Foundations of Inquiry · Lesson 024 · November 13, 2026
Learning objectives
By the end, you can distinguish correlation from a causal claim, explain counterfactual reasoning, identify a plausible confounder, and design a fairer test of an explanation.
From a pattern to a cause
Two quantities can move together without one causing the other. A causal claim asks whether changing one factor would change an outcome, holding relevant alternatives in mind. Observational associations are valuable clues, but shared causes, reverse causation, selection and chance can produce misleading patterns.
The counterfactual question
Imagine two otherwise comparable versions of a student: in one version the student receives a ten-minute practice quiz; in the other, they do not. The causal effect for that student would be the difference between their outcomes in those two versions. We cannot observe both versions of the same person at the same moment, so experiments and carefully designed observational studies try to estimate the missing comparison.
Worked example: a fair comparison
Suppose 40 fictional students volunteer for a study. Researchers randomly assign 20 to take a practice quiz and 20 to study without it. Later, 16 of the quiz group and 12 of the comparison group answer a target question correctly. The observed success rates are 16/20 = 80% and 12/20 = 60%; the estimated difference is 20 percentage points (0.80 − 0.60 = 0.20). This is a difference in these hypothetical groups, not proof of a universal 20-point effect. Small samples have uncertainty, and random assignment supports causal inference only when implementation and outcome measurement are sound.
What could go wrong?
If students choose whether to take the quiz, motivation or prior preparation might influence both participation and scores. That is potential confounding. Even randomized trials can suffer from attrition, unequal instruction, measurement problems or chance imbalance. Do not confuse a controlled comparison with a guarantee of certainty.
Try it: design a mini-study
Ask whether using a checklist reduces missed steps in a simple, safe classroom task. Write a measurable outcome (number of missed steps out of 10), decide how participants would be assigned, standardize instructions, and explain what data would change your mind. If you cannot randomize, name at least two alternative explanations you would need to investigate.
Reflection
What is the difference between “students who quiz themselves score higher” and “giving a practice quiz improves scores”? Which statement is descriptive, and which requires a causal design?
Knowledge check
- What is the counterfactual in a causal question?
- Calculate the risk difference when 9/15 succeed in group A and 6/15 in group B.
- Does randomization remove every possible source of bias?
Answer key
- The outcome that would have occurred under an alternative exposure or intervention for the same unit.
- 9/15 = 60%; 6/15 = 40%; difference = 20 percentage points.
- No. It reduces systematic baseline confounding in expectation, but chance imbalance, attrition, measurement error and implementation problems can remain.
Limits
Ethical constraints, sample size, external validity, unmeasured factors and the assumptions behind any statistical model all limit causal conclusions. This lesson’s numbers are invented for instruction, not evidence of an actual intervention.
