Name: regression toward the mean in data
Uploaded: 2020-02-12T11:07:40.000Z
Duration: 1 min 52 s
Channel: JoVE

K12 Standards

Texas Essential Knowledge and Skills

High School

Biology

BIO.2

BIO.2.B

Regression Toward the Mean

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&rsquo;s blood pressure, her diastolic value measures 95 mmHg.&nbsp;

The doctor then enters and compares this number to that of all of his patients, and notes that&mdash;when graphed&mdash;these values demonstrate a normal, bell-shaped distribution.

Here, the woman&rsquo;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 &ldquo;extreme&rdquo; pressure regressed to the mean for all the patients. It&rsquo;s rare for someone&rsquo;s results to be far from the average repeatedly, even at the higher end.

This inclination is called regression toward the mean&mdash;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 o

regression toward the mean

Regression toward the mean (&ldquo;RTM&rdquo;) is a phenomenon in which extremely high or low values&mdash;for example, and individual&rsquo;s blood pressure at a particular moment&mdash;appear closer to a group&rsquo;s average upon remeasuring. Although this statistical peculiarity is the result of random error and chance, it has been problematic across various medical, scientific, financial and psychological applications. In particular, RTM, if not taken into account, can interfere when researchers try to extrapolate results observed in a small sample to a larger population of interest.

Descriptive Statistics, Inferential Statistics and RTM 

The field of statistics has two main subcategories, termed descriptive and inferential (for review, see Beins &amp; McCarthy, 2019 and Franzoi, 2011). As the name suggests, the former seeks to &ldquo;describe&rdquo; data derived from a particular sample, e.g., newborns at a specific United States hospital whose mothers took a prenatal vitamin during pregnancy. Descriptive statistics typically include measures of central tendency (like the mean), gauges of variability (such as standard deviation), and graphs summarizing sample results. For example, descriptive statistics for our newborn example might include average birthweight and standard deviation, as well as a frequency distribution graph of birthweights for babies born at the hospital within the last year. Importantly, descriptive statistics only pertain to the sample being investigated, and, by themselves, can&rsquo;t be used to draw conclusions about a larger population&mdash;in this case, all newborns in the United States born to mothers who took prenatal pills.

In contrast, inferential statistics are used by researchers to &ldquo;infer&rdquo; or draw conclusions about a population based on results calculated for a representative sample. Here, researchers might compare the average birthweight of babies born at the hospital to prenatal-taking mothers to that of newborns whose mothers did not. It might initially be observed that prenatal babies have a higher mean birthweight than non-prenatal babies. Using complex mathematical equations, inferential statistics can then determine if the difference between these two averages is significant&mdash;defined in science as having less than a 5% probability of being due to chance. If this is the case, conclusions can then be drawn about the greater population&mdash;in this instance, that throughout the country, newborns whose mothers took prenatal pills have a higher birthweight than those whose mothers did not.

Unfortunately, RTM can make it appear as if there is a significant difference between groups&mdash;due to a treatment, like prenatal medication above&mdash;when in reality no meaningful disparity exists, and any discrepancies are the result of random chance. Sometimes researchers even publish data stating that a particular regimen has been effective, when in fact their results stem from this statistical phenomenon; this has been the case for programs aimed at childhood obesity, among others (Skinner, Heymsfield, Pietrobelli, Faith, &amp; Allison, 2015). Luckily, methods in inferential statistics have been developed that evaluate and take into account RTM, allowing researchers to be more confident in the veracity of their data, and the efficacy of any treatment (Barnett, van der Pols &amp; Dobson, 2005).

RTM Across Different Fields 

RTM has wide-reaching implications. In medical and scientific research, it has been observed for blood pressure (Bland &amp; Altman, 1994), female bone density (Cummings, Palermo, Browner, et al., 2000), fetal heart rate (Park, Hoh, &amp; Park, 2012), and even semen quality (Baker &amp; Kovacs, 1985), to list a few examples. However, RTM extends beyond medical observations, and has been recorded in the stock market (Murstein, 2003), performance of flight students (Kahneman &amp; Tversky, 1973), and has even been used as an explanation for why certain couples get divorced (as reviewed in Murstein, 2003). Thus, this statistical phenomenon affects numerous fields, from medicine to finances, and should be carefully considered by researchers using statistics to draw conclusions.

Regression toward the mean (&ldquo;RTM&rdquo;) is a phenomenon in which extremely high or low values&mdash;for example, and individual&rsquo;s blood ...

Education

JoVE Core

Social Psychology

Foundations of Social Psychology

Research Methods

KEY TERMS AND CONCEPTS

regression toward the mean in data

Regression toward the mean is a statistical pattern in which very high or very low values move closer to the average when they are measured again. A blood pressure reading taken at one moment is one example. The change is usually caused by random error and chance, not by a real underlying shift.

This idea matters because it can affect many kinds of research. If scientists do not account for regression toward the mean, they may think a treatment worked when the difference was really just a chance effect. It can also make it hard to use results from a small sample to draw conclusions about a larger population.

Statistics is often divided into descriptive statistics and inferential statistics. Descriptive statistics describe the sample being studied. They include the mean, standard deviation, and graphs such as a frequency distribution. For example, researchers could use them to describe birthweight data from newborns at one hospital whose mothers took prenatal vitamins.

Descriptive statistics only apply to that sample. They cannot, by themselves, support conclusions about all newborns in the United States. Inferential statistics do that larger job. They use a representative sample to infer or draw conclusions about a population.

In a prenatal vitamin study, researchers might compare the average birthweight of babies whose mothers took prenatal pills with babies whose mothers did not. If the difference is significant, it means there is less than a 5% chance that it happened because of chance. Researchers could then make a broader claim about newborns in the larger population.

Regression toward the mean can make a treatment look effective even when no meaningful difference exists. The results may seem significant, but the pattern may simply reflect random chance. This issue has appeared in research on childhood obesity programs, among others. For that reason, inferential methods have been developed to test for regression toward the mean and account for it.

The effects of regression toward the mean are not limited to medicine. Researchers have observed it in blood pressure, female bone density, fetal heart rate, and even semen quality. It has also been reported in the stock market, in flight student performance, and as one explanation for why some couples get divorced. Because it appears in many fields, researchers must consider it carefully when using statistics to draw conclusions.

Regression Toward the Mean in Data

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Regression toward the mean is a statistical pattern in which very high or very low values move closer to the average when they are measured again. A blood pressure reading taken at one moment is one example. The change is usually caused by random error and chance, not by a real underlying shift. This idea matters because it can affect many kinds of research. If scientists do not account for regression toward the mean, they may think a treatment worked when the difference was really just a...

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Statistical analysis helps determine whether differences between an experimental group and a control group are meaningful. After data are collected, researchers check whether the results are likely to be real or just due to chance. If a difference is caused by chance, it is not considered meaningful. In psychology, a group difference is usually called significant when the chance of it happening by accident is 5 percent or less. Another way to say this is that if the experiment were repeated...

key terms and concepts

Learn how regression toward the mean can change repeated measurements, affect sample results, and create misleading conclusions in statistics and research.

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Regression Toward the Mean in Data

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