Listed below are various other data of this nature that I have to illustrate that the rarer an outcome the greater tends to be the relative difference in rates of experiencing and the smaller tends to be the relative difference in avoiding it (with a brief description of the nature of the illustration). It should be kept in mind that it does not matter whether the issue is discussed in terms of a favorable outcome or the corresponding adverse outcome or whether the focus is on whether the outcome is decreasing or increasing. Differences is usage in the parenthetical descriptions may reflect inconsistency/inexactness on my part or may involve whether the data show what tends to happen or what in fact would happen. That is, with respect the latter, data in the second and third rows of Table 2 in "Race and Mortality Revisited" (at 330), for example, show the directions of changes in measures between the two rows that would in fact occur if everyone with incomes above 75% of the poverty line were enabled to escape poverty but merely show what would tend to occur in the case of a general reduction in poverty.
Other data of the type used here that illustrate the referenced statistical pattern include:
(a) income and credit score data (showing that the lower an income or credit score requirement, the greater tend to be relative racial differences in failure to meet the requirement while the smaller tend to be relative racial differences in meeting the requirement);
(b) life tables (showing that the higher the age, and thus the lower are overall rates of reaching it, the greater tend to be relative racial and gender differences in failure to reach it while the smaller tend to be relative racial and gender differences in reaching it);
(c) NHANES data on systolic blood pressure and folate level (showing that general improvement in control of systolic blood pressure and general increases in folate tend to increase relative differences in the adverse outcomes (hypertension, low folate) while reducing relative differences in the corresponding favorable outcomes (avoiding hypertension, adequate folate);
(d) Framingham Studies data (showing how improving heart attack risk profiles in a way that generally reduces heart attack risk tends to increase relative gender differences in heart attack risk while reducing relative gender differences in risks of avoiding heart attacks);
(e) health numeracy data (showing that the lower the health numeracy level, the greater tend to be relative differences between rates at which insured and uninsured persons fail to reach it, while the smaller tend to be relative differences between the rates at which they reach it);
(f) literacy data (showing that the lower the level of reading proficiency, the larger the relative racial difference in failing to reach the level and the smaller the relative racial difference in reaching it);
(g) truancy data (showing that greater the level of truancy, the larger the relative racial difference in rates of reaching the level);
(h) California prison data (showing that the greater number of convictions of incarcerated persons, the larger is the relative racial difference in reaching or exceeding the number and the smaller is the relative racial difference in rate of failure to reach the level).
Such data illustrate why restricting an outcome to those most susceptible to it will tend to increase relative differences in rates of experiencing the outcome and reduce relative differences in rates of avoiding the outcome. The illustrations may be compared to illustrations such as discussed in my Maryland State Department of Education (June 26, 2018) (at 3-4) that use black and white rates of (a) one or more suspensions and (b) multiple suspensions to show how eliminating what otherwise would be first suspensions will tend to increase relative racial differences in rates of being suspended one or more times while reducing relative racial differences in having no suspensions). The illustration may also be compared to illustrations discussed in a June 29, 2020 BMJ response that uses mortality rates of different racial or gender groups among younger and older seriously ill COVID-19 patients in the United Kingdom to show how giving the older patients the same chances of survival as the younger patients would increase relative racial/ethnic and gender differences in mortality, but reduce relative racial/ethnic and gender differences in survival, among the older patients. They may also be compared to illustrations based on the effects of altering a point on the x-axis for an array of two normal distributions, such as shown, for example, in Figure 1 of “Divining Difference,” Chance (Fall 1994) or Figure 1 (slide 23) of the 2015 University of Massachusetts Medical School seminar titled “The Mismeasure of Health Disparities in Massachusetts and Less Affluent Places, on the proportions of each of two group that would fall on either side of the point and the resultant effects of measures of difference between the proportions of each group on either side of the point.
Such illustrations should be contrasted with the illustrations based on what in point of fact typically occurs when an outcome is restricted to those most susceptible to it, of which there are many illustrations in the references in the first paragraph and scores of pages on this site. The latter illustrations, while showing that the patterns that an informed observer should expect to see in fact usually do occur, especially when there is a large change in the prevalence of an outcome, do not show why such patterns occur. The illustrations that are the focus of this page should also be contrasted with the illustrations of the way relative differences in adverse outcomes tend to be larger, while relative differences in the corresponding favorable outcomes smaller, where the outcomes are less common, such as is the focus of the University of Massachusetts Medical School seminar mentioned in the paragraph above or such as reflected in the larger relative differences in adverse outcomes, but smaller relative differences in the corresponding favorable outcomes, among higher-income compared with lower-income loan applicants or younger cancer patients compared with older cancer patients. But it should be recognized many of the latter types of patterns can be regarded as illustrating whygiving the less advantaged subpopulation the same favorable/adverse outcome prospects as the more advantaged subpopulation will tend to increase relative demographic differences in adverse outcome among the less advantaged subpopulation, as in the situation discussed in the June 29, 2020 BMJ response mentioned above. Thus, certain distinctions between the types of illustrations may be regarded as involving matters of perspective.
