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Statistical Thinking for the 21st Century

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Statistical Thinking for the 21st Century

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.

Introductory StatisticsStatistics
Author
Russell A. Poldrack
Publisher
Stanford University
Source
LibreTexts
License
CC BY-NC
Language
EN
Category
Basic Sciences
Read online Download PDF (open licence)
Contents· 203 sections
  1. 01: Introduction
  2. 1.01: What Is Statistical Thinking
  3. 1.02: Dealing with Statistics Anxiety
  4. 1.03: What Can Statistics Do for Us
  5. 1.04: The Big Ideas of Statistics
  6. 1.05: Causality and Statistics
  7. 1.06: Suggested Readings
  8. 02: Working with Data
  9. 2.01: What Are Data
  10. 2.02: Discrete Versus Continuous Measurements
  11. 2.03: Suggested Readings
  12. 2.04: Appendix
  13. 2.05: What Makes a Good Measurement
  14. 03: Introduction to R
  15. 3.01: Why Programming Is Hard to Learn
  16. 3.02: Using RStudio
  17. 3.03: Getting Started with R
  18. 3.04: Variables
  19. 3.05: Functions
  20. 3.06: Vectors
  21. 3.07: Math with Vectors
  22. 3.08: Data Frames
  23. 3.09: Using R Libraries
  24. 3.10: Working with Data Files
  25. 3.11: Suggested Readings and Videos
  26. 04: Summarizing Data
  27. 4.01: Why Summarize Data
  28. 4.02: Summarizing Data Using Tables
  29. 4.03: Idealized Representations of Distributions
  30. 4.04: Suggested Readings
  31. 05: Summarizing Data with R (with Lucy King)
  32. 5.01: Introduction to the Tidyverse
  33. 5.02: Creating or Modifying Variables Using Mutate()
  34. 5.03: Tidyverse in Action
  35. 5.04: Looking at Individual Variables Using Pull() and Head()
  36. 5.05: Computing a Frequency Distribution (Section 4.2.1)
  37. 5.06: Computing a Cumulative Distribution (Section 4.2.2)
  38. 5.07: Data Cleaning and Tidying with R
  39. 06: Data Visualization
  40. 6.01: Anatomy of a Plot
  41. 6.02: Principles of Good Visualization
  42. 6.03: Accommodating Human Limitations
  43. 6.04: Correcting for Other Factors
  44. 6.05: Suggested readings and videos
  45. 07: Data Visualization with R (with Anna Khazenzon)
  46. 7.01: The Grammar of Graphics
  47. 7.02: Getting Started
  48. 7.03: Lets Think Through a Visualization
  49. 7.04: Plotting the Distribution of a Single Variable
  50. 7.05: Plots with Two Variables
  51. 7.06: Creating a More Complex Plot
  52. 7.07: Additional Reading and Resources
  53. 08: Fitting Models to Data
  54. 8.01: Appendix
  55. 8.02: What Is a Model
  56. 8.03: Statistical Modeling- An Example
  57. 8.04: What Makes a Model Good
  58. 8.05: Can a Model Be Too Good
  59. 8.06: The Simplest Model- The Mean
  60. 8.07: The Mode
  61. 8.08: Variability- How Well Does the Mean Fit the Data
  62. 8.09: 8.8 Using Simulations to Understand Statistics
  63. 8.10: Z-scores
  64. 09: Fitting Simple Models with R
  65. 9.01: Mean
  66. 9.02: Median
  67. 9.03: Mode
  68. 9.04: Variability
  69. 9.05: Z-scores
  70. 10: Probability
  71. 10.01: What Do Probabilities Mean
  72. 10.02: Suggested Readings
  73. 10.03: Appendix
  74. 10.04: What Is Probability
  75. 10.05: How Do We Determine Probabilities
  76. 10.06: Probability Distributions
  77. 10.07: Conditional Probability
  78. 10.08: Computing Conditional Probabilities from Data
  79. 10.09: Independence
  80. 10.10: Reversing a Conditional Probability- Bayes Rule
  81. 10.11: Learning from Data
  82. 10.12: Odds and Odds Ratios
  83. 11: Probability in R
  84. 11.01: Basic Probability Calculations
  85. 11.1.01: Empirical Frequency (Section 10.2.2)
  86. 11.02: Conditional Probability (Section 10.4)
  87. 12: Sampling
  88. 12.01: How Do We Sample
  89. 12.02: Sampling Error
  90. 12.03: Standard Error of the Mean
  91. 12.04: The Central Limit Theorem
  92. 12.05: Confidence Intervals
  93. 12.06: Suggested Readings
  94. 13: Sampling in R
  95. 13.01: Sampling Error (Section @refsamplingerror)
  96. 13.02: Central Limit Theorem
  97. 13.03: Confidence Intervals (Section @refconfidence-intervals)
  98. 14: Resampling and Simulation
  99. 14.01: Monte Carlo Simulation
  100. 14.02: Randomness in Statistics
  101. 14.03: Generating Random Numbers
  102. 14.04: Using Monte Carlo Simulation
  103. 14.05: Using Simulation for Statistics- The Bootstrap
