STAT 350: Introduction to Statistics — Pedagogical Overview

Course Identity

STAT 350 at Purdue University is a calculus-based introductory statistics course designed for students who will perform statistical analysis in their disciplines — engineering, life sciences, social sciences, and related fields. The prerequisite is Calculus 2 (integration), and students are expected to demonstrate integration skills on both homework and exams. The course is taught across multiple campuses (Purdue West Lafayette, Purdue Indianapolis) and in multiple session formats (fall/spring semesters, summer session, winter session), each with its own pacing and exam structure but a shared curriculum and shared materials.

The course is authored and maintained by Timothy Reese and delivered by a team of instructors and teaching assistants. It is built around an open-access Sphinx-based webbook that serves as the primary learning resource — not a supplemental website, but the course textbook itself.

Philosophical Orientation

The course introduction states its thesis clearly: the focus lies on “developing critical thinking skills” and “understanding the underlying reasons behind concepts before learning how to apply them.” The phrase “why before how” appears repeatedly in the materials and shapes every design decision visible in the webbook.

This is not a cookbook course. Students are not handed formulas and told to plug in numbers. Instead, each concept is motivated by a question — why do sample statistics vary? why can we quantify our uncertainty about a population parameter? why does comparing group means require decomposing variability? — and the machinery is built in response to that question. The formulas arrive as answers, not as starting points.

At the same time, the course does not shy away from mathematical formality. Proofs, derivations, and precise notation are present throughout. The computational variance formula is derived from first principles. The sampling distribution of the mean is developed through expectation algebra. The least-squares estimators in regression are obtained by minimizing SSE, not just stated. This places the course in a distinctive middle ground: more rigorous than a typical “applied stats” service course, but always anchored to practical interpretation and real data.

Structural Architecture

13 Chapters, 63 Lectures

The course follows a deliberate arc:

Block	Chapters	Topic	Role
Descriptive Foundation	1–3	Introduction, Graphical Summaries, Numerical Summaries	Describe the visible surface of data
Probability Theory	4–6	Probability, Discrete Distributions, Continuous Distributions	Understand the data-generating mechanism
Bridge	7	Sampling Distributions	Connect data to theory via the CLT
Study Design	8	Experimental Design	Ensure the conditions that make inference valid
Inference Core	9–10	Confidence Intervals, Hypothesis Testing	Foundational inference for one population
Extensions	11–13	Two-Sample Methods, ANOVA, Simple Linear Regression	Extend inference to comparisons and relationships

This structure has a clear narrative logic. Chapters 1–3 teach students to see data. Chapters 4–6 teach the probability machinery that explains why data look the way they do. Chapter 7 is the critical bridge — the Central Limit Theorem connects the empirical world of Chapters 1–3 to the theoretical world of Chapters 4–6, and makes everything that follows in Chapters 9–13 possible. Chapter 8 steps back to address study design, ensuring students understand that inference is only valid when the data collection process meets certain conditions.

The inference pipeline in Chapters 9–13 builds cumulatively:

Chapter 9 — Confidence intervals and bounds for a single mean (σ known → σ unknown → t-distribution)
Chapter 10 — Hypothesis testing for a single mean (same σ-known → σ-unknown progression, plus Type I/II errors, power)
Chapter 11 — Two-sample procedures (independent samples with known σ → pooled → Welch → paired)
Chapter 12 — One-way ANOVA (extends two-sample to k groups, introduces F-distribution, Tukey HSD)
Chapter 13 — Simple linear regression (least squares, diagnostics, LINE assumptions, inference on slope, prediction)

Each chapter builds directly on the previous one’s machinery. Students who understand the single-sample t-test can see how the two-sample t-test is a natural generalization; students who understand the two-sample t-test can see how ANOVA extends the comparison to multiple groups; and students who understand all of these can see regression as inference applied to a continuous relationship.

Lectures as Standalone Units

Each lecture (e.g., “10-1: Hypothesis Testing — Errors and Power”) opens with an embedded YouTube video, downloadable PPTX slides, and a “Road Map” admonition listing the specific learning objectives. The written content then develops the topic with worked examples, R code demonstrations, and exercises with toggle-able solutions.

