Regression to the mean
In short
Regression to the mean is a statistical phenomenon: when a measurement comes out unusually high or low, the next one tends to be closer to the average. It isn’t a force that pulls things back to normal. It happens because an extreme result is usually a mix of something real and luck, and luck doesn’t repeat the same way. The psychological problem is that people don’t expect it and invent causes for it.
What it says
The discovery. Francis Galton (1886) measured the height of 930 adult children and their parents, that is 205 pairs of parents. To compare men and women, he multiplied the women’s heights by 1.08. He then compared the average height of the two parents with the children’s height. The rule he found: on average, how far the children are from the population average is about two thirds of how far the parents are. The children of very tall parents are tall, but less so than their parents. The children of very short parents are short, but less so than their parents. Galton called this “regression towards mediocrity”.
Galton saw this as a law of heredity. Today we know it is a general statistical phenomenon. Morton and Torgerson (2003) describe it this way: it occurs whenever you select a group for extreme values on one measurement and then take a second measurement that is not perfectly correlated with the first. The weaker the link between the two measurements, the larger the effect. The more extreme the selected values, the more room they have to move back toward the average.
How it fools us. Tversky and Kahneman (1974) say that people don’t develop correct intuitions about regression. They don’t expect it where it is bound to occur, and when they notice it, they invent causal explanations for it. Their example comes from a discussion with experienced flight instructors. The instructors had noticed that after they praised an exceptionally smooth landing, the next one was usually worse, and after they harshly criticized a rough landing, the next one was usually better. They concluded that praise hurts and criticism helps. Tversky and Kahneman show that no such explanation is needed: a very good performance is usually followed by a worse one, and the other way round, whatever the instructor says.
In medicine. Morton and Torgerson (2003) give several examples from health care:
- Tests. In women treated for osteoporosis, it is tempting to think the treatment isn’t working in those who lost bone in the first year. Yet more than 80% of them gained bone in the second year, with no change in treatment.
- New treatments. If a doctor tries a new treatment first on the sickest patients, they will seem to respond very well, partly through regression alone.
- Placebo. Part of what looks like a placebo effect in clinical trials may be regression: trials enroll patients chosen precisely because their symptoms are severe.
- Public health. Measures taken after an unusual spike in road accidents seem to work, because the spike was often due to chance.
- League tables. If the hospitals at the bottom of a league table get extra resources, most of them will climb, while those at the top, once rewarded, will fall.
Barnett, van der Pols and Dobson (2005) add that the effect is more visible when the measurement has large errors and when only a subgroup selected on its first value is followed up.
Example
An example built for this text: a sales team has its worst month in two years. Management replaces the manager, and the next month sales go up. Maybe the new manager really is better. But an extremely bad month would probably have been followed by a better one anyway. To find out how much the change mattered, you need to compare with teams where nothing changed, or follow several months.
How to apply it
The steps below are a practical approach we propose, based on the sources cited.
- Ask why you picked the case. If you stepped in because something was extreme, such as the worst result or an unusual spike, part of the improvement would have come anyway.
- Compare with a control group. Morton and Torgerson recommend, where possible, studies in which cases are assigned at random: some get the intervention, others don’t. The difference between the groups shows the real effect.
- Use several measurements. A single extreme value is easily misleading. The average of several measurements, as doctors do with blood pressure, reduces the effect.
- Don’t judge praise or criticism by the next attempt. A good attempt is usually followed by a worse one, whatever you say. Judge by the long-term trend.
- Expect peaks not to repeat exactly. The best year, the best employee, the best month will probably be followed by results closer to average, without anything having gone wrong.
Limits and nuances
- It is a group effect, not an individual certainty. Morton and Torgerson stress that a single person or a single hospital may not move back toward the average, or may even move further away.
- It doesn’t mean interventions don’t work. Regression can exaggerate a real effect or create one that doesn’t exist. Only a comparison with a control group separates the two.
- Its size depends on how closely the measurements are linked. Where the result depends a lot on luck or measurement error, the effect is large. Where it depends mostly on stable things, the effect is small.
- Galton’s interpretation was wrong. He believed he had found a law specific to heredity. But the phenomenon appears in any repeated data with imperfect correlation.
- The instructor example is an observation, not an experiment. Tversky and Kahneman use it as an illustration. It is not a study that measures the effect of praise on pilots.
Sources
- Francis Galton (1886). Regression towards mediocrity in hereditary stature
- Amos Tversky, Daniel Kahneman (1974). Judgment under uncertainty: Heuristics and biases
- Veronica Morton, David J. Torgerson (2003). Effect of regression to the mean on decision making in health care
- Adrian G. Barnett, Jolieke C. van der Pols, Annette J. Dobson (2005). Regression to the mean: What it is and how to deal with it
See also: Circle of competence