This pathway is designed for introductory teaching, tutoring and self-study. No assumed R knowledge; advanced mathematics is clearly separated from the core.
Mathematical foundations pathway
Eight optional mathematical units from probability to regression.
14 weekly worksheets
Independent weekly practice and formative checks
Core learning outcomes
- Construct testable research questions and distinguish observational from experimental designs.
- Summarise data using justified graphs and descriptive statistics.
- Explain probability, sampling variability, confidence intervals and hypothesis tests.
- Choose, interpret and critique common statistical methods.
- Produce an ethical, reproducible analysis with appropriately bounded claims.
Weekly timetable
| Week | Unit | Evidence of learning | Estimated class time |
|---|---|---|---|
| Prep | What is statistics? | Distinguish statistical reasoning from code. | 40–45 min |
| 1 | Research design | Connect a research question to a unit of observation. | 70–90 min + optional lab |
| 2 | Data and measurement | Create a data dictionary and audit missingness. | 70–90 min + optional lab |
| 3 | Descriptive statistics | Interpret a mean alongside its distribution. | 70–90 min + optional lab |
| 4 | Probability | Distinguish conditional probabilities. | 70–90 min + optional lab |
| 5 | Sampling, intervals and power | Explain confidence-interval coverage correctly. | 70–90 min + optional lab |
| 6 | Hypothesis testing | Interpret a p-value conditionally. | 70–90 min + optional lab |
| 7 | t-tests | Choose a t-test based on the study design. | 70–90 min + optional lab |
| 8 | Correlation | Explain why correlation does not prove causation. | 70–90 min + optional lab |
| 9 | Regression | Critique slope estimates and residuals. | 70–90 min + optional lab |
| 10 | ANOVA | Distinguish omnibus and multiple comparisons. | 70–90 min + optional lab |
| 11 | Chi-square | Inspect expected counts and within-group percentages. | 70–90 min + optional lab |
| 12 | Non-parametric tests | Choose rank-based alternatives for a reason. | 70–90 min + optional lab |
| 13 | Reproducibility and ethics | Produce a reproducible ethical report. | 70–90 min + optional lab |
| 14 | Capstone research project | Carry an analysis independently from question to claims. | 70–90 min |
Suggested weekly learning cycle
- 15 min: research question and prior-knowledge check.
- 20 min: concepts, visual reasoning and a worked example.
- 20 min: student explanation and short problem set.
- 15–25 min: optional R lab or additional conceptual exercise.
- 10 min: limitations, feedback and exit ticket.
- 30–60 min optional independent practice before the next week.
Path A — psychology / social science
Emphasise research design, variables, descriptives, interpretation, t-tests, correlation, ANOVA, chi-square, non-parametric alternatives, responsible reporting and base R practice. PALS0046 is a plausible reference but not verified as the student's module.
Path B — mathematical statistics
Supplement the core with combinatorics, conditional probability, random variables, common distributions, expectation and variance, sampling distributions, standard error, the central limit theorem, estimator properties and formal derivations. Our existing stretch prompts are starting points, not a full replacement for UCL STAT0002, STAT0003 or STAT0004.
Recommended assessment architecture
Use formative weekly exit tickets, independent concept exercises and optional R worksheets. The capstone uses a 100-point rubric in the assessment centre; these weights are proposed teaching tools, not actual UCL grade weights.