The Human Truth Foundation

Statistical Regression
Causes of Strange Beliefs and Pseudoscience

By Vexen Crabtree 2017

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#psychology #thinking_errors

The regression fallacy occurs when people extract too much meaning from chance events under specific circumstances. Disease and fortune come and go: because of the law of regression when things are at their worst they are likely to simply get better on their own no matter what we do. But when things are bad, some will "try" all manner of superstitious, meaningless and misguided practices - including all kinds of alternative therapies. Social psychologist David Myers agrees: "when things reach a low point... whatever we try - going to a psychotherapist, starting a new diet-exercise plan, reading a self-help book - is more likely to be followed by improvement than by further deterioration"1. Because we rarely employ controls and statistical analysis in our personal lives, it seems that any attempted solution, from the zany to the insane, has actually worked. This is the cause of untold numbers of superstitions, magical practices, religious beliefs and pseudoscience, and can sometimes lead large numbers of people astray, especially when stories and anecdotes are published by the press.2,3,4

This is why many cults, religions and pseudo-therapeutic fads prey on the weak, depressed, down-and-outs and those who have recently experienced catastrophe. Such people are more likely to try new religions5.

The solution is to be more cognizant of Human thinking errors. Cause and effect must be analyzed statistically, carefully, and by (social) scientists who know how to discount confounding factors. Simply put: do not assume that some action or event causes a change in the frequency of another event without investigating it properly; no matter how much it goes against common-sense to deny the correlation, cognitive thinking errors such as the regression fallacy can easily lead us to false conclusions based on limited data.

1. Anecdotes, Desperation and Luck: The Causes of Error

If you pick cards randomly from a pack (perhaps, the lower value of the card, the less likely we are to win the game), when we pick a low card it is likely to be followed by a higher card. When we pick a few low cards in a row, we are equally likely to pick a higher card next time. If, when we have picked a series of low cards, we perform some action (such as putting on a hat), we can mistakenly attribute the ending of the losing streak to the fact that we just put on a hat. On average, things return to the normal, and with a series of results this is called the regression to average.

Tversky and Kahneman (1974) noted [that we often] fail to recognize the statistical phenomenon of regression toward the average. Because exam scores fluctuate partly by chance, most students who get extremely high scores on an exam will get lower scores on the next exam. Because their first score is at the ceiling, their second score is more likely to fall back ('regress') toward their own average than to push the ceiling even higher.

"Social Psychology" by David Myers (1999)1

Many kinds of pain, especially back pain, come and go. We are likely to seek some sort of alternative treatment when things are at their worst, which is exactly the time that things will start getting better on their own. Scientists call this regression to the mean.

"Unnatural Acts: Critical Thinking, Skepticism, and Science Exposed!" by Robert Todd Carroll (2011)4

The social psychologist David Myers explains that "when things reach a low point, we will try anything, and whatever we try - going to a psychotherapist, starting a new diet-exercise plan, reading a self-help book - is more likely to be followed by improvement than by further deterioration"1, and this statistical naïvety often leads people into thinking some supernatural 'luck' or religious 'reward' has taken place. This explains why a conversion to a new religion when done at a low point in one's life, often leads to an improvement. The same with making sacrifices to a new god, or praying harder than normal; if done during desperate times (such as during drought, alcoholism or financial ruin), the chances are things will get better simply because the law of regression takes effect, but in practice many would mistakenly attribute their reversed fortunes to their new supernatural affiliation.

This would explain why many cults and religions prey on the weak, depressed, down-and-outs and those who have recently experienced catastrophe. Such people are more likely to try new religions5. The Synagogue Church of All Nations (SCOAN) is one example Christian faith-healing church, finding support amongst the poor, ill-educated and desperate victims of cancers and AIDS (click for more on SCOAN). It is amongst these people that they find recruits are most likely to attribute their recovery to the religion, and therefore such people tend to cling to their new religion harder than others who would be tempted to judge the religion on more openly rational grounds.

The 'evidence' can often appear very convincing, but, with a lack of controls and without proper statistical analysis, mistaken conclusions are very easy to make and once established it can be hard to convince people that they are wrong. Social psychologist and critical thinker Thomas Gilovich has explained the basics of statistical regression perfectly well:

Book CoverRandom values will fluctuate, and whenever you get especially high values they are very frequently followed by more normal lower values. This is called the regression effect, and it is an important part of year-one statistics studies. [...]

Problems unfold in fits and starts, with periods of deterioration mixed with episodes of improvement. It is these temporary periods of relief that give rise to erroneous perceptions of a treatment's effectiveness. When, after all, will a treatment most likely be applied? Generally, it will be administered when there is a marked deterioration in the person's condition. And, as with all trends characterized by considerable fluctuation in improvement and deterioration, such low points will tend to be followed by periods of improvement even if the treatment is completely ineffective. [...]

When a 'treatment' is introduced immediately after a flare-up in a person's symptomatology, almost any outcome can appear to support its effectiveness. If the treatment is followed by improvement, it will be deemed a success as just described. The treatment might also be considered successful if the person merely stays the same: After all, the treatment was able to arrest the person's slide and successfully stabilize his or her condition. [... Even] failures can sometimes be accounted for in ways that leave one's faith in the treatment intact. Perhaps the dosage was insufficient. Maybe the patient waited too long before seeking help. [...]