  104. 14.06: Suggested Readings
  105. 15: Resampling and Simulation in R
  106. 15.01: Generating Random Samples (Section @refgenerating-random-numbers)
  107. 15.02: Simulating the Maximum Finishing Time
  108. 15.03: The Bootstrap
  109. 16: Hypothesis Testing
  110. 16.01: Null Hypothesis Statistical Testing (NHST)
  111. 16.02: Null Hypothesis Statistical Testing- An Example
  112. 16.03: The Process of Null Hypothesis Testing
  113. 16.04: NHST in a Modern Context- Multiple Testing
  114. 16.05: Suggested Readings
  115. 17: Hypothesis Testing in R
  116. 17.01: Simple Example- Coin-flipping (Section 16.3.5.1)
  117. 17.02: Simulating p-values
  118. 18: Quantifying Effects and Desiging Studies
  119. 18.01: Confidence Intervals
  120. 18.02: Effect Sizes
  121. 18.03: Statistical Power
  122. 18.04: Suggested Readings
  123. 19: Statistical Power in R
  124. 19.01: Power Analysis
  125. 19.02: Power Curves
  126. 19.03: Simulating Statistical Power
  127. 20: Bayesian Statistics
  128. 20.01: Generative Models
  129. 20.02: Bayes Theorem and Inverse Inference
  130. 20.03: Doing Bayesian Estimation
  131. 20.04: Estimating Posterior Distributions
  132. 20.05: Choosing a Prior
  133. 20.06: Bayesian Hypothesis Testing
  134. 20.07: Suggested Readings
  135. 20.08: Appendix-
  136. 21: Bayesian Statistics in R
  137. 21.01: A Simple Example (Section 20.3)
  138. 21.02: Estimating Posterior Distributions (Section 20.4)
  139. 21.03: Bayes Factors (Section 20.6.1)
  140. 22: Modeling Categorical Relationships
  141. 22.01: Example- Candy Colors
  142. 22.02: Pearsons chi-squared Test
  143. 22.03: Contingency Tables and the Two-way Test
  144. 22.04: Standardized Residuals
  145. 22.05: Odds Ratios
  146. 22.06: Bayes Factor
  147. 22.07: Categorical Analysis Beyond the 2 X 2 Table
  148. 22.08: Beware of Simpsons Paradox
  149. 22.09: Additional Readings
  150. 23: Modeling Categorical Relationships in R
  151. 24: Modeling Continuous Relationships
  152. 24.01: An Example- Hate Crimes and Income Inequality
  153. 24.02: Is income Inequality Related to Hate Crimes
  154. 24.03: Covariance and Correlation
  155. 24.04: Correlation and Causation
  156. 24.05: Suggested Readings
  157. 24.06: Appendix-
  158. 25: Modeling Continuous Relationships in R
  159. 25.01: Computing Covariance and Correlation (Section 24.3)
  160. 25.02: Hate Crime Example
  161. 25.03: Robust Correlations (24.3.2)
  162. 26: The General Linear Model
  163. 26.01: Linear Regression
  164. 26.02: Fitting More Complex Models
  165. 26.03: Interactions Between Variables
  166. 26.04: Beyond Linear Predictors and Outcomes
  167. 26.05: Criticizing Our Model and Checking Assumptions
  168. 26.06: What Does Predict Really Mean
  169. 26.07: Suggested Readings
  170. 26.08: Appendix
  171. 27: The General Linear Model in R
  172. 27.01: Linear Regression (Section 26.1)
  173. 27.02: Model Criticism and Diagnostics (Section 26.5)
  174. 27.03: Examples of Problematic Model Fit
  175. 27.04: Extending Regression to Binary Outcomes.
  176. 27.05: Cross-validation (Section 26.6.1)
  177. 28: Comparing Means
  178. 28.01: Testing the Value of a Single Mean
  179. 28.02: Comparing Two Means
  180. 28.03: The t-test as a Linear Model
  181. 28.04: Bayes Factor for Mean Differences
  182. 28.05: Comparing Paired Observations
  183. 28.06: Comparing More Than Two Means
  184. 28.07: Appendix
  185. 29: Comparing Means in R
  186. 29.01: Testing the Value of a Single Mean (Section 28.1)
  187. 29.02: Comparing Two Means (Section 28.2)
  188. 29.03: The t-test as a Linear Model (Section 28.3)
  189. 29.04: Comparing Paired Observations (Section 28.5)
  190. 29.05: Analysis of Variance (Section 28.6.1)
  191. 30: Practical statistical modeling
  192. 30.01: The Process of Statistical Modeling
  193. 31: Practical Statistical Modeling in R
  194. 32: Doing Reproducible Research
  195. 32.01: How We Think Science Should Work
  196. 32.02: How Science (Sometimes) Actually Works
  197. 32.03: The Reproducibility Crisis in Science
  198. 32.04: Questionable Research Practices
  199. 32.05: Doing Reproducible Research
  200. 32.06: Doing Reproducible Data Analysis
  201. 32.07: Conclusion- Doing Better Science
  202. 32.08: Suggested Readings
  203. 33: References