Thinking with and describing data
9 draft lessons in this unit
Fourteen-week teaching sequence · First-pass curriculum
One complete course. Four units. Fourteen weeks.
Begin with designing a question, learn how to reason about incomplete evidence, and finish by carrying out a reproducible empirical investigation.
Curriculum status: The entire first-pass reading sequence is now drafted. This is not yet a classroom-reviewed or video-complete course. The reading material remains subject to mathematical and editorial review. The assessment and capstone framework is available for instructional development, not accreditation.
Read or print the complete 45-chapter manuscript →
What a student should learn
Sampling, probability, and distributions
12 draft lessons in this unit
Statistical estimation and inference
13 draft lessons in this unit
Models, causal limits, and research practice
11 draft lessons in this unit
Weekly course of study
- Week 01
Questions and study design
Identify the population, variables, study design, and inferential limits.
Week 1 investigation: Design a statistical study, manipulate recruitment and assignment, and self-check eight decisions →
Weekly lecture: Read the presentation script →
Weekly deliverable: Submit a research question and study-design critique. See detailed assignment →
- Week 02
Describing evidence without misleading the reader
Inspect raw records, summarize center and spread, and construct honest graphics.
Weekly lecture: Read the presentation script →
Weekly deliverable: Audit and visualize a small dataset with captions. See detailed assignment →
- Week 03
Association and sampling design
Distinguish descriptive association from population inference; inspect selection and clustering.
Weekly lecture: Read the presentation script →
Weekly deliverable: Compare representative and systematically selected samples. See detailed assignment →
- Week 04
Probability foundations
Count outcomes and compute conditional probabilities under explicit models.
Weekly lecture: Read the presentation script →
Weekly deliverable: Construct a conditional probability tree and explain its denominators. See detailed assignment →
- Week 05
Base rates and discrete distributions
Use Bayes, expected values, binomial and Poisson models.
Weekly lecture: Read the presentation script →
Weekly deliverable: Interpret rare-event evidence and validate a count model. See detailed assignment →
- Week 06
Continuous and sampling distributions
Use density areas, normal probabilities, and the central limit theorem.
Weekly lecture: Read the presentation script →
Weekly deliverable: Explain a simulated sampling distribution. See detailed assignment →
- Week 07
Confidence intervals for means and proportions
Interpret coverage, t intervals, Wilson score intervals, and data assumptions.
Weekly lecture: Read the presentation script →
Weekly deliverable: Calculate and interpret two intervals, including limitations. See detailed assignment →
- Week 08
Comparing two groups
Analyze independent means, paired changes, and differences in proportions.
Weekly lecture: Read the presentation script →
Weekly deliverable: Choose the appropriate two-group procedure based on design. See detailed assignment →
- Week 09
Null hypothesis tests and categorical data
Explain p-values and compare observed to expected category counts.
Weekly lecture: Read the presentation script →
Weekly deliverable: Report a test, effect size, assumptions, and a cautious conclusion. See detailed assignment →
- Week 10
Power and multiple comparisons
Balance study-design risks and recognize selective reporting.
Weekly lecture: Read the presentation script →
Weekly deliverable: Critique an underpowered or selectively reported study. See detailed assignment →
- Week 11
Randomization and bootstrap methods
Enumerate assignments and resample empirical data.
Weekly lecture: Read the presentation script →
Weekly deliverable: Document a reproducible inference simulation. See detailed assignment →
- Week 12
Confounding and linear regression
Investigate Simpson's paradox, fitted lines, residuals, and slope uncertainty.
Weekly lecture: Read the presentation script →
Weekly deliverable: Analyze a bivariate dataset and diagnose a model. See detailed assignment →
- Week 13
Additional models and causal limitations
Study ANOVA, logistic regression, causal designs, and missingness.
Weekly lecture: Read the presentation script →
Weekly deliverable: Compare models and audit omitted observations. See detailed assignment →
- Week 14
Reproducible analysis and capstone
Fit a multivariable model, document the analysis, and submit a transparent report.
Weekly lecture: Read the presentation script →
Weekly deliverable: Complete the capstone research project and self-critique. See detailed assignment →
Assessment and capstone
Each unit uses conceptual checks, numerical applications, and an explanation of the inference limits. The final research capstone requires a documented empirical question, a data audit, analysis, interpretation, reproducible R code, and a scored rubric.
Read the instructor laboratory guide, experiment in the R Workbench, and inspect the historical air-quality field notebook.
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