Learning outcomes
- Explain the key idea in your own words.
- Apply the concept to a realistic but fictional research scenario.
- Identify assumptions and limits before interpreting numbers.
Conceptual lesson
A research question should be measurable, bounded and answerable using data. Replace “Are students successful?” with “Are study hours associated with quiz scores among these volunteers?” The unit of observation is a person; a row typically represents one observation. Descriptive, associational and causal questions need different evidence.
Observational studies record existing differences. Randomised experiments allocate treatment conditions by design. Random sampling is not random assignment: the former supports external generalisation, while the latter can support causal interpretation under suitable conditions. Neither should be confused with the other.
Define variables operationally before collecting data: what counts as success, study time or attendance? Consider data collection, confounders, consent, ethics and missingness before analysing results.
Worked research example
Research question for 36 fictional records: “Do the quiz-score distributions differ among groups A, B and C?” The groups are observational labels, not experimental treatments. Any differences cannot be interpreted as proof that a teaching method works better.
Common reasoning trap
Changing the research question after viewing the smallest p-value confuses exploration with confirmatory testing.
Practice tasks
- 1. Rewrite “Students who study more score higher” as descriptive, associational and causal questions.
- 2. Identify the unit of observation, a possible target population, two variables and one confounder.
- 3. Explain one difference between observational research and randomised experimentation.
Explain your reasoning, not just the numerical result.
Optional R practice
Download the fictional CSV into your working folder, then run the script below or download the .R file. No additional packages are needed.
Download CSV · Download R lab · Module 0 refresher
# Statistics Lab / ferdo — synthetic data (no real student records)
# Save stats_synthetic.csv in your working directory.
d <- read.csv("stats_synthetic.csv", stringsAsFactors = TRUE)
stopifnot(nrow(d) == 36, all(c("score_pre","score_post","group") %in% names(d)))
# Groups are observational labels: differences cannot establish a treatment effect.
d <- read.csv("stats_synthetic.csv")
str(d)
head(d)
table(d$group)
# Q: which columns are measurements, and which are identifiers?Stretch: mathematical track
Discuss why random assignment can balance confounders in expectation when estimating treatment effects.
Exit ticket
Write one evidence-bounded claim and one limitation about this week's example.
This week's student workbook
Four original written problems (20 marks) and a formative four-question self-check.