趋均数回归

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 moment—appear closer to a group’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 & McCarthy, 2019 and Franzoi, 2011). As the name suggests, the former seeks to “describe” 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’t be used to draw conclusions about a larger population—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 “infer” 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—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—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—due to a treatment, like prenatal medication above—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, & 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 & Dobson, 2005).

RTM Across Different Fields

RTM has wide-reaching implications. In medical and scientific research, it has been observed for blood pressure (Bland & Altman, 1994), female bone density (Cummings, Palermo, Browner, et al., 2000), fetal heart rate (Park, Hoh, & Park, 2012), and even semen quality (Baker & 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 & 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.