. 1.1: What Is Statistical Thinking?
  16. 1.2: Dealing with Statistics Anxiety
  17. 1.3: What Can Statistics Do for Us?
  18. 1.4: The Big Ideas of Statistics
  19. 1.5: Causality and Statistics
  20. 1.6: Suggested Readings
  21. 2: Working with Data
  22. 2.1: What Are Data?
  23. 2.2: Discrete Versus Continuous Measurements
  24. 2.3: Suggested Readings
  25. 2.4: Appendix
  26. 2.5: What Makes a Good Measurement?
  27. 3: Introduction to R
  28. 3.1: Why Programming Is Hard to Learn
  29. 3.2: Using RStudio
  30. 3.3: Getting Started with R
  31. 3.4: Variables
  32. 3.5: Functions
  33. 3.6: Vectors
  34. 3.7: Math with Vectors
  35. 3.8: Data Frames
  36. 3.9: Using R Libraries
  37. 3.10: Working with Data Files
  38. 3.11: Suggested Readings and Videos
  39. 4: Summarizing Data
  40. 4.1: Why Summarize Data?
  41. 4.2: Summarizing Data Using Tables
  42. 4.3: Idealized Representations of Distributions
  43. 4.4: Suggested Readings
  44. 5: Summarizing Data with R (with Lucy King)
  45. 5.1: Introduction to the Tidyverse
  46. 5.2: Creating or Modifying Variables Using Mutate()
  47. 5.3: Tidyverse in Action
  48. 5.4: Looking at Individual Variables Using Pull() and Head()
  49. 5.5: Computing a Frequency Distribution (Section 4.2.1)
  50. 5.6: Computing a Cumulative Distribution (Section 4.2.2)
  51. 5.7: Data Cleaning and Tidying with R
  52. 6: Data Visualization
  53. 6.1: Anatomy of a Plot
  54. 6.2: Principles of Good Visualization
  55. 6.3: Accommodating Human Limitations
  56. 6.4: Correcting for Other Factors
  57. 6.5: Suggested readings and videos
  58. 7: Data Visualization with R
  59. 7.1: The Grammar of Graphics
  60. 7.2: Getting Started
  61. 7.3: Let’s Think Through a Visualization
  62. 7.4: Plotting the Distribution of a Single Variable
  63. 7.5: Plots with Two Variables
  64. 7.6: Creating a More Complex Plot
  65. 7.7: Additional Reading and Resources
  66. 8: Fitting Models to Data
  67. 8.1: Appendix
  68. 8.2: What Is a Model?
  69. 8.3: Statistical Modeling- An Example
  70. 8.4: What Makes a Model “Good”?
  71. 8.5: Can a Model Be Too Good?
  72. 8.6: The Simplest Model- The Mean
  73. 8.7: The Mode
  74. 8.8: Variability- How Well Does the Mean Fit the Data?
  75. 8.9: 8.8 Using Simulations to Understand Statistics
  76. 8.10: Z-scores
  77. 9: Fitting Simple Models with R
  78. 9.1: Mean
  79. 9.2: Median
  80. 9.3: Mode
  81. 9.4: Variability
  82. 9.5: Z-scores
  83. 10: Probability
  84. 10.1: What Do Probabilities Mean?
  85. 10.2: Suggested Readings
  86. 10.3: Appendix
  87. 10.4: What Is Probability?
  88. 10.5: How Do We Determine Probabilities?
  89. 10.6: Probability Distributions
  90. 10.7: Conditional Probability
  91. 10.8: Computing Conditional Probabilities from Data
  92. 10.9: Independence
  93. 10.10: Reversing a Conditional Probability- Bayes’ Rule
  94. 10.11: Learning from Data
  95. 10.12: Odds and Odds Ratios
  96. 11: Probability in R
  97. 11.1: Basic Probability Calculations
  98. 11.1.1: Empirical Frequency (Section 10.2.2)
  99. 11.2: Conditional Probability (Section 10.4)
  100. 12: Sampling
  101. 12.1: How Do We Sample?