The lectures are granular enough to function as standalone study units — a student reviewing for the final exam can go directly to “9-2: CI for σ Known” without reading the surrounding sections — but they are also sequenced to build on each other within a chapter.

22 Worksheets

The worksheets bridge lectures and exams. They are structured problem sets that require students to work through multi-step statistical procedures by hand and with R, scaffolded with learning objectives, guided questions, and hidden solutions (using sphinx-togglebutton dropdowns). Topics range from early-course skills (data visualization, summary statistics) through the full inference pipeline (confidence intervals, hypothesis tests, ANOVA, regression).

Worksheets consistently require students to:

State the problem setup (hypotheses, conditions, parameter of interest)
Show the computational work (formulas with substitutions)
Interpret the result in context (not just “reject H0” but what that means for the research question)
Verify with R code

9 R Reference Documents

A dedicated R section provides getting-started guides, function references (split into two parts), a ggplot2-specific guide, best practices, a dataset catalog, and tutorial assignments. The course uses R as its computational platform exclusively, with a strict ggplot2-only policy for graphics (no base R plot(), hist(), boxplot(), etc.).

Exam System

The assessment structure adapts to the session format:

Session	Exams	Format
Fall/Spring (16-week)	Exam 1, Exam 2, Final	In-person proctored, 120 min final
Summer (8-week)	Exam 1, Exam 2, Final	Online proctored (Respondus LockDown Browser), 80 min midterms, 140 min final
Winter (4-week)	Final only	Online proctored (Respondus LockDown Browser), 140 min

A JavaScript-based “seasonal switcher” dynamically loads the appropriate exam page variant (regular, summer, winter) so students always see the correct policies for their session.

The webbook includes worked solutions for past exams — not just answer keys, but full step-by-step derivations with R verification code. These serve as both study resources and modeling of the expected quality of exam responses.

Pedagogical Conventions and Standards

Precision Requirements

The course enforces strict numerical precision standards:

P-values: 5 significant digits of resolution (e.g., p = 0.03421, not p = 0.034)
Test statistics: 3 literal decimal places
Critical values: 4 literal decimal places
General numeric answers: 4 decimal places unless stated otherwise

These are not arbitrary — they teach students that precision matters in statistical reporting, and that premature rounding propagates error through multi-step calculations.

Terminology Discipline

The course enforces specific phrasing conventions that reflect careful statistical thinking:

Conclusions of hypothesis tests must use phrases like “sufficient evidence to conclude” or “insufficient evidence to conclude” — never “statistically significant” (which obscures the logic), never “accept H0” (which misrepresents the asymmetry of the testing framework), and never “prove” (which overstates what statistical evidence can establish).
Outliers are referred to as “potential outliers” or “flagged observations” when identified by the 1.5×IQR rule, reflecting that the rule is a screening criterion, not a definitive classification.
Binomial normal approximation uses the single condition np(1−p) ≥ 15 rather than the two-condition form np ≥ 10 AND n(1−p) ≥ 10 found in many textbooks. This is a deliberate choice: the single condition is tighter and better calibrated.

Histogram Standards

From Chapter 3 onward, all histograms must use:

Density scaling on the y-axis (after_stat(density) in ggplot2)
A red kernel density curve overlay (geom_density)
A blue normal distribution overlay (stat_function(fun = dnorm))

This triple-layer display teaches students to simultaneously see the empirical distribution, a nonparametric smooth, and the theoretical normal model — reinforcing the habit of visually assessing normality that becomes critical in later inference chapters.

“Work Required” Philosophy

A correct answer without supporting work is considered incorrect. This is stated on every exam and reinforced throughout the worksheets. The rationale is pedagogical: the course assesses understanding of procedure, not just computational ability. A student who arrives at the right number by an incorrect or unjustified method has not demonstrated the learning objective.

Consistency Grading

Exams use a “consistency grading” policy where later parts of a problem are graded using the student’s earlier answers, even if those answers were wrong. This rewards logical coherence and penalizes inconsistency. A student who makes an arithmetic error in Part (a) but correctly applies their (wrong) value in Parts (b)–(d) can still earn substantial credit. The constraint: the earlier answer must be “plausible” — an impossible value (e.g., a negative variance) forfeits this benefit.

