Overview

Statistics begins with a simple difficulty: the information available is incomplete. This course studies how probability and statistical reasoning help distinguish what is known, what is estimated and what remains uncertain.

Rather than presenting a catalogue of tests, the course is organized around questions of evidence. Learners examine conditioning, base rates, sampling, likelihood, estimation, uncertainty, regression and common sources of misleading inference.

Examples are drawn from research, business, public policy and data analysis so that the same reasoning habits can be transferred across domains.

Learning objectives

By the end of the course, learners should be able to:

• reason with conditional probabilities and base rates;
• distinguish population quantities from sample estimates;
• interpret confidence, likelihood and uncertainty without common verbal errors;
• recognize selection bias, multiple testing and regression pitfalls;
• evaluate whether statistical evidence supports a stated claim;
• formulate useful follow-up questions when evidence is incomplete.

Intended participants and prerequisites

Course structure

The course is organised into six units. Each unit combines concise explanation, worked examples and short analytical exercises.

Unit	Subject	Principal questions
1	Probability and conditioning	How should beliefs change when new information arrives?
2	Random variables and expectation	How are uncertain outcomes summarized and compared?
3	Sampling and estimation	How can a finite sample inform a larger population?
4	Likelihood and uncertainty	How should evidence about unknown parameters be represented?
5	Regression and association	What does an estimated relationship mean, and what does it fail to establish?
6	Statistical failure modes	How do selection, multiplicity and weak assumptions produce misleading conclusions?

Teaching and assessment

Teaching is delivered through concise lectures, technical notes, worked examples and guided exercises. AI-supported interaction may be used to explain concepts, generate additional practice and challenge a learner's reasoning, but assessment remains based on the learner's demonstrated understanding.

Component	Purpose	Weight
Short exercises	Check understanding of the principal concepts	40%
Applied investigation	Use the course framework on a new problem or dataset	30%
Final assessment	Integrated reasoning across the course	30%

A certificate of completion is issued only when the required assessments have been completed at the stated standard. Participation alone does not constitute completion.

Faculty

Materials and technical requirements

Learning environment

Learners need a current web browser and access to the Gordon learning platform. Where a course uses code, spreadsheets, datasets or external readings, the relevant requirements are identified inside the unit.

Course materials

Required readings, datasets and practice materials are identified within each unit. Public courses are designed so that required core materials can be accessed without a separate tuition charge.