An intriguing demonstration of this phenomenon was provided by an experiment in which the participants played the role of a teacher trying to encourage a hypothetical student to arrive for school on time at 8:30 A.M.. A computer displayed the "student's" arrival time, which varied from 8:20 to 8:40, for each of 15 consecutive days, one at a time. On each day, the participants were allowed to praise, or reprimand, or issue no comment to the student. Predictably, the participants elected to praise the student whenever he was early or on time, and to reprimand him when he was late. The student's arrival time, however, was pre-programmed and thus was not connected to the subject's response for the previous day. Nevertheless, due to regression alone, the student's arrival time tended to improve (to regress toward 8:30) after he was punished for being late, and to deteriorate (again, by regressing to 8:30) after being praised for arriving early. As a result, 70% of the subjects concluded that reprimand was more effective than praise in producing prompt attendance by the student. [...] Likewise, children who do exceptionally well in school exams in one year are very likely to do less well the year after, and sports peoples' exceptional trials are likely to be followed by less exceptional first years.

"How We Know What Isn't So: The Fallibility of Human Reason in Everyday Life"
Thomas Gilovich (1991)2

When strange techniques, alternative therapies and religious solutions are indulged in, things often continue to get worse. Most established practices have theoretical excuses to explain why this is so. Dr Ben Goldacre explains:

Homeopaths increase the odds of a perceived success in their treatments even further by talking about 'aggravations', explaining that sometimes the correct remedy can make symptoms get worse before they get better, and claiming that this is part of the treatment process. Similarly, people flogging detox will often say that their remedies might make you feel worse at first, as the toxins are extruded from your body: under the terms of these promises, literally anything that happens to you after a treatment is proof of the therapist's clinical acumen and prescribing skill.

"Bad Science" by Ben Goldacre (2008)3

It must be clear that a great many erroneous conclusions can arise from the regression fallacy. Any wild and zany remedy may appear to work if it is attempted during a low point, and, the resultant beliefs can drive a person's beliefs far away from reality. Superstitions, magical practices, religious beliefs and pseudoscience can all result from beliefs drawn from small-scale experiments in our personal lives.

2. Stopping Natural Disasters By Enforcing Religious Rules

Religion, magic and supernaturalism of all kinds is the prime area where the regression fallacy plays a part in reinforcing, and creating, strange and crazy beliefs. Gilovich provides us with an example:

A flurry of deaths by natural causes in the northern part of the country led to speculation about some new and unusual threat. It was not determined whether the increase in the number of deaths was within the normal fluctuation in the death rate that one can expect by chance. Instead [...] a group of rabbis attributed the problem to the sacrilege of allowing women to attend funerals, formerly a forbidden practice. The remedy was a decree that subsequently barred women from funerals in the area. The decree was quickly enforced, and the rash of unusual deaths subsided.

"How We Know What Isn't So: The Fallibility of Human Reason in Everyday Life"
Thomas Gilovich (1991)6

The faulty belief that the intervention led to the regression of the number of deaths back towards the average can easily reinforce the whole community's belief system because the regression fallacy was not recognized. In such an environment, where people expect certain results, no critical thinking is applied. The Rabbis should have enforced their solution in half the land, and compared the regression rates from the control area to the "remedied" area. They would have found that average deaths decreased in both and if they done enough tests, that the death rate was not connected to the gender of funeral attendees.

3. Prayer

I can imagine the same innocent-seeming mistakes of reasoning effecting entire societies' beliefs. At low points in peoples' lives, things are likely to get better by chance. Yet, if a person prays to a God when things go bad, it will appear to them that the prayer was effective. Such a belief is then reinforced as they consciously seek to pray at any low-point. Failing to recognize such regression can cause and support many superstitions, and leads to belief in many nonsensical things such as curses, streaks of 'good luck' or 'bad luck' being associated with various random omens, signs, portents and rituals, etc.

Current edition: 2017 Mar 07
Parent page: The Human Truth Foundation

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References: (What's this?)

Book Cover

Book Cover

Armstrong, Karen
(2005) A Short History of Myth: Volume 1-4. 2008 Kindle edition. First published in Great Britain in 2005 by Canongate Books Ltd.

Carroll, Robert Todd. (1945-2016). Taught philosophy at Sacramento City College from 1977 until retirement in 2007. Created The Skeptic's Dictionary in 1994.
(2011) Unnatural Acts: Critical Thinking, Skepticism, and Science Exposed!. E-book. Amazon Kindle digital edition. Published by the James Randi Educational Foundation.

Gilovich, Thomas
(1991) How We Know What Isn't So: The Fallibility of Human Reason in Everyday Life. Paperback book. 1993 edition. Published by The Free Press, NY, USA.

Goldacre, Ben. MD.
(2008) Bad Science. Published by Fourth Estate, an imprint of HarperCollins Publishers, London, UK.

Myers, David
(1999) Social Psychology. Paperback book. 6th ('international') edition. Originally published 1983. Current version published by McGraw Hill.


  1. Myers (1999) p115-116.^^
  2. Gilovich (1991) p23-27,128.^^
  3. Goldacre (2008) chapter 4 "Homeopathy" digital location 628.^^
  4. Carroll (2011) chapter 1 "Believing in the Palpably Not True" p12-13.^^
  5. Armstrong (2005) p117.^^
  6. Gilovich (1991) p23,27.^

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