The regressive fallacy

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John Jackson © UK-Skeptics

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This fallacy is committed when the natural fluctuations around an average position are not taken into account when providing explanations of events.

Regression or “regression to the mean (or average)” refers to the tendency of a variable characteristic to move away from extreme values towards the average value.

The weather is a good example of this tendency. Occasionally in the UK we get some very nice weather. It is, however, far from average and soon returns to its normal gloomy self. Likewise with excessive rain. We occasionally get excessive rainfall, but it soon returns to its normal value. Most of the time the weather is average and these unusual occurrences are fluctuations or deviations around the average. We get peaks and troughs but things always return back to their normal or average values.

The same principle occurs with most measurements such as golf scores, your ability to do crossword puzzles, the amount of pain caused by a medical condition, etc.

The regressive fallacy is most commonly committed in relation to chronic illnesses. People will seek out treatments when they are feeling at their worst. Due to “regression to the mean”, their condition will improve with time; however, they will attribute their improvement to the remedy rather than normal fluctuation.

Examples:

• Someone may swear that chiropractic works as every time their bad back becomes painful they visit their chiropractor, and a few days after chiropractic treatment, it improves again.
  
  
• People may be convinced that Emu Oil is effective for arthritis as whenever their knees, for example, get particularly bad they rub Emu Oil into them and they improve over the next day or two.

In both cases the regressive fallacy can explain what’s going on. As can be seen in the diagram below, the blue line represents a typical course for a “flare up” of a condition. The condition is at an average level, then tends to dip to a low as the symptoms get worse before returning back to the average.

When the symptoms are at or around their worst, people will be more likely to take some form of medication. As can be seen from the diagram, any form of treatment or remedy taken at points A, B, or C will be followed by the improvement as the condition returns back to its average. This can lead to the illusion of ineffective treatments actually working.

Note: a remedy taken at point A will see a slight worsening before the improvement. Alternative practitioners put this down to a “healing crisis” – they often claim that the slight worsening of symptoms is due to the body expelling “toxins” and claim that it’s proof that their remedy has started working.

Other examples.

1. In sport, football strikers, for example, often go through a hot patch where they score prolifically, followed by a lean spell where they get scrutinised and criticised for being out of form. In reality, the hot and cold spells are just fluctuations around their average.
   
   
2. In a test for psychic ability the psychic has to predict what the card will be from a pack of Zener Cards. The score expected by guessing is 25 out of 125 but in the first run the psychic scores 38/125. In a second run he scores 33/125. In subsequent runs he scores around the expected value of 25/125. Is this evidence of a gifted psychic whose scores are diminishing due to the decline effect or regression to the mean after a high score that arose purely by chance?
   
   
3. An increase in accidents on a particular road is a prerequisite for the introduction of speed cameras on that road. So, after a particularly high number of accidents on some roads, the police introduce speed cameras to reduce speeding and, by assumption, accidents. It is found that the number of accidents reduces on these roads in the following year. Does this prove that speed cameras are an effective road-safety measure or has the accident rate simply fallen back to the average after a chance peak?

The regressive fallacy can work in the opposite direction too. There was the notion that athletes who appeared on the cover of the US magazine Sports Illustrated were jinxed by appearing on the cover as after they had done so their performance would always drop afterwards. Of course, they were on the cover of the magazine simply because their performance had recently peaked and now, as would be expected by regression to the mean, their form was simply moving back toward its average value.

Whenever an intervention is performed because of a fluctuation around an average position or value and a conclusion is reached, a fallacy can occur because of the mis-attribution of cause and effect. This can give rise to a powerful illusion however, as it is often reinforced by repeated behaviour; particularly with regard to chronic illnesses: whenever action is taken because of peaks and troughs around an average and the value returns to normal, it can reinforce the idea that the action is efficacious.