Why does regression of the mean

Cambridge University Press, Laird N. Further comparative analysis of pre-test post-test research designs. Am Statistician ; 37 : — Senn S. Regression to the mean. Statist Meth Med Res ; 6 : 99 — Oxford University Press is a department of the University of Oxford. It furthers the University's objective of excellence in research, scholarship, and education by publishing worldwide. Sign In or Create an Account. Sign In. Advanced Search. Search Menu.

Article Navigation. Close mobile search navigation Article Navigation. Volume Article Contents Abstract. RTM at the subject level. RTM at the group level.

Quantifying the effect of RTM. Some real-life examples of RTM. Identifying and dealing with RTM. Regression to the mean: what it is and how to deal with it. E-mail: a. Oxford Academic. Google Scholar. Jolieke C van der Pols. Annette J Dobson. Select Format Select format. Permissions Icon Permissions. Abstract Background Regression to the mean RTM is a statistical phenomenon that can make natural variation in repeated data look like real change. Regression to the mean , repeated measures , intervention , clinical trials , observational studies , longitudinal studies , statistics , epidemiological research design.

Figure 1. Open in new tab Download slide. Figure 2. Figure 3. Figure 4. An approach which is often more practical is to use analysis of covariance ANCOVA which has high statistical power and adjusts each subject's follow-up measurement according to their baseline measurement. Table 1 Analysis of change follow-up result minus baseline in log-transformed betacarotene measurements.

Mean change. P -value. Open in new tab. Clin Chem. Statist Meth Med Res. Am J Cardiol. J Chron Dis. Am J Epidemiol. Acta Obstet Gynecol Scand. Arch Intern Med. It is also the case that depressed children who spend some time standing on their head or hug a cat for twenty minutes a day will also show improvement.

Whenever coming across such headlines it is very tempting to jump to the conclusion that energy drinks, standing on the head or hugging cats are all perfectly viable cures for depression. These cases, however, once again embody the regression to the mean:. Depressed children are an extreme group, they are more depressed than most other children—and extreme groups regress to the mean over time. The correlation between depression scores on successive occasions of testing is less than perfect, so there will be regression to the mean: depressed children will get somewhat better over time even if they hug no cats and drink no Red Bull.

We often mistakenly attribute a specific policy or treatment as the cause of an effect, when the change in the extreme groups would have happened anyway.

This presents a fundamental problem: how can we know if the effects are real or simply due to variability? Luckily there is a way to tell between a real improvement and regression to the mean. That is the introduction of the so-called control group, which is expected to improve by regression alone. The aim of the research is to determine whether the treated group improve more than regression can explain.

In real life situations with the performance of specific individuals or teams, where the only real benchmark is the past performance and no control group can be introduced, the effects of regression can be difficult if not impossible to disentangle. We can compare against industry average, peers in the cohort group or historical rates of improvement, but none of these are perfect measures. Luckily awareness of the regression to the mean phenomenon itself is already a great first step towards a more careful approach to understanding luck and performance.

If there is anything to be learned from the regression to the mean it is the importance of track records rather than relying on one-time success stories. I hope that the next time you come across an extreme quality in part governed by chance you will realize that the effects are likely to regress over time and will adjust your expectations accordingly.

Read Next. Mental Models Reading Time: 9 minutes. The Imperfect Correlation and Chance At this point, you might be wondering why the regression to the mean happens and how we can make sure we are aware of it when it occurs. In order to understand regression to the mean, we must first understand correlation. No Correlation On the contrary, there are measures which are solely dependent on the same factor. Perfect Correlation There are few if any phenomena in human sciences that have a correlation coefficient of 1.

Weak to Moderate Correlation This variation and the corresponding lower degree of correlation implies that, while height is generally speaking a good predictor, there clearly are factors other than the height at play. Kahneman explains: […] If the correlation between the intelligence of spouses is less than perfect and if men and women on average do not differ in intelligence , then it is a mathematical inevitability that highly intelligent women will be married to husbands who are on average less intelligent than they are and vice versa, of course.

The Cause, Effect, and Treatment We should be especially wary of the regression to the mean phenomenon when trying to establish causality between two factors.

Consider the example Kahneman gives: Depressed children treated with an energy drink improve significantly over a three-month period. Regression to the mean refers to the tendency of results that are extreme by chance on first measurement—i. Results subject to regression to the mean are those that can be influenced by an element of chance. In our school district, for example, the kids who scored the poorest on the first math test likely included some who normally know the answers but, by chance, did not that day.

Perhaps they were tired, sick, distracted, etc. These kids were going to do better on the second test whether they received the remedial program or not, bringing up the average score among the 50 poorest performers.

You can see why researchers have to consider regression to the mean when they are studying the effectiveness of a program or treatment. This is especially the case when program effectiveness is based on measurements of people or organizations at the extremes—the unhealthiest, the safest, the oldest, the smartest, the poorest performing, the least educated, the largest, etc. Regression to the mean is mostly harmless, but it becomes a problem when the change it creates is misinterpreted. For example, imagine you ran a hospital and were told that hospital-acquired infections were five times higher than average last month.

A colleague tells you they know the cause and it can solved by using more prophylactic antibiotics. Regression to the mean is unwittingly exploited by quacks who often see patients when they are at their lowest. As many diseases have a natural ebb and flow, seeing patients when they are at their worst is the best time to exploit regression to the mean, because any treatment will appear to cause improvements in enough patients to make it look broadly effective.

Telling the difference between regression to the mean and a real change can be difficult. A chronically ill patient may have a very bad day, but is that the early warning of a downward trajectory or just a blip due to a random cluster of events, such as a bad meal, poor sleep, or an ill-judged sprint for the bus? Regression to the mean is everywhere.