This page is based on data in a July 12, 2012 Gallup article titled “In U.S., Blacks Most likely to Be Very Obese, Asians Least.” A table in the report shows for various racial/ethnic groups rates of falling into three obese classes defined by Body Mass Indexes: Obese Class I = BMI 30.00 to 34.99; Obese Class II = BMI 35.00 to 39.99; Obese Class III – BMI 40.00 and above. Table 1 below is based on the article’s table that shows that black and white rates of falling into each of the Obese Classes are 20.8% and 16.4% for Class I, 8.8% and 5.6% for Class II, and 6.0% and 3.1% for Class 3.
For the reasons discussed in places such as my Intermediate Outcomes and Truancy Illustration pages, the rates from the article are translated into rates of (a) falling into any class (i.e., being obese at all), (b) falling into Classes II or III, and (c) falling into Class III. These are shown in the first two data columns. The third and fourth data columns then show the rates as which blacks and whites do not fall into the categories (denoted BF and WF for rates of experiencing the corresponding favorable outcomes). The fifth and sixth data columns show the relative differences in rates of experiencing the adverse outcome (as reflected by the ratio of the black rate to the white rate) and the relative differences in rates of avoiding the outcome (as reflected by ratio of the white rate of avoiding the outcome to the black rate of avoiding the outcome).
Table 1. Black and white rates of falling into certain levels of obesity and not falling into those level, with relative risks for experiencing the outcomes and avoiding the outcomes (ref. bb2025 b1).
B/W Ratio Adverse Outcome
W/B Ratio Favorable Outcome
II or III
Moving down the rows, one observes the effect of improving weight control such as enable all persons who are currently in Class I to escape obesity (Row 2 compared with Row 1) and the effects of further improving weight control to enable all persons in both Classes I and II to escape obesity (Row 3 compared with Row 2). The improvements would reduce the relative difference between black and white rates of being obese but increase the relative difference between rates at which blacks and whites avoid obesity. The data similarly show that the improvements would cause whites to experience the larger proportionate decrease in rates of experiencing the adverse outcomes while causing blacks to experience the larger proportionate increase in rates of avoiding the outcomes. As discussed in many of the references, that reducing an outcome tends to cause (a) a larger proportionate decrease in rates of experiencing the outcome for the group with the lower baseline rate for the outcome while causing a (b) larger proportionate increase in the opposite outcome for the other group is simply a corollary to the pattern whereby the rarer an outcome (a) the greater tends to be the relative difference in rates of experiencing it and (b) the smaller tends to be the relative difference in rates of avoiding it. For a discussion of why, rather being counterintuitive, the coexistence of (a) and (b) is inevitable, and that in fact (a) and (b) are the same things, see note 14 (at 10) of the Letter to American Statistical Association (Oct. 8, 2015).
Two further observation on these data. First, according to the method described in "Race and Mortality Revisited" (termed EES for estimated effect size or, more formally, probit d'), the difference between the forces causing black and white rate to differ vary negligibly from row to row (being .302 in the first, .314 in the second, and .312 in the third. That means that given the black and white rates of being obese are 35.6% and 25.1%, and that the black rate of falling into Class III was 6.0%, one would estimate a probable white rate of 3.166% for falling into Class III. A slightly different figure would be derived from the actual (i.e., less rounded) black and white rates in the first row and black rate in the third row. See the discussion in my California Reading Instruction Competence Assessment web page regarding the way that given the passing rates of various groups for the first time they take a test may, any group’s passing rate after multiple administrations of the test, one may closely estimate any other group’s pass rate after multiple administrations of the test. But I would not expect estimates like this generally to as closely approximate reality as in the instant case or the case of the California test.
Second, given that obesity is an important risk factor for death from COVID-19, the data in the table also illustrate the way that improvements in COVID-19 care such as, for example, to give persons in Obese Class III the same survival prospects as persons in Obese Class II will tend to increase relative differences in rates at which persons infected with COVID-19 die from the disease while decreasing relative racial differences in rates at which such persons survive the disease. The same point, which is made explicitly above with regard to data on seriously ill COVID-19 patients in the United Kingdom, could be illustrated with NHANES data on systolic blood pressure that is the subject of item (c) of the above list of illustrative data.