This page, which discusses that one cannot analyze data on rates at which advantaged and disadvantaged groups fall within an intermediate category, is still a sketch. It warrants some simplification. It also warrants some amplification with reference to the Department of Education presentation of data on single suspension and multiple suspensions in its March 2014 Data Snapshot: Early Childhood Education that is the subject of my August 24, 2015 letter to Department of Health and Human Services and Department of Education, as well as analyses of data on outcomes like moderate low birth rate, postneonatal mortality, and various types of cardiac care. Also, there are no doubt better data to illustrate the points than the maternal mortality data now used.
Usually, when observers analyze data on demographic differences involving hierarchical categories, they restrict the analyses to rates of falling above or below certain points, as, for example, in analyses of self-rated health (SRH), where categories commonly include (a) Excellent, (b) Very Good, (c) Good, (d) Fair, and (b) Poor. Researchers typically analyze differences in SRH in terms of (a) Health Less Than Good (or its opposite) or (b) Health Good or Better (or its opposite) or some like dichotomization. Few would think to analyze differences between rates of falling into (or out of) the Very Good category, the Good category, or the Fair category, though some might analyze rates of falling into (or out of) the Excellent category or the Poor category (that is, in or out of the extreme categories).[i] Similarly, few would think to analyze rates at which two student groups received grades of B or grades of C or grades of D,
While one may have an interest in examining distributions across the categories, information about differing rates of falling into an intermediate category cannot even identify which is the disadvantaged group (as, for example, where 30% students from Group X and 40% of students from Group Y receive C grades).
Further, the method for appraising a difference in the circumstances of two groups reflected by a pair of outcome rates that I maintain in “Race and Mortality Revisited,” Society (July/Aug. 2014), is the only sound method (or type of method) can only be applied to hierarchically dichotomized data.[ii]
Table 1, which is a variation on Table 1 of "Race and Mortality Revisited," illustrates the point, while also succinctly illustrating the pattern that I commonly describe as that whereby the rarer an outcome the greater tends to be the relative difference in experiencing it and the smaller tends to be the relative difference in avoiding it. I note, however, that said pattern would be more precisely stated in terms that “the more the outcome is restricted toward the end of the overall distribution” rather than “the rarer the outcome,” a distinction of some pertinence to the discussion below.
The table shows the pass and fail rates of an advantaged group (AG) and a disadvantaged group (AG) at two points in circumstances where the scores of the two groups are normally distributed with means that differ by half a standard deviation, along with the ratio of AG pass rate to the DG pass rate and the ratio of the DG fail rate to the AG fail rate. I include in the EES column (for estimated effect size) the .50 figure that could be derived from pass (or fail) rates.
Table 1. Illustration of effects on relative differences in pass and fail rates of lowering a cutoff from a point where 80% of AG passes to a point where 95% of AG passes, with EES
DG/AG Fail Ratio
The figures in Table 1 actually reflect three categories: (a) persons scoring above the higher cutoff (80% of AG and 63% of DG); (b) person scoring between the two cutoffs (15% of AG and 24% of DG) and (c) persons falling below the lower cutoff (5% of AG and 13% of DG). One can make sense out of (a) and (c) with respect to an appraisal of the strength of the forces causing outcome rates to differ. But one cannot make any sense out of (b).
Whereas it is uncommon for observers to try and make sense out of rates at which two groups fall within an intermediate category, some demographic analyses in fact attempt to do so. One area of study where this occurs is that involving the interpretation of demographic differences in discipline rates, where observers separately analyze differences in rates of in-school suspension (ISS), out-of-school suspension (OSS), or (c) expulsions. But both ISS and OSS are intermediate categories and cannot be separately analyzed. To the extent the point is not obvious with respect to ISS, the reader should bear in mind that there are four categories of students, one of which is students not disciplined at all. Thus, the descending category of advantage akin to the SRH categories discussed above would be (a) no suspension, (b) ISS, (c) OSS, and (d) expulsion.
The only sound ways to appraise such data would be in terms of the following categories or their opposites: (a) ISS or worse (that is, all three combined), OSS or worse (that is, OSS or expulsion), or (c) expulsion. Such is the approach I employ in the main Discipline Disparities page, though there the categories (based on the data available) are: (a) OSS, (b) total expulsion, (c) expulsion, total cessation.
Separate analyses of ISS are entirely unsound (though one could learn things from comparisons of (a) ISS or worse with (b) OSS or worse. Efforts to separately analyze OSS are theoretically unsound. But often there are too few expulsions to cause results to differ materially from an OSS or worse analysis. See discussion of this subject in the Connecticut Disparities subpage of the Discipline Disparities page.
Table 2 (based on the Curtin/Hoyert paper’s Table 1) presents the categories and the rates for Non-Hispanic whites and non-Hispanic blacks, along with the ratio of the black rate to the white rate of experiencing the outcome and the ratio of the white rate to the black rate of failing to experience the outcome.
Table 2. Black and white rates of experiencing certain types of morbidity or mortality as a result in pregnancy (per 100,000 births), with ratios of the black to white rate of experiencing the outcome and white to black rates of failing to experience the outcome (b6420a1).
B/W Adv Ratio
W/B Fav Ratio
Admission to intensive care unit
Pregnant at time of death
Not pregnant, but preg within 42 days
Not pregnant, but preg within 43 days to one year
The authors appraised disparities in terms of the ratio of the black rate to the white rates, noting the racial gap in mortality was largest when the woman as still pregnant. And on the basis of the generally larger ratios for morbidity than mortality the authors observed:
“This greater difference for maternal mortality compared with morbidity needs further exploration and is suggestive of differences in healthcare quality and access when morbidities are present. However, it may reflect differential underreporting of the morbidities by racial/ethnic groups.”
