Some of the subpages may provide substantial detail, while others simply present statements describing the situations. See also my “Maryland Discipline Study Shows Usual – But Misunderstood – Effects of Policies on Measures of Racial Disparity,” Gunpowder Gazette (Dec. 16, 2019), which discusses a study showing that general reductions in suspensions in Maryland schools between the 2008-09 and 2013-14 school years had been accompanied by an increase in the ratio of the statewide black suspension rate to the statewide white suspension rate, and that, during that period, 20 of the 23 Maryland school districts for which data on black and overall suspension rate reductions could be analyzed there occurred an increase in the ratio of the black suspension rate to suspension rate for other students. See also the Minnesota Disparities subpage regarding a study finding that in all 73 districts in Minnesota where the matter could be analyzed general reductions in suspensions were accompanied by increases in the ratio of the black suspension rate to the white suspension rate.
Also of note is a 2019 article in Educational Psychologist by Girvan et al., “Tail, Tusk, and
Trunk: What Different Metrics Reveal About Racial Disproportionality in School Discipline.” The article is noteworthy because it is by members of the Positive Behavioral Support and Intervention Community that has long promoted the belief that generally reducing suspensions will tend to reduce relative differences in suspensions. At the sixth and seventh pages, however, the article, while generally employing the reasoning of my “Race and Mortality Revisited,” Society (July/Aug. 2014), recognizes that generally reducing suspensions will tend to increase relative racial differences in suspensions while reducing absolute differences in such rates. This is one of the few instances where educational researches even recognized that it was possible for relative racial difference in rates of experiencing and outcome and absolute differences in rates of experiencing the outcome to change in opposite directions.
The Relative Versus Absolute Differences in School Discipline subpage of the Discipline Disparities page is also of particular relevance to this subpage. While I have not examined the matter carefully, I have assumed that in all or almost all of the situations described in the subpages mentioned in the first paragraph where reductions in discipline rates were accompanied by increases in relative racial differences in discipline rates, the absolute differences declined. When there occurs a general decrease in discipline rates, the absolute difference does not have to increase, just as the relative does not have to increase. But, at least where the reductions in discipline rates is very large, rarely will one fail to find the pattern where the absolute difference decreases while the relative difference increases.
In July 2019, the Metropolitan Educational Research Consortium of Virginia Commonwealth University issued a report titled “Understanding Racial Inequity in School Discipline Across the Richmond Region.” Like similar work purporting to increase understanding of discipline disparities issues, the report reflects the view that Positive Behavioral Interventions and Support and Restorative Justice programs that generally reduce suspensions should reduce relative racial differences in discipline rates.
But, as all researchers ought to expect but that virtually no researchers in fact expect, the report shows that reductions in in the Richmond Region increased relative racial differences in suspension and that increases in suspension reduced relative racial differences in suspensions. A chart on page 8 of the report showed that the during a 2010 to 2014 period in which suspension rates generally declined the black ratio of the black suspension rate to the white suspension rates increased from 3.8 (19%/5%) to 5.0 (15%/3%). It also showed that during the period of general increases in suspensions that occurred between 2014 and 2016, the ratio decreased from the 5.0 figures noted above to 4.0 (20%/5%). The same chart shows that that the absolute differences between rates changed in the opposite direction of the relative difference both for the period 2010 to 2014 and period 2014 to 2016.
According to the approach of the "Race and Mortality Revisited" and the Girvan article referenced in the preparatory note, the probit d' values for the differences would be .767 in 2010, .844 in 2014, and .803 in 2016. The changes are small. But one should also recognize that these changes are based on the rounded numbers. Thus, for example, if the 2014 figures are in fact 14.6% and 3.4%, the probit d' figure for that year would be .771. The same considerations apply to each of the sets of figures, and unrounded numbers could show larger as well as smaller probit d' valued and larger as well as smaller differences between such values.
The study discusses the use of both relative and absolute differences to measures disparity. But it does not seem to reflect an awareness that the two can, and in the discipline context typically do, yield opposite conclusions about the comparative size of a disparity. Accordingly, it does not suggest how a policy or administrator should be regarded when, as a result of policies or actions of an administrator, one measure of disparity increases while another measure decreases.
The study also reflects a failure to understand the ways absolute differences and relative differences yields opposite conclusion about the comparative size of disparities in different settings. Figure 3 at 23 provides bar charts on suspension rates for elementary and secondary school. The bars show suspension rates in elementary and secondary school of 9% and 29% for blacks and 2% and 8% for whites and the study regards the increase from 9% to 29% as especially stark for blacks. But while blacks showed the larger absolute increase between the two levels, whites showed the larger relative increase. Thus, whereas the black rate was 4.5 times the white rate in elementary school (where suspension were less common), the black rate was 3.6 times the white rate in secondary schools). See figure 8 of "Race and Mortality Revisited" regarding the comparative size of measures of racial disparity in pre-school and K12.
The study also states (at 29): “There was also a statistically significant relationship between intense school segregation and the Black-White discipline gap. Schools that were intensely segregated had a Black-White discipline gap of 11%; schools that were more diverse had
a gap of about 7% (see Figure 3A in appendix A).” By “%,” the study means percentage points. I cannot find in the study the actual rates. But while the absolute racial difference would typically be higher in the intensely segregated schools, the relative racial difference would be lower in such schools.
An understanding of this issue is also important with respect to drawing inferences about processes. The study, like other studies, seems to find significance in the size of disparities for subjective offenses (in this case, measured in absolute terms). But those originally finding significance on the bases of the comparatively large size of differences for subjectively-identified offenses versus objectively-identified offenses did so based on the comparative size of relative differences. Those doing so, however, did so without understanding the reasons why relative differences would be comparatively large for subjectively-identified offenses, as discussed on the Offense Type Issuessubpage of the Discipline Disparities page of jpscanlan.com. In any case, absolute differences commonly would be larger for objectively-identified offenses than subjectively identified ones. See Appendix Table 1 to the Offense Type Issues subpage.