15.16
Regression Toward the Mean
Regression toward the mean (“RTM”) is a phenomenon in which extremely high or low values—for example, and individual’s blood pressure at a particular…
Sometimes, people think that certain events are under personal control. For instance, they may assume that their favorite athlete will always perform at their best, and therefore, may be surprised when an amazing performance is followed by an average one.
Notably, this trend occurs for multiple variables with normal distributions. For example, when a physician takes the patient’s blood pressure, her diastolic value measures 95 mmHg.
The doctor then enters and compares this number to that of all of his patients, and notes that—when graphed—these values demonstrate a normal, bell-shaped distribution.
Here, the woman’s result falls at the extreme end of the curve. Concerned, the doctor retests her blood pressure; surprisingly, he finds that the diastolic number decreased.
In other words, the previously observed “extreme” pressure regressed to the mean for all the patients. It’s rare for someone’s results to be far from the average repeatedly, even at the higher end.
This inclination is called regression toward the mean—the tendency for an extreme value, upon reassessment, to be followed by a less radical score, essentially moving nearer to the group mean.
Consequently, if a therapy only influences individuals with initially extreme results, it’s likely an ineffective strategy. However, if a treatment lowers a group’s average—like for blood pressure—this is strong evidence of its success.
Without awareness of this statistical phenomenon, the doctor might have distributed blood pressure medication when, in fact, his patient didn’t need treatment.
In the end, results based on outliers shouldn’t be taken too seriously.
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Q1: What is regression toward the mean and why does it occur?
Regression toward the mean is the tendency for extreme values to move closer to the group average upon remeasurement. This statistical phenomenon results from random error and chance. For example, an athlete's exceptional performance is often followed by average performance, or a patient's extremely high blood pressure reading typically decreases on retesting, not due to treatment but because extreme scores are naturally rare.
Q2: How can regression toward the mean mislead researchers about treatment effectiveness?
Regression toward the mean can create the false appearance of treatment success when none exists. If researchers select participants with extreme initial values and observe improvement on retesting, the change may reflect natural statistical regression rather than treatment efficacy. Without accounting for this phenomenon, researchers might publish ineffective interventions as successful, as occurred with some childhood obesity programs.
Q3: What is the difference between descriptive and inferential statistics in relation to regression toward the mean?
Descriptive statistics summarize data from a specific sample, such as average birthweight and standard deviation. Inferential statistics draw conclusions about larger populations based on sample results. Regression toward the mean complicates inferential statistics by potentially making random differences appear significant, leading researchers to incorrectly infer population-level treatment effects when differences stem from chance alone.
Q4: Why should extreme outlier results be interpreted cautiously in medical research?
Extreme outlier results are rare occurrences in normally distributed data. When retested, these values typically regress toward the mean, appearing less extreme simply due to statistical chance. A physician who observes a patient's extremely high blood pressure and retests it may see improvement without any intervention, potentially leading to unnecessary treatment decisions if the phenomenon is not understood.
Q5: In what fields beyond medicine does regression toward the mean occur?
Regression toward the mean extends across numerous disciplines including finance, psychology, and sports. It has been observed in stock market performance, flight student performance evaluations, and even divorce rates among couples. This wide-reaching statistical phenomenon affects any field using statistics to draw conclusions, making awareness essential for researchers across medicine, science, and social sciences.
Q6: How can researchers account for regression toward the mean when evaluating treatment success?
Researchers can use inferential statistical methods specifically designed to evaluate and account for regression toward the mean. Strong evidence of treatment efficacy comes when a therapy lowers an entire group's average, not just improves extreme cases. These statistical approaches increase confidence in data veracity and allow researchers to distinguish genuine treatment effects from natural statistical regression.
Q7: Why is retesting important for distinguishing real effects from regression toward the mean?
Retesting reveals whether initial extreme values represent true characteristics or random fluctuations. If a single measurement shows an extreme result but retesting shows regression toward the mean, the initial value likely reflected chance variation. Conversely, if repeated measurements consistently show treatment-induced changes across a group's average, this provides stronger evidence of genuine treatment effectiveness rather than statistical artifact.