An analyst finds that students who use the campus library more have higher CGPAs (correlation 0.45, p-value 0.01) and concludes "library use causes higher grades". Critique this. What does the p-value actually mean, and how could you test causation?
Show the explanation
Correlation does not show causation. A correlation of 0.45 says the two variables tend to move together. It does not say why. The alternatives:
- Confounding: a third factor drives both. Motivated or well-organised students both visit the library more and score better.
- Reverse causation: students who already do well may enjoy studying in the library.
- Selection effects: for example, only students living near campus are counted.
- Chance: if you test many variable pairs, some will look significant by luck. This is the multiple-comparisons problem, sometimes called p-hacking.
What the p-value means. Assume the null hypothesis is true: here, no real association in the population. The p-value is the probability of getting data at least as extreme as what was observed, under that assumption. A p-value of 0.01 means that if there were truly no association, a correlation this strong would show up about 1% of the time.
What the p-value does not mean
- It is not the probability that the null hypothesis is true, and not a 99% chance that the effect is real.
- It says nothing about causation or about how large the effect is. A tiny, useless effect can have a very small p-value in a huge sample. Report effect sizes and confidence intervals.
- Passing a 0.05 cut-off is a convention, not proof. Results near the threshold deserve caution. Replication matters.
How to get at causation
- Randomised controlled experiment (A/B test): randomly assign students to, say, a library-study programme or not. Randomisation balances the confounders on average, so a difference in outcomes can be attributed to the treatment.
- When an experiment is not possible, use observational causal methods, each with its own assumptions: controlling for measured confounders (regression, matching or propensity scores), difference-in-differences, instrumental variables, regression discontinuity, natural experiments.
- Domain reasoning: is there a plausible mechanism, a dose–response pattern, and a time order where the cause comes before the effect?
A good interview answer: "This is evidence of association, not causation. I'd check for confounders like prior academic performance, report the effect size with a confidence interval, and, if the decision matters, run a randomised pilot."
Original UniCircle question. Last reviewed 22 Oct 2026.