The Role of R in the Course

R is not an add-on in this course — it is woven into the fabric of instruction. Every lecture that involves computation includes R code blocks demonstrating the relevant functions. The code is not pseudocode or simplified for presentation; it runs and produces the output shown.

Key design decisions about R usage:

ggplot2 exclusively. No base R graphics. This gives students one consistent, composable grammar for all visualizations, from histograms and boxplots through residual diagnostics and QQ-plots.
Code recognition, not code writing, on exams. Students are tested on their ability to read R code and interpret output, not to write code from memory. This focuses the exam on statistical reasoning rather than syntax recall.
Base R for computation. While ggplot2 is the plotting standard, the course uses base R functions for computation: mean(), sd(), var(), t.test(), aov(), TukeyHSD(), lm(), predict(). No tidyverse data manipulation (dplyr, tidyr, etc.) is used in the instructional materials.
tapply() over group_by()/summarise(). For group-wise computations, the course uses tapply(), keeping the dependency footprint minimal and avoiding the cognitive overhead of piping.
Copy button on all code blocks. The sphinx-copybutton extension strips prompts and lets students paste code directly into R, removing a friction point for practice.

Accessibility and Technology

MathJax v4 with Semantic Enrichment

The webbook uses MathJax v4 (not v3) with semantic enrichment, speech generation, and braille label support enabled. This means all mathematical notation — from simple inline expressions to multi-line derivations — is accessible to screen readers and assistive technology. The configuration explicitly enables:

enrich: true — semantic enrichment for better speech output
speech: true — generates aria-labels for formulas
braille: true — generates aria-braillelabels
collapsible: true — allows users to collapse complex expressions

This is a meaningful accessibility commitment in a math-heavy course.

Interactive Elements

The webbook uses several Sphinx extensions to create an interactive learning experience:

sphinx-design — Cards, grids, tab sets, dropdowns, badges, and styled admonitions throughout
sphinx-togglebutton — Hide/show toggles for exercise solutions, allowing students to attempt problems before seeing answers
sphinx-copybutton — One-click code copying with prompt stripping
Embedded YouTube videos — Every lecture begins with a recorded video lecture
Supabase-hosted images — All figures served from a CDN for consistent loading
External interactive tools — An “Interactive Probability and Statistical Inference Guide” helps students build flowcharts for choosing the right statistical procedure

Multi-Session Delivery

The JavaScript seasonal switcher is a notable engineering choice. Rather than maintaining three separate sites for the fall/spring, summer, and winter sessions, the course maintains variant RST files (e.g., exam1.rst, exam1-summer.rst, exam1-winter.rst) that share the same Sphinx reference labels. A client-side script detects the session and loads the appropriate content. This means the instructional material is shared, but session-specific logistics (exam dates, proctoring software, time limits) are tailored.

The Statistical Narrative

From Description to Inference

The course tells a coherent story. It opens by asking: “What do we see in data?” (Chapters 1–3). It then asks: “What process generated this data?” (Chapters 4–6). It bridges these with: “How do statistics computed from samples relate to the parameters of the generating process?” (Chapter 7). And it builds the inference toolkit: “Given what we observe, what can we conclude about what we cannot observe?” (Chapters 9–13).

This narrative is not implicit — it is stated explicitly in the course roadmap and reinforced at the opening of each chapter. The Chapter 9 introduction, for example, begins: “After developing the foundational tools of probability theory, exploring random variables, and understanding sampling distributions, we have finally arrived at the core of statistical practice: statistical inference.”

The Inference Decision Tree

The course teaches students to navigate an increasingly complex decision tree:

What is the parameter of interest? (mean, difference of means, variance, slope)
How many populations? (one → Ch 9/10; two → Ch 11; k → Ch 12; continuous relationship → Ch 13)
What is known? (σ known vs. unknown → z vs. t; equal variances vs. not → pooled vs. Welch)
What is the question? (estimation → CI/CB; testing → HT with specified α)
Are conditions met? (normality, independence, equal variance — which check depends on which procedure)

The “Interactive Probability and Statistical Inference Guide” exists specifically to help students build this decision tree for themselves before the final exam.

