Introduction to Modern Statistics (2nd edition)

by Mine Çetinkaya-Rundel, Johanna Hardin

Introduces foundational statistical concepts through real-world case studies and data analysis principles.

📄 Executive Summary

Introduction to Modern Statistics (2nd edition) provides an entry-level introduction to modern statistical thinking and practical data analysis. Designed for introductory college courses and self-directed learners, the book assumes minimal mathematical preparation beyond basic algebra and requires no prior background in statistics or computer programming. While the conceptual narrative is computing language agnostic, it integrates closely with the R programming language through accompanying software labs and browser-based tutorials. The text guides readers through the entire analytical workflow, starting with data collection and study design before advancing to exploratory analysis, regression modeling, foundational inference, and inferential modeling.

The curriculum progresses systematically across six main parts. It begins with data structures, observational studies versus randomized experiments, and the distinction between random sampling and random allocation, which establishes whether conclusions can be generalized or interpreted causally. Readers then learn exploratory techniques for categorical and numerical data using graphical summaries and summary statistics. The book then introduces regression models, covering simple linear regression, multiple linear regression, and logistic regression for binary outcomes. A central organizing idea is the parallel presentation of computational and mathematical approaches to inference. Rather than relying solely on classical formulas, the book teaches hypothesis testing and confidence intervals through simulation methods—specifically *randomization tests* and *bootstrapping*—alongside classical mathematical models based on normal, Student's t, chi-squared, and F distributions.

Throughout the text, readers develop practical skills in formulating hypotheses, quantifying uncertainty, and interpreting data responsibly. The book teaches how to evaluate model assumptions, assess residual behavior, select parsimonious models using criteria such as adjusted R-squared and the Akaike information criterion, and evaluate prediction error using cross-validation. In its concluding section, the book unifies modeling and inference by showing how to conduct hypothesis tests and build confidence intervals for regression coefficients. By the end of the text, readers should be able to design studies, summarize multivariable datasets, fit and evaluate predictive models, conduct appropriate inferential tests, and communicate findings in clear, contextual language.

To remain focused on core introductory concepts, the book intentionally leaves several advanced statistical techniques outside its scope. It does not cover interaction terms in multiple regression, hierarchical or multilevel models, or regularized fitting techniques such as Ridge regression and LASSO. It also omits advanced mathematical derivations and complex resampling schemes for multivariable data. By establishing a solid foundation in both simulation-based and formulaic inference, the textbook prepares readers for intermediate study in statistical modeling and data science.

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Front Matter
Part I: Introduction to Data
Chapter 1: Hello data
Chapter 2: Study design
Chapter 3: Applications: Data
Part II: Exploratory Data Analysis
Chapter 4: Exploring categorical data
Chapter 5: Exploring numerical data
Chapter 6: Applications: Explore
Part III: Regression Modeling
Chapter 7: Linear regression with a single predictor
Chapter 8: Linear regression with multiple predictors
Chapter 9: Logistic regression
Chapter 10: Applications: Model
Part IV: Foundations of Inference
Chapter 11: Hypothesis testing with randomization
Chapter 12: Confidence intervals with bootstrapping
Chapter 13: Inference with mathematical models
Chapter 14: Decision Errors
Chapter 15: Applications: Foundations
Part V: Statistical Inference
Chapter 16: Inference for a single proportion
Chapter 17: Inference for comparing two proportions
Chapter 18: Inference for two-way tables
Chapter 19: Inference for a single mean
Chapter 20: Inference for comparing two independent means
Chapter 21: Inference for comparing paired means
Chapter 22: Inference for comparing many means
Chapter 23: Applications: Infer
Part VI: Inferential Modeling
Chapter 24: Inference for linear regression with a single predictor
Chapter 25: Inference for linear regression with multiple predictors
Chapter 26: Inference for logistic regression
Chapter 27: Applications: Model and infer
Appendix A: Exercise Solutions
References