Sunday, April 20, 2008

Solutions to Logical Fallacy I-III

Here are the solutions to the first three sentences that contained a logical fallacy. I showed the six sentences on a poster at the Antwerp conference, and during the poster session people had to guess what the fallacies were. And they won Belgium chocolate! (actually I gave everyone a piece, either for brilliance or effort! :-) The three who gave the clearest correct answers were Dave Rowley, Robin Lickley, and Luc de Nil. The majority knew that they were wrong, but they were unable to clearly formulate why the reasoning was not correct.

I: Correlation-Causality Fallacy

A parent said: "My kid started stuttering after our car accident. Therefore, his stuttering was caused by the accident."

It is true that both events, onset of stuttering and car accident, happened close to each other, but a correlation (relationship between them) must not imply that the accident caused stuttering. There are alternative interpretations. For example, both events happened by chance around the same time, and only a study of 1000 car accidents can exclude the chance factor. If all kids that are in a car accident start stuttering, the chance interpretation needs to be rejected. But, of course, there are millions of kids who had a car accident and did not develop stuttering, and the vast majority of kids who do stutter did not have had a car accident. It helps to look at all cases, and not just focus on one single one.

If A and B are correlated, the interpretation "A causes B" is only one of four possible interpretations. The alternative interpretations are:
1) the correlation between A and B happen by chance. (The car accident happened randomly, and by pure coincidence the kid started stuttering around the same time.)
2) B causes A. (The onset causes the car accident, e.g. the kid was acting strangely before the onset of stuttering and the concerned mother crashed the car out of nervousness!)
3) C causes A and B. (The parents' house was burgled, the kid started stuttering and the parent crashed the car!)

II: Correlation-Causality Fallacy

A therapist said: "We have compiled reliable statistics on 1000 kids over the last 20 years, and we notice that many kids start stuttering around the time of the birth of a younger sibling. Therefore, the emotional effects must cause stuttering at least in some kids."

It is true that many kids start stuttering around the time of the birth of a younger sibling. This is a subtle fallacy related to the third alternative interpretation. Imagine the onset of stuttering is at the age of 20, how many would have younger siblings born at that time? None! What is the most likely age that anyone has a younger sibling born? Around the age of 3, because parents have their children in one go and spaced by two or three years. I use empirical data from a large-scale fertility study and found that 25% of kids between the age of 2.5 and 3.5 witness the birth of a younger sibling. Therefore, both onset of stuttering and the birth of younger sibling are individually linked at age 3, and therefore age 3 links both event.

III: Trigger-Cause Fallacy

A therapist said: "We have compiled reliable statistics on 1000 kids over the last 20 years, and we notice that a traumatic event is often close to onset of stuttering. Therefore, traumatic events can cause stuttering."

It might well be true that the occurence of a traumatic link is statistically closer to onset of stuttering than it should be. However, this does not imply a causal link. We need to be more careful with the word cause. In fact, an alternative and most likely interpretation is that a traumatic event is a trigger (the last drop) that makes stuttering appear. The kid might well have started stuttering anyway even without a traumatic event, but the traumatic event led to a shock and accelerated the appearance. In fact, it might even delay appearance but we would never be able to witness such a delay because trauma and onset is more spaced in time. Think of your old car, it will break down earlier if you do a long journey now and in 2 weeks later if you postpone the journey by two weeks. Surely, you would not assign a cause to the journey!

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