Regression to the Mike: A Statistical Explanation of Why an Eligible Friend of Mine Is Still Single (and Some Implications for Medical Research)

Andrew J. Vickers, PhD

Disclosures

August 07, 2007

Mike is nice looking, has a great sense of humor, and has a good job and a fabulous apartment in a popular part of town. He is, however, still single, and he thinks that the apartment is to blame. Over the past few years, he has rented out the second bedroom to a variety of single friends, and, without fail, all have succumbed to what he terms "the curse of Mike": They meet someone, get married, and move out.

Mike has come to believe that the second bedroom has some kind of magic romantic properties (so much so that he has considered moving into it). His friends think that his single condition is related to a repressed resistance to commitment buried deep in his subconscious. My explanation, of course, is statistical: In its general form, it is known as "regression toward the mean." Take any phenomenon of note at all -- a guy in his 30's being single; Mr. Jones' unexpectedly high blood pressure; Mrs. Jones' arthritis having a flare-up; it being a particularly warm January -- then wait a while, go back, and take a look. Chances are that things will have returned to a more average stage: The man got married; the Joneses are feeling better; and it was below freezing for most of February.

Here is a simple illustration. Have a class of students roll a die, and then ask anyone who rolled a 1, 2, or 3 to leave the room and have the remainder roll again. In most cases, the second die roll will be lower than the first. Lest this seem a trivial example, note that it is exactly what we do in many clinical trials: We measure patients' pain or blood pressure or anxiety, exclude anyone with low scores (on the grounds that they are not in need of treatment), and then measure again after a few weeks. Because of regression to the mean, we'd expect that many patients would get better just by chance. This is just one of the reasons why it is so important to have control groups in clinical trials.

Perhaps my favorite example of regression to the mean is the "curse of Sports Illustrated." The so-called "curse" is based on the observation that athletes making the cover of Sports Illustrated typically have a rapid decline in performance, or get injured, shortly after being featured. Now of course the reason why athletes get picked out to be put on the cover is that they have done something spectacular ("Pedro's amazing April," etc), and at any randomly picked subsequent time are likely to be just average. ("Pedro gives up a two-run shot in the bottom of the ninth and then goes on the DL.") Another sporting regression to the mean is that most coaches are confident in their ability to help an athlete to bounce back after a particularly poor performance. Again, this is because no matter what you do -- whether you scream, comfort, or threaten -- the athlete is likely to have an average (ie., better than poor) game next time out.

Regression to the mean pops up in as many diverse areas of medical research as it does for sports (and dating). A quick example: The observation that trials with lower control event rates also have smaller drug effects is nothing other than regression to the mean. So whether you are trying to cure cancer, palliate pain, or lower blood pressure (or just meet someone nice), it is worth bearing in mind that things tend to average out in the end.

Note: The author will not respond to requests for Mike's phone number.

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