Module 0 — What Is Statistics?
Version: 1.0 · Level: First-year university · Duration: 40–45 min · Prerequisite: No R required.
Central question
How do we move from a number to a claim — and where must we stop?
Learning outcomes
- Explain statistics as reasoning with data under uncertainty.
- Distinguish a population from a sample and an observation.
- Separate description of observed data from inference about a wider population.
- Explain why association is not the same as causation.
- Recognise selection bias and write a well-bounded statement.
What is statistics?
Statistics is the discipline of investigating questions about the world using data, accounting for variation, measurement and uncertainty. We describe observations and, with appropriate designs and assumptions, make inferences about a wider population.
Fictional observational example
Eight volunteers in a hypothetical class reported study hours before a short quiz and their resulting scores. These are not real UCL student records.
| Student | Study hours | Quiz score |
|---|---|---|
| 1 | 1 | 50 |
| 2 | 2 | 55 |
| 3 | 2 | 62 |
| 4 | 3 | 64 |
| 5 | 4 | 70 |
| 6 | 5 | 72 |
| 7 | 5 | 78 |
| 8 | 6 | 86 |
Descriptive result: The mean study time is 3.5 hours and the mean quiz score is 67.125 among these eight volunteers. These cannot automatically be generalised to all students. Volunteers may be subject to selection bias, and the apparent association does not establish a causal relationship.
Three misconceptions
- Description = generalisation: An observed group mean is not automatically a population mean.
- Association = causation: Prior knowledge, motivation and other explanations remain possible.
- More data = automatic validity: Systematic selection or measurement bias may persist in large datasets.
Teaching sequence: 40–45 minutes
- 0–5: What question could statistics help answer?
- 5–12: Inspect observations and distinguish sample from target population.
- 12–22: Predict and calculate means; interrogate generalisation.
- 22–30: Explore bias and causation.
- 30–40: Complete the five-question self-check.
- 40–45: Exit ticket and optional R bridge.
Five self-check questions
- Do the eight volunteers form a sample or the entire population?
- Is the claim “The eight volunteers averaged 67.125 points” descriptive or inferential?
- Does this observational dataset prove that study time causes higher scores?
- Why might voluntary participation introduce bias?
- Rewrite “All students study for 3.5 hours” so that its scope is accurate.
Exit ticket: Rewrite “More studying definitely makes everyone successful” while describing the evidence and at least one limitation.
Optional R bridge
study <- data.frame(
id = 1:8,
study_hours = c(1,2,2,3,4,5,5,6),
quiz_score = c(50,55,62,64,70,72,78,86)
)
mean(study$study_hours) # 3.5
mean(study$quiz_score) # 67.125
plot(study$study_hours,study$quiz_score,
xlab="Study hours",ylab="Quiz score",pch=19)The plot displays association, not proof of causation.