Books: "Intermediate Statistics with R" by Mark C. Greenwood (developed for courses like STAT 217 at Montana State University)

"Books: "Intermediate Statistics with R" by Mark C. Greenwood (developed for courses like STAT 217 at Montana State University) "

 

"Intermediate Statistics with R" by Mark C. Greenwood (developed for courses like STAT 217 at Montana State University) is a comprehensive textbook designed to transition students from introductory statistical concepts to advanced data analysis and linear modeling.

The text places a heavy emphasis on modern R programming—specifically utilizing the tidyverse suite for data wrangling and ggplot2 for data visualization—while balancing both parametric testing and modern randomization-based (nonparametric) methods.

Core Structural Themes

1. Modern R Workflow Optimization: The book bypasses legacy base-R plotting in favor of the Grammar of Graphics (ggplot2), training users to build clear, customizable, and high-visibility statistical plots.

2. Dual-Path Inference: Every major statistical test is explored through two lenses:

   • Parametric Tests: Traditional distribution-based testing (e.g., $F$-tests, $t$-tests, $\chi^2$ distributions).

   • Randomization/Resampling Tests: Nonparametric computer-intensive methods (e.g., permutation tests and bootstrapping) to build an intuitive grasp of p-values and sampling distributions without assuming strict normality.

3. The Replication Crisis and Statistical Literacy: The text explicitly addresses the pitfalls of over-relying on arbitrary p-value thresholds ($p < 0.05$), publication bias, and multiple-testing errors.

Chapter-by-Chapter Core Summary

Chapter 1: Preface & Environment Setup

• Concepts: Initial setup of RStudio, foundational exploratory data analysis (EDA), and document compilation using R Markdown.

• Visuals & Coding: Focuses on foundational summary statistics, quantitative distributions via histograms and boxplots, and introduces the basics of the tidyverse grammar.

Chapter 2: (R)e-Introduction to Statistics & Resampling

• Concepts: Moves past basic two-sample situations. It connects traditional hypothesis testing to computer-driven permutation tests for comparing two groups. It also introduces bootstrapping as a powerful tool for generating robust confidence intervals.

• Key Topics: Data wrangling using dplyr (filtering, mutating, summarizing), handling density curves, and visualizing raw distributions using "pirate-plots" or advanced violin plots.

Chapter 3: One-Way ANOVA (Analysis of Variance)

• Concepts: Extends the comparison of means to three or more independent groups.

• Key Topics: Demystifies the underlying linear model equations using both cell means coding and reference coding. It breaks down Sums of Squares (SS), Mean Squares (MS), and the derivation of the $F$-statistic.

• Diagnostics: Teaches model validation using residual diagnostics and Quantile-Quantile (Q-Q) plots.

• Post-Hoc Testing: Covers pairwise comparisons adjusting for family-wise error rates using Tukey’s HSD (Honest Significant Difference) paired with compact letter displays.

Chapter 4: Two-Way ANOVA

• Concepts: Analyzes the simultaneous impact of two categorical explanatory variables on a single quantitative response variable.

• Key Topics: Explores the critical concept of interaction effects (where the impact of one variable depends on the level of another). It outlines experimental design types, observational studies, and addresses issues with un-replicated or unbalanced designs.

Chapter 5: Chi-Square ($\chi^2$) Tests

• Concepts: Shifts focus from quantitative outcomes to categorical outcomes using contingency ($R \times C$) tables.

• Key Topics: Differentiates between the Test of Homogeneity and the Test of Independence.

• Inference: Compares traditional $\chi^2$ distributions against permutation-based $\chi^2$ benchmarks, followed by an examination of standardized Pearson residuals to pinpoint exactly which cells drive the overall differences.

Chapter 6: Correlation and Simple Linear Regression (SLR)

• Concepts: Investigates the linear relationship between two continuous, quantitative variables.

• Key Topics: Estimating the Pearson correlation coefficient ($r$), checking grouped relationships, and using the Least Squares method to build an optimal regression line. It defines the coefficient of determination ($R^2$) to evaluate model fit and explains the effects of high-leverage outliers or influential data points.

Chapter 7: Simple Linear Regression Inference & Transformations

• Concepts: Moves from descriptive modeling to inferential analysis of regression parameters.

• Key Topics: Constructing confidence intervals and running hypothesis tests for both the slope ($\beta_1$) and intercept ($\beta_0$). It showcases randomization-based inferences for slopes alongside parametric tests.

• Data Transformations: Explains log-transformations—including $\log(y)$, $\log(x)$, and log-log models—to handle non-linear relationships or non-constant variance (heteroscedasticity). It also contrasts confidence intervals (for the mean response) with prediction intervals (for a specific new observation).

Textbook Target Audience

This resource is best suited for intermediate students, data analysts, or researchers who have a basic understanding of introductory statistics and want to learn how to apply linear models, ANOVA, and resampling methods using reproducible R code. Every chapter wraps up with a standalone code summary sheet and practical dataset exercises.

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