Statistical Inference and Probability breaks down the complex topic of inferential statistics with accessible language and detailed examples. It covers a range of topics, including: probability and sampling distributions; inference and regression; power, effect size and inverse probability.

Table of Contents

• List of Figures and Tables
• About the Author
• 1 The Challenge and Promise of Inference
• What Is Inference?
• Informal Inference: The Tyranny of Causal Narratives
• Cognitive Illusions
• Scientific Inference
• Statistical Inference
• Exploration and Inference: Detectives and Lawyers
• The NHST Wars
• Inference, Reproducibility and Replication
• Inference in Action: The Salk Vaccine Trial
• Inference in Action: Fertility and Development
• The World Before Statistics
• What Knowledge I Assume
• The Structure of This Book
• 2 Probability, Randomness, Probability Distributions and Sampling Distributions
• What is Probability?
• Some Elementary Descriptive Statistics and Notations
• Trials and Sample Spaces
• The Law of Large Numbers
• Bernoulli Trials
• The Probability Distribution
• Bar Charts and Histograms
• Heights of Union Soldiers
• Probability Distributions and Variables
• Conditional Probability With Categorical Variables
• Conditional Probability With Continuous Variables
• Pearson's r
• Conditional Probabilities With a Continuous and Categorical Distribution
• What Have We Done?
• Appendix: Simulating Coin Flips With Excel
• 3 Bernoulli, Coke and Pepsi
• A Series of 10 Trials
• Statistical Inference and Research Design
• The Null Hypothesis
• Short Run Probabilities: The Binomial Distribution
• The Sampling Distribution and p-Values
• Alpha, Significance, Confidence and Type I Errors
• Improbable Expectations, Definite Results
• Why the Double Negative and All the Bother?
• The Logic of NHST
• From Statistical Inference to Scientific Inference
• What Does Significant Mean?
• Appendix: A Famous Experiment: Milk First or Tea First?
• 4 Samples and Populations
• The Difficulty of Measurement
• The Illusion of Representative Samples
• The Sampling Distribution, Samples and Populations
• Flipping the Logic: One Sample From a Distribution
• Standard Errors
• Confidence Intervals for Point Estimates
• The t-Distribution
• Examining Differences in Means and Proportions
• Calculating Standard Errors for Categorical Variables
• The Binomial Formula in Action: Stop and Search
• Chi-Square and Contingency Tables
• Chi-Square and Goodness of Fit
• Fisher's Exact Test
• Appendix: Degrees of Freedom
• 5 Inference and Regression
• Introduction
• The Analysis of Variance
• The Regression Equation
• Regression as the Analysis of Unconditional and Conditional Variance
• Correlation and Regression
• Regression and ANOVA
• Multiple Regression
• Inference in Regression: The F-Statistic and Standard Errors
• An Example of Multiple OLS Regression
• What Can Go Wrong With Multiple Regression?
• Transformation
• Appendix: A Refresher on Powers and Logarithms
• Powers
• Arithmetic Rules of Powers
• Powers Can Be Negative
• Powers Need Not Be Whole Numbers
• Logarithms
• The Logit
• 6 Power, Effect Size and Inverse Probability
• Introduction
• Thomas Bayes: Prior and Posterior Probabilities
• Taxi for Kahneman and Tversky
• A More Substantial Application: Medical Tests
• Covid-19
• Breast Cancer Screening
• 7 What Does Sound Inference Comprise?
• The ASA Debate
• Ten Steps of Inference
• The Six Principles of the ASA
• From the Six Principles to ATOM
• Contemporary Scientific Research
• Glossary
• References