  102. 12.2: Sampling Error
  103. 12.3: Standard Error of the Mean
  104. 12.4: The Central Limit Theorem
  105. 12.5: Confidence Intervals
  106. 12.6: Suggested Readings
  107. 13: Sampling in R
  108. 13.1: Sampling Error (Section @ref{samplingerror})
  109. 13.2: Central Limit Theorem
  110. 13.3: Confidence Intervals (Section @ref{confidence-intervals})
  111. 14: Resampling and Simulation
  112. 14.1: Monte Carlo Simulation
  113. 14.2: Randomness in Statistics
  114. 14.3: Generating Random Numbers
  115. 14.4: Using Monte Carlo Simulation
  116. 14.5: Using Simulation for Statistics- The Bootstrap
  117. 14.6: Suggested Readings
  118. 15: Resampling and Simulation in R
  119. 15.1: Generating Random Samples (Section @ref{generating-random-numbers})
  120. 15.2: Simulating the Maximum Finishing Time
  121. 15.3: The Bootstrap
  122. 16: Hypothesis Testing
  123. 16.1: Null Hypothesis Statistical Testing (NHST)
  124. 16.2: Null Hypothesis Statistical Testing- An Example
  125. 16.3: The Process of Null Hypothesis Testing
  126. 16.4: NHST in a Modern Context- Multiple Testing
  127. 16.5: Suggested Readings
  128. 17: Hypothesis Testing in R
  129. 17.1: Simple Example- Coin-flipping (Section 16.3.5.1)
  130. 17.2: Simulating p-values
  131. 18: Quantifying Effects and Desiging Studies
  132. 18.1: Confidence Intervals
  133. 18.2: Effect Sizes
  134. 18.3: Statistical Power
  135. 18.4: Suggested Readings
  136. 19: Statistical Power in R
  137. 19.1: Power Analysis
  138. 19.2: Power Curves
  139. 19.3: Simulating Statistical Power
  140. 20: Bayesian Statistics
  141. 20.1: Generative Models
  142. 20.2: Bayes’ Theorem and Inverse Inference
  143. 20.3: Doing Bayesian Estimation
  144. 20.4: Estimating Posterior Distributions
  145. 20.5: Choosing a Prior
  146. 20.6: Bayesian Hypothesis Testing
  147. 20.7: Suggested Readings
  148. 20.8: Appendix-
  149. 21: Bayesian Statistics in R
  150. 21.1: A Simple Example (Section 20.3)
  151. 21.2: Estimating Posterior Distributions (Section 20.4)
  152. 21.3: Bayes Factors (Section 20.6.1)
  153. 22: Modeling Categorical Relationships
  154. 22.1: Example- Candy Colors
  155. 22.2: Pearson’s chi-squared Test
  156. 22.3: Contingency Tables and the Two-way Test
  157. 22.4: Standardized Residuals
  158. 22.5: Odds Ratios
  159. 22.6: Bayes Factor
  160. 22.7: Categorical Analysis Beyond the 2 X 2 Table
  161. 22.8: Beware of Simpson’s Paradox
  162. 22.9: Additional Readings
  163. 23: Modeling Categorical Relationships in R
  164. 24: Modeling Continuous Relationships
  165. 24.1: An Example- Hate Crimes and Income Inequality
  166. 24.2: Is income Inequality Related to Hate Crimes?
  167. 24.3: Covariance and Correlation
  168. 24.4: Correlation and Causation
  169. 24.5: Suggested Readings
  170. 24.6: Appendix-
  171. 25: Modeling Continuous Relationships in R
  172. 25.1: Computing Covariance and Correlation (Section 24.3)
  173. 25.2: Hate Crime Example
  174. 25.3: Robust Correlations (24.3.2)
  175. 26: The General Linear Model
  176. 26.1: Linear Regression
  177. 26.2: Fitting More Complex Models
  178. 26.3: Interactions Between Variables
  179. 26.4: Beyond Linear Predictors and Outcomes
  180. 26.5: Criticizing Our Model and Checking Assumptions
  181. 26.6: What Does “Predict” Really Mean?
  182. 26.7: Suggested Readings
  183. 26.8: Appendix
  184. 27: The General Linear Model in R
  185. 27.1: Linear Regression (Section 26.1)
  186. 27.2: Model Criticism and Diagnostics (Section 26.5)
  187. 27.3: Examples of Problematic Model Fit
  188. 27.4: Extending Regression to Binary Outcomes.
  189. 27.5: Cross-validation (Section 26.6.1)
  190. 28: Comparing Means
  191. 28.1: Testing the Value of a Single Mean
  192. 28.2: Comparing Two Means
  193. 28.3: The t-test as a Linear Model
  194. 28.4: Bayes Factor for Mean Differences
  195. 28.5: Comparing Paired Observations
  196. 28.6: Comparing More Than Two Means
  197. 28.7: Appendix
  198. 29: Comparing Means in R
  199. 29.1: Testing the Value of a Single Mean (Section 28.1)
  200. 29.2: Comparing Two Means (Section 28.2)
  201. 29.3: The t-test as a Linear Model (Section 28.3)
  202. 29.4: Comparing Paired Observations (Section 28.5)
  203. 29.5: Analysis of Variance (Section 28.6.1)
  204. 30: Practical statistical modeling
  205. 30.1: The Process of Statistical Modeling
  206. 31: Practical Statistical Modeling in R
  207. 32: Doing Reproducible Research
  208. 32.1: How We Think Science Should Work
  209. 32.2: How Science (Sometimes) Actually Works
  210. 32.3: The Reproducibility Crisis in Science
  211. 32.4: Questionable Research Practices
  212. 32.5: Doing Reproducible Research
  213. 32.6: Doing Reproducible Data Analysis
  214. 32.7: Conclusion- Doing Better Science
  215. 32.8: Suggested Readings
  216. 33: References
  217. Back Matter
  218. Index
  219. Index
  220. Glossary
  221. Detailed Licensing