What error is it to assume a test causes a response when it in fact only correlates with another test that causes a response?

Question

Researchers conducted two different types of test on a large group of people. After that, the researchers subjected participants to situations like Z and noted their response R. Those with high scores on test T2 had a good response. Likewise, those with low scores on test T2 had a bad response. Therefore, researchers conclude that the score of test T2 affects the response R.

However, the underlying truth is:

1. Score of test T1 affects response R.
2. Fact 2: Score of test T1 affects score of test T2.
3. Fact 3: Score of test T2 does not affect the response R.

Here, the researchers wrongly assumed that the score of test T2 affects the response R. However, it is not true because the real culprit is test T1.

What error have the researchers made, and what is the correct statistical procedure for this scenario? I.e., What error is it to assume a test causes a response when it in fact only correlates with another test that causes a response?

Answer 1

If "affect" means "cause" then what you are saying is that there is a causal relation of the score on test 1 with the score on test 2 and the score on test 1 with the response R but the resulting correlation between test 2 and the response is not indicating a causal relationship between test 2 and response R but rather a result of the connection of test 2s scores with test 1s score.

Answer 2

The researchers have assumed that correlation means causation.

The error is related to what is known as the "third variable problem". I.e., there is a third variable that is causing both the predictor test and the criterion variable.

There are many classic examples of this:

• Ice cream consumption correlates with drowning; the third variable is the weather; hot weather causes ice cream consumption and swimming which in turn causes drowning.