Quantitative Reasoning Activity

Correlation VS Causation

Objective:Students will identify whether a relationship between two quantities is correlationalor causal. This will in turn teach students to express quantitative evidence (or lack thereof) in support (or in opposition) of an argument in terms of statistical evidence and how it is contextualized.

Background:Correlation means that A and B tend to happen at the same time, whereas causation means A implies B. The two concepts are often and erroneously used interchangeably. This leads to cases where correlation is used to give the impression that there is a causal relationship. It is therefore especially important to understand the difference between them. Students should learn to ask themselves: Is that correlation or causation? If it is correlation, what might be an underlying cause? When two quantities A and B are correlated, it can sometimes be explained by an underlying cause, some event that is causing both A and B.

The following example may seem a bit silly, but it illustrates how two things can be correlated even when they have nothing in common.

Activity: Students should read the article “Eating Breakfast May Beat Teen Obesity” on WebMD ( In it, there are the following statements.

“regular breakfast eaters seemed more physically active than breakfast skippers”
“teens who regularly ate breakfast tended to gain less weight and had lower body mass index than breakfast skippers”

For each one, answer the questions:

Is the statement describing correlation or causation?
Is there an underlying cause that can explain both events?
Is the statement misleading?

Suggested Solutions:

a.1. Correlation.

2. Maybe being health conscious causes people to be physically active and eat breakfast.

3. The statement isn’t technically saying anything incorrect. It could even be argued that it isn’t misleading at all since it uses the word “seemed”, which is not a very strong word. However, the average person reading that sentence might believe that it’s saying that there is reason to believe that eating breakfast gives you the energy to be physically active. In fact, it’s possible that the causal relationship is actually reversed. Maybe activity causes breakfast. Maybe people who are active tend to be hungry in the morning. This could even mean that being active and not eating breakfast would cause weight loss, since you’re doing exercise and lowering your calorie intake.

1. Correlation.

2. Maybe people who sleep late and don’t get enough sleepwake up later and then miss breakfast; and simultaneously lack of sleep causes obesity. In other words, lack of sleep could be the underlying cause of skipping breakfast and being obese.

Maybe physical activity causes eating breakfast and not being obese, and this is what explains the correlation between skipping breakfast and obesity, i.e. skipping breakfast and obesity happen together, but only because the person is inactive. This would mean that eating breakfast wouldn’t help prevent obesity, being active would however.

3. Again, the statement is not incorrect, but it is not explicit about the relationship being correlational as opposed to causal.

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