Power and Error as First-Class Concepts

Chapter 10 does not treat Type I error, Type II error, and power as afterthoughts. They are introduced at the beginning of the hypothesis testing unit (10-1), before the first formal test is conducted. The logic is: before you learn the mechanics of testing, you need to understand what can go wrong and how the framework controls error. Power curves are part of the exam material, and students may be asked to interpret or sketch them.

LINE Assumptions in Regression

Chapter 13 treats the LINE assumptions (Linearity, Independence, Normality, Equal variance) not as a memorized checklist but as a structured diagnostic framework. Each assumption is connected to a specific diagnostic tool:

Linearity → residuals vs. fitted plot
Independence → context of data collection
Normality → QQ-plot of residuals
Equal variance → residuals vs. fitted (constant spread)

The course distinguishes between which assumptions are needed for point estimation (linearity and independence suffice for least squares) and which are needed for inference (normality and equal variance are additionally required for valid t-tests and prediction intervals).

Exam Design and Philosophy

Comprehensive Assessment

The final exam is comprehensive, covering all 13 chapters with approximately 60% post-Exam 2 material and 40% earlier material. This is not a policy of convenience — it reflects the cumulative nature of the subject. A student who has forgotten sampling distributions cannot reason about confidence intervals; a student who has forgotten probability cannot reason about p-values.

Format

Exams begin with objective questions (True/False at 2 points each, Multiple Choice at 3 points each) and proceed to free-response problems. The objective section mixes topics from across the course, while free-response problems are multi-part, requiring students to set up, compute, interpret, and connect — mirroring the structure of the worksheets.

The Crib Sheet Philosophy

For in-person exams, students are allowed two 8.5×11” crib sheets (both sides). The summer/winter online exams allow unlimited printed materials. But the course explicitly recommends one or two well-organized sheets, and the rationale is stated as pedagogy:

“The act of compressing the course material is part of studying. When you force yourself to fit the most important formulas, definitions, procedures, and worked examples onto one or two pages, you are doing the cognitive work that builds real understanding.”

This is a thoughtful framing: the crib sheet is not a concession to open-note exams but a deliberately designed study activity.

Worked Solutions as Teaching Tools

Past exam solutions in the webbook are not just answer keys — they are full worked solutions with:

Problem statements reproduced for context
Step-by-step derivations using formal notation
R code verification of every numerical answer
Interpretation of results in the context of the original question

This transforms past exams from a “practice quiz” resource into a modeling resource: students see exactly what a complete, correct, well-communicated solution looks like.

The Webbook as an Open Resource

The entire course textbook is open-access, hosted on GitHub Pages, and built with standard open-source tooling (Sphinx, reStructuredText, Python). This is notable for several reasons:

No textbook cost. Students are not required to purchase a commercial textbook.
Living document. The webbook is continuously updated — errors are corrected, examples are refined, new exam solutions are added each semester.
Reproducibility. Every R code block in the webbook can be run by students to verify the results. The course does not rely on screenshots or edited output.
Consistency. Because the same document serves all sections and sessions, students in different sections see exactly the same instructional content (with only logistics varying by session).

The technical stack — Sphinx with sphinx_rtd_theme, MathJax v4, sphinx-design, sphinx-togglebutton, sphinx-copybutton, linuxdoc.rstFlatTable, myst_parser — is production-grade documentation tooling applied to educational content. The result is a resource that looks and navigates like professional technical documentation, which is itself a subtle message: statistics is a rigorous discipline, and its teaching materials should reflect that.

Summary

STAT 350 is a carefully engineered course that takes introductory statistics seriously — as a subject, as a skill, and as a mode of thinking. The webbook is not a slide deck reformatted for the web; it is a purpose-built textbook with a coherent narrative, precise conventions, computational verification, and accessibility infrastructure. The pedagogical philosophy — “why before how,” correct terminology, precision requirements, consistency grading, and the crib sheet as study tool — reflects a course designed to produce students who can reason statistically, not just compute statistically.