Monday, August 13, 2012

regressive fallacy

The regressive fallacy is an error in causal reasoning: the failure to take into account natural and inevitable fluctuations when ascribing causes to events (Gilovich 1993: 26). Golf scores and chronic back pain, for example, inevitably fluctuate. Periods of low scores or little or no pain are eventually followed by periods of higher scores or more intense pain. Ignoring natural fluctuations can easily lead to the availability bias driving one to confirm a favored causal explanation based on little more than that one thing happened after the other (the post hoc fallacy).

A professional golfer with chronic back pain or arthritis, for example, might try a copper bracelet on his wrist or magnetic insoles in his shoes when he is not playing or feeling well. He notices that his scores are improving and his pain is diminishing or gone. He concludes that the copper bracelet or the magnetic insole is the cause of his feeling and playing better. He doesn't consider that the scores and the pain are probably improving due to natural and expected fluctuations. Nor does it occur to him that he could check a record of all his golf scores to see what kind of fluctuation in scoring has occurred in the past. If he takes his average score as a base, most likely he would find that after a very low score he tended to shoot not a lower score but a higher score in the direction of his average. Likewise, he would find that after a very high score, he did not tend to shoot another higher score but rather would shoot a lower score in the direction of his average. In fact, overall it is inevitable that a golfer's scores tend toward the average.

This tendency to move toward the average away from extremes was called "regression" by Sir Francis Galton (1822-1911) in a study of the average heights of sons of very tall and very short parents. (The study was published in 1885 and was called "Regression Toward Mediocrity in Hereditary Stature.") He found that sons of very tall or very short parents tend to be tall or short, respectively, but not as tall or as short as their parents. On reflection, Galton's discovery seems like common sense: it seems obvious that children can't get taller or shorter ad infinitum.

Many people are led to believe in the causal efficacy of questionable therapies and treatments because of the regressive fallacy. The intensity and duration of an illness or of pain from arthritis, chronic backache, gout, etc., fluctuate. A remedy such as acupuncture, a chiropractic spinal manipulation, a homeopathic potion, or a magnetic belt is likely to be sought when the illness or pain is at its worst. The illness or pain in most cases would begin to lessen after it has peaked. It is easy to deceive ourselves into thinking that the remedy we sought caused our reduction in suffering. It is because of the ease with which we can deceive ourselves about causality in such matters that scientists do controlled experiments to test causal claims. Such experiments reduce the chances of self-deception and confirmation bias that inevitably accompany personal experience.


  1. People do not like being told this. It destroys their dreams (their golf scores will continue to improve) and hope that their pain will go away. Skeptics have to find ways to challenge people without knocking the chair out from under them.
    How can the fallacy be adjusted so the person delivering the 'bad' news isn't seen as being bad and the lessons learned will be beneficial.
    Brian Iverson

  2. I don't think this post is up to your normal outstanding standard of posting. And I don't think this lapse represents an example of you regressing toward the mean.

    The problem is that the phenomenon of regression toward the mean is a mathematical quirk arising out of imperfect correlations. It is not a phenomenon that has explanatory value for changes in the lives of any particular individual. Regression to the mean is observed with data for subgroups found at either extreme end of a distribution of scores for a particular variable. Although some in the subgroup may be linked to an even more extreme score on the same variable measured at a different time or for another variable, most of those with the most extreme scores will tend to be relatively less extreme. Regression to the mean is a matter of tendency toward less extreme relative position not less extreme magnitude of scores in absolute terms.

  3. Nearly 30 years ago, when I was in my late 30s, I knew a man who suffered from arthritis and who wore a copper bracelet. He maintained that it made his arthritis much less bad. It occurred to me that prevention is better than cure, so I bought a copper bracelet for myself. It was very cheap. I wore it for about 15 years, until it broke. Somehow, I never got round to buying a replacement. I am now 66, and have no arthritis. True story, but exactly what can one extract from it?
    You might say that my use of the bracelet as a prophylactic was a brilliant decision, which has kept me free of arthritis up till now (and maybe not a second longer). Or you might say that I'm simply not the type that gets arthritis. Absence of arthritis (or anything else) is a negative condition, and nothing can ever be proved using negative conditions alone. Of course, if I came from a family which was very prone to arthritis (I don't), and if I was the only member who had used the bracelet AND the only one who had avoided the condition, it would seem intuitively likely that there was an association. In that case, one would search for a mechanism.
    Aho! Perhaps I should buy another bracelet. They probably cost a lot more now, maybe as much as a pub lunch and a couple of pints.