Before addressing the principal point of this page, I note the following regarding the author’s observation regarding the potential role of differences in healthcare and access in the larger relative differences in mortality than morbidity. The situation where relative differences in adverse outcomes tend to be greater for mortality than morbidity (though relative differences in the corresponding favorable outcome tend to be greater for morbidity than mortality) is the standard pattern whereby, as the outcome becomes less common the relative difference in experiencing it tends to increase while the relative difference in avoiding it tends to decrease. It might be compared to the patterns shown in Table 3 below (which is an excerpted version of Table A of the Reporting Heterogeneity subpage of the Measuring Health Disparities (MHD) whereby relative difference between rates at which advantaged and disadvantaged fall below Very Good SRH is greater than the relative difference between rates at which the groups experience Bad SRH (using the nomenclature of the study discussed on the subpage), while the relative difference between rates of experiencing SRH better than Bad is smaller than the relative difference between rates of experiencing rates of Very Good or better SRH.
Table 3. Rates at which primary education (PE) and tertiary education (TE) groups experience less than Very Good SRH and experience rates of bad SRH, with ratios of PE to TE rates of experiencing the outcome and ratios of TE to PE rates of avoiding the outcome.
Primary Education Rate
Tertiary Education Rate
Less than very good SRH
But neither comparative size of the relative difference in the adverse outcomes in the two rows or nor the comparative size of the relative differences in the favorable outcomes in the two rows provides a basis for drawing inferences about processes. That is, healthcare presumably plays a larger role in experiencing/avoiding Bad SRH than in experiencing/avoiding less than Very Good SRH. But there is no more reason to believe some aspect of healthcare as increasing the disparity from the first to the second row (as measured in terms of the relative difference in the adverse outcome) than there is in believing that some aspect of healthcare is reducing the disparity (as measured in terms of the relative differences in the favorable outcome). See "Race and Mortality Revisited" at 339-41 regarding drawing inferences about processes based on
Turning to the principal subject of this page, notice that the morbidity categories in Table 2 are neither mutually exclusive nor hierarchical, while the mortality categories in Table 2 are mutually exclusive and hierarchical. While there might be points to me made about the patterns in the morbidity categories, I will not seek to make such points here.
Table 4 presents information based on the same underlying information as Table 2, but modified as follows. Table 4 eliminates the different morbidity categories and combines the figures into a single row for total morbidity. This certainly overstates the actual overall rates for both blacks and whites given that some persons fall into more than one category. But it yields a figure that still can be useful for illustrating the general pattern (shown in the first two rows) whereby the relative difference tends to be larger for mortality (essentially, the most extreme morbidity cases) than morbidity, while the relative difference in avoiding the outcome is greater for morbidity than mortality. The table includes the EES (for estimated effect size, as explained in "Race and Mortality Revisited").
Table 4. Black and white overall maternal morbidity and mortality rates and mortality rates within analyzable subcategories of mortality, with rate ratios and EES (ref b6418a2)
B/W Adv Ratio
WB Fav Ratio
Preg at death or w/in 42 days (Rows 6 and 7 of Table 2
Preg at death (Row 6 of Table 2)
The EES shows that the disparity is greater for mortality than morbidity. The measure may or may not be sound in this context. For, as noted, the figures for total morbidity are questionable. Also, an outcome like maternal mortality is rare enough that the issues discussed on the Irreducible Minimums subpage of MHD may be of consequence. But any conclusions about the comparative size of racial differences in maternal morbidity and racial differences in maternal mortality (and inferences based on such conclusions) would have to be based on a measure such as the EES, rather than either of the relative differences (or other standard measures that are affected by the frequency of an outcome).
The main point of this page, however, is best illustrated by the subcategories of mortality in Rows 2 to 4 of Table 4. Rows 6 to 8 of Table 2 are subcategories of Row 5 (all mortality). But only Row 6 (pregnant at time of death), replicated in Row 4 of Table 4, is an extreme category that might be effectively analyzed separately, while Rows 7 and 8 are intermediate categories that cannot be analyzed separately. That is, within the All categories, the increasing order of susceptibilities is Row 8 (not pregnant, but pregnant within 43 days to one year), the group that is best able to survive pregnancy with prospect to survive completely; Row 7 (not pregnant, but pregnant within 42 days), the group next most likely to survive pregnancy with prospect for complete survival; and Row 6 (pregnant at time of death), the group most susceptible to mortality resulting from pregnancy. These three categories might be compared to grades of C, D, and F. Thus, as suggested by the discussion above regarding analyses of differences in grades, we can analyze the All category (which includes all three subcategories) (akin to analyzing grades C or below) (Row 1 in Table 4); Rows 7 and 6 combined (akin to analyzing grades D or below) (Row 3 in Table 4); or Row 6 alone (akin to separately analyzing grade F) (Row 4 in Table 4.
Analyzing these categories in terms of relative differences in the adverse or favorable outcome, we observes the usual patterns of increasing relative differences as the outcome becomes less common (is restricted toward the end of the overall distribution), while decreasing relative differences in rates of avoiding the outcome. We also observe that the EES changes little from row to row.
[ii] The method involves deriving from a pair of favorable or adverse outcome rates the difference between the means of the underlying distributions. I commonly term the result the EES, for estimated effect size.