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The regressive fallacy is the failure to take into account natural and inevitable fluctuations of things when ascribing causes to them (Gilovich 1993: 26). Things like stock market prices, golf scores, and chronic back pain inevitably fluctuate. Periods of low prices, low scores, and little or no pain are eventually followed by periods of higher prices, scores, pain, etc. To ignore these natural fluctuations and tendencies leads to self-deception regarding their causes and to post hoc reasoning.
For example, a professional golfer with chronic back pain or arthritis might try a copper bracelet on his wrist or magnetic insoles in his shoes. He is likely to try such gizmos 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. It never dawns on him 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 before he used the gizmo and see if the same kind of pattern has occurred frequently 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 a higher score but rather would shoot a lower score in the direction of his average.
This tendency to move toward the average away from extremes was called "regression" by Sir Francis Galton 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.
The professional golfer could check his scores because records are kept of each game played. Professional golfers frequently are featured in testimonials for some gizmo guaranteed to improve your golf score. Never does the golfer refer to a proper study done on golf scores (one which doesn't use optional starting and stopping) which demonstrates that the improvement, if any, is not due to natural fluctuation and regression.
Many people are led to believe in the causal effectiveness of worthless remedies because of the regressive fallacy. The intensity and duration of pain from arthritis, chronic backache, gout, etc., fluctuates. A remedy such as a chiropractic spinal manipulation or a magnetic belt is likely to be sought when the pain is at its worst. The 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 pain. 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.
Even if a quack remedy does not work, it is often not blamed for its ineffectiveness. For example, when comedian Pat Paulsen sought "alternative" medical treatment for cancer in Tijuana, his daughter did not criticize the treatment as useless when her father died. Paulsen had reportedly had some good days while on the "alternative" treatments, which would have been expected by natural fluctuation. His daughter claimed that the treatment worked, but had failed in her father's case because they had sought the treatment too late. When he was diagnosed with brain and colon cancer, his wife Noma was quoted in press reports as saying that the doctor in Tijuana "is confident it can be cured. The doctors here say it can't. We like the ones over there a lot better." An official press release on his death claimed he died from pneumonia, not cancer. A family spokesman was quoted as saying: "His cancer was under control after undergoing alternative treatment in Mexico. He succumbed at 2pm on Thursday after complications brought on by pneumonia and kidney failure after recent non-cancer related surgery." His wife did not think the alternative therapy was worthless. She said: "We want to thank our team of doctors in Mexico who treated my husband humanely and with respect, and who were with him 24 hours a day trying to save his life."
See also ad hoc hypothesis, cold reading, communal reinforcement, control study, Occam's razor, optional starting and stopping, pathological science, placebo effect, post hoc fallacy, selective thinking, self-deception, subjective validation, testimonial, and wishful thinking.