# What logical fallacy is made in this statement?

Consider this text:

Researchers conducted two different types of test on a large group of people. After that, the researchers subjected the people 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.

Fact 1: Score of test T1 affects response R.

Fact 2: Score of test T1 affects score of test T2.

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 logical fallacy(s) did the researchers made?

This is a very important concept in statistical experiments, with the issue being a confounding variable. The researchers are making the common mistake of assuming that correlation implies causation, whereas many examples (such as yours) explicitly demonstrate that this is not true. There are a host of methods meant to avoid this kind of mistake, like having a control, pairing subjects, etc.

I don't know of a particularly formal formulation of this error, but it can be called the false cause fallacy.

• -1'd, for the reason that there are no conclusions being made here about causation. researchers in the described example are looking for an interaction, not testing for causality. There is no logical fallacy here. what has occurred is researchers have not correctly run the statistical operations. The correct formula is either a moderation or mediation analysis, where it's possible to find the strength of the relationship between T2 and R by controlling for the effects of T1 on T2, showing the relation to be between T1 and R Sep 10, 2012 at 6:48
• @Seldom Sorry, but I think you're working with a slightly unusual definition of "affect". I'm quite certain that the OP's meaning was causation, i.e. the same "affect" as "light received from Sun affects temperature" and "time spent on homework affects final grade." Sep 10, 2012 at 14:18
• +1 against the -1. The word "affect" means "to act on; produce an effect or change in". The researches have assumed that correlation is causation. This is the "cum hoc ergo propter hoc" fallacy. Sep 10, 2012 at 20:19
• .. thinking about this more, if 'affect' is conflated with cause, then this is indeed an example of cum hoc ergo propter hoc. i'm currently doing a unit in advanced stats for the behavioural sciences, and this change of terminology is a little confusing. For clarity i've just posted this question at the Cross Validated beta here. Affect is a fairly vague term in the wretched world of statistics, which i have not seen in common usage. A regression, moderation or mediation analysis would correct for this error. Sep 11, 2012 at 1:52
• ^ which detect interactions and correlations, not causation. Sep 11, 2012 at 1:56

There is an ambiguity in your notion of 'affects' here.

If you mean they are statistically correlated, this cannot happen, the correlates of correlates are proportionally correlated.

If your notion of 'affects' is about causation rather than prediction, you need a theory of causation linking T2 to R, in terms of which the experiments about T1 would need to be reframed, in order to establish what you indicate.

Statistics indicate where to look for causation, but they do not express or test for causation itself. Their error, if they are discussing causation without a causal theory is to misunderstand that correlation does not imply causation.