Three pupils ran a survey for the school science fair. They asked everyone in their year whether they had eaten breakfast that morning, and then compared the answers with the term's test scores.
The result was clear. Pupils who ate breakfast scored higher on average, and the difference was too large to be chance. Their first draft ended with the sentence: eating breakfast improves test scores.
Their teacher asked them one question. What else is true of a pupil who eats breakfast on a school morning?
They thought about it and produced a list. That pupil probably went to bed at a reasonable hour. That pupil probably was not rushing. That pupil lives in a household where somebody has time in the morning. Any of those could raise a score on its own, and none of them is breakfast.
The survey could not separate them, because it had only observed what pupils already did. To show that breakfast itself does the work, somebody would have to assign it — and that is a different and much harder study.
The teacher told them this was not a failure of their work. Noticing what a study cannot show is part of doing the study.
They changed the last sentence to: eating breakfast is associated with higher scores in this year group. It is a smaller claim, and it is the one their data can carry. It won the fair.