Course Worksheets

This section contains the complete collection of in-class worksheets designed for active learning in STAT 350. These materials form the pedagogical core of our flipped classroom approach.

Pedagogical Philosophy

These seventeen worksheets represent a comprehensive journey through fundamental probability and statistical concepts, designed specifically for active learning. Rather than passively receiving information through traditional lectures, students engage directly with statistical concepts through guided exploration, computation, and collaborative problem-solving.

The worksheets follow a deliberate sequence that builds conceptual understanding systematically:

Foundation: Data Exploration (Worksheet 1)

Students begin by developing fluency with data—learning to visualize, summarize, and interpret real datasets using R. This establishes the critical skill of “letting data speak” before imposing formal models.

Building Uncertainty Framework (Worksheets 2-6)

Before making statistical claims, students must understand probability as the mathematical language of uncertainty. Starting with basic probability rules and set theory, students progressively work through:

  • Conditional probability and Bayes’ theorem (understanding how information updates beliefs)

  • Discrete distributions (counting outcomes when possibilities are listable)

  • Random variables and expectation (quantifying average behavior and variability)

Bridging to Continuous Phenomena (Worksheets 7-10)

Real-world measurements require continuous probability models. Students explore:

  • General continuous distributions (extending probability to measurements)

  • Uniform and exponential distributions (simple continuous models)

  • The normal distribution (the cornerstone of statistical inference)

  • Checking normality assumptions (connecting theory to practice)

The Inference Bridge (Worksheets 11-12)

These pivotal worksheets transform probability knowledge into statistical reasoning:

  • Sampling distributions reveal how statistics behave across repeated samples

  • The Central Limit Theorem explains why normal distributions emerge everywhere

  • Properties of estimators (bias, variance) guide choosing good statistical methods

Single Population Inference (Worksheets 13-15)

With foundations established, students tackle their first real inference problems:

  • Confidence intervals (quantifying uncertainty in estimates)

  • Hypothesis testing for one mean (making decisions with data)

  • Understanding errors and power (knowing the limitations of conclusions)

Comparative Analysis (Worksheets 16-17)

Most real questions involve comparisons. Students extend single-sample methods to:

  • Comparing two independent groups (treatment vs. control)

  • Analyzing paired measurements (before/after studies)

  • Choosing appropriate methods based on study design

Multiple Groups and Relationships (Worksheets 18-22)

Advanced topics prepare students for realistic research scenarios:

  • ANOVA for comparing multiple groups simultaneously

  • Multiple testing corrections (avoiding false discoveries)

  • Simple linear regression (modeling relationships between variables)

Implementation Guidelines

For Flipped Sections

Before Class: Review assigned lecture videos and readings covering theoretical foundations.

During Class: Work through worksheets in small groups (2-4 students) with instructor guidance

Key Benefits:

  • Immediate application of concepts

  • Real-time feedback from instructors

  • Peer learning through collaboration

  • Active engagement throughout class

For Traditional and Asychonous Sections

Students in traditional lecture and asychonous sections are strongly encouraged to work through these worksheets independently or in study groups. The structured progression provides a more cohesive learning experience than typical textbook problems.

Self-Study Tips:

  • Complete worksheets in order—concepts build sequentially

  • Actually run all R code rather than just reading it

  • Write out explanations for conceptual questions

  • Form study groups to discuss solutions

Why These Worksheets Matter

Traditional homework assignments typically present problems for independent completion after lectures, creating a disconnect between concept introduction and application. These worksheets offer several pedagogical advantages:

Integrated Learning

By combining R programming with theoretical concepts throughout, students immediately see how statistical theory connects to practical data analysis.

Guided Discovery

Questions build progressively within each worksheet, mimicking how statisticians actually approach problems.

Immediate Clarification

In flipped classrooms, instructors can address misconceptions as they arise rather than after submission and grading.

Conceptual Depth

The worksheets encourage deep thinking about “why” rather than just “how,” preparing students for real-world statistical practice.

The Critical Role of Simulation

Throughout these worksheets, simulation serves as a powerful pedagogical tool that transforms abstract concepts into tangible experiences:

Breaking Free from Dangerous Rules of Thumb

Common statistical “rules” like “use z when n > 30” or “5% is always the right significance level” are often presented in introduction level text books in highschool but are an oversimplifications that often lead to incorrect statistical analyses. Through simulation, students discover when and why these rules fail:

  • A sample of n = 30 from a heavily skewed population will often still produce non-normal sampling distributions

  • The “30 rule” ignores the critical role of population shape and variability

  • What matters isn’t sample size alone, but how sample size interacts with the population’s characteristics and the properties of the statistical estimator under consideration.

By simulating from various populations (symmetric, skewed, heavy-tailed, multimodal), students see firsthand when normal approximations break down and when they’re reliable. They learn to assess each situation rather than applying mechanical rules that give false confidence thus building a better intuition for real-world use cases.

Visualizing Uncertainty

By generating thousands of samples and observing how statistics vary, students develop intuition about sampling distributions that no amount of formula manipulation can provide. They see confidence intervals “in action”—understanding that 95% coverage means exactly what it says through repeated sampling.

Testing Assumptions

Students use simulation to explore what happens when assumptions are violated. What if the data isn’t normal? What if samples aren’t independent? By breaking assumptions deliberately and observing consequences, students learn when to be concerned and when methods are robust.

Understanding Variability

Simulation reveals that different samples yield different results—not due to errors, but as a fundamental property of random sampling. This experiential understanding of variability is crucial for interpreting real-world data where we get only one sample.

Connecting Theory to Practice

Abstract concepts like “Type I error rate” become concrete when students simulate thousands of hypothesis tests under the null hypothesis and count false rejections. The Central Limit Theorem transforms from mysterious formula to observable phenomenon as students watch sampling distributions converge to normality.

This simulation-based approach ensures students develop genuine statistical intuition rather than relying on oversimplified rules that fail in practice. When faced with new situations, they can reason from principles rather than searching for memorized procedures.

Worksheets

Individual Worksheets