# Statistical fallacy when not controlling for variables?

When someone says "You never see a Ferrari rust like a Honda", the logical flaw is that a Honda is typically used as daily drivers thru severe winters, while a Ferrari is a 2nd or 3rd car limited to sunny weekend use.

Obviously, you must control for variables such as mileage and weather condition. Is there a name for this fallacy? Logical Fallacy? Base rates fallacy? Differences in groups being compared?

• It seems the kind of reasoning you're referring to would be a kind of inference of causation from correlation, and I don't know if there's a nice name for this, although "post hoc" fallacy (from post hoc ergo propter hoc) might work. Dec 3, 2015 at 21:13

You could call it the omitted variable bias, (although that doesn't have "fallacy" in the name). It is a form of endogeneity; closely related to the omitted variable bias / another form of endogeneity is the ecological fallacy, which does have "fallacy" in the name.

For what it's worth, I'm not sure the statement as you present it ("You never see a Ferrari rust like a Honda") is legitimately a fallacy. It is simply a statement of an empirical observation (and is presumably correct). If someone concluded that Farraris can't rust like Hondas, that would be a fallacy.

There isn't a "fallacy" named after confounding, as far as I know. But if someone mistakenly suggested a causal relationship (like car brand and rusting), we called that a "spurious relationship."

This is not a statistical (associational) fallacy, this is a logical fallacy of a causal claim. Let's take the statement: "you never see a Ferrari rust like a Honda". Statistically this means that the observed rusting in the "population" of Ferraris is somehow different from the observed rusting in the "population" of Hondas. This might be true and it would not be a statistical fallacy at all.

The fallacy comes into play when someone uses that to infer that this observed association is caused by a specific mechanism, such as the intrinsic qualities of Ferraris or Hondas. So, when you claim: "the logical flaw is that a Honda is typically used as daily drivers thru severe winters, while a Ferrari is a 2nd or 3rd car limited to sunny weekend use" what you are doing is explaining a possible causal mechanism that also leads to such association, so the observed association cannot rule out two different causal models.

Therefore, even if the association is legitimate in the population, what might not be legitimate is the causal explanation to that association. This logical fallacy of inferring a specific causal mechanism from association is usually called "false cause". But this fallacy is just the old simple "affirming the consequent" fallacy --- the causal model that Ferrari's are better than Honda's would generate the observed association. But it's a fallacy to conclude that, because the association is true, this specific causal model is true. There are several competing models that could generate the same observed association, such as your alternative explanation of how Ferraris and Hondas will have different usage patterns.

This "spurious" association can come up for several reasons, not only failing to "control" for a variable. When it's due to failure of control of a common cause, we usually call this "confounding bias". But you can actually create a non causal association by controlling for wrong variables. As shown in this other answer, in the model below, "controlling" for the type of car owned by the patient would bias the effect estimate:

This is usually called "collider bias" or "selection bias". You can also have biases due to controlling for mediators, due to measurement error and so on.

You may call it confounding or mediation depending on the exact relationship between the control variables and the variables of interest

• I think he wants a name for a fallacy rather than the phenomenon itself. Dec 3, 2015 at 21:11

"Correlation does not imply Causation".

Clearly CarMake has a very strong CORRELATION with rust: CarMake=Honda often has rust, CarMake=Ferrari never has rust.

But that does not mean that CarMake CAUSES rust. Instead, ConsumerDesireForLuxuryCar causes CarMake=Ferrari, and ConsumerDesireForLuxuryCar also cause TakingCareOfCar which causes NoRust.

I wouldn't disagree with the other answers, but "Correlation does not imply Causation" is a very commonly used phrase in statistics and it succintly captures this situation (and many others too).

• I'm looking for the step beyond "Correlation is not Causation". It's obvious C != C, but WHY is Correlation not Causation in this rust example? Is it just the lurking variable or mileage or seasonal use? Dec 12, 2015 at 1:40