Kern County is a California County between Los Angles and Fresno comprising the Bakersfield Metropolitan Area. Its population was about 840,000 (2010). As of the December 2017 it had 264 public schools with approximately 176,000 students.
In October 2014 a group individuals and organizations sued the Kern County High School District for racial and ethnic discrimination in the imposition of discipline. The case was settled in June 2017 pursuant to an agreement that, in addition to providing $600,000 in fees for plaintiffs’ attorneys and certain monetary and other relief to particular individuals, provided for certain modifications to practices and the monitoring of data on disciplinary outcomes by race.
Both the complaint and the agreement reflect the mistaken belief that programs that generally reducing discipline rates will tend to reduce (a) relative (percentage) racial/ethnic differences in rates of experiencing the outcomes and (b) the proportions racial/ethnic racial minorities make up of persons experiencing the outcomes.
According to the complaint the district had 2,205 expulsions in the 2009-10 school year, but reduced that figure to 256 in the 2012-13 school year and 80 in the 2013-14 school year. In describing the effects of the reductions on measures of disparity, the complaint stated (at 2):
These reductions did not appear to reflect any change in the disparate effect of the expulsion polices, and in 2012-13, the last year for which disaggregated data is available, 56.6 % of Latino students were expelled (compared to 60.5% in 2009-10), 21.9% of African-American students were expelled (compared to 14.5% in 2009-10), and 17.9% of the White student population was expelled (compared to 22.7% in 2009-2010).
Statements like “56.6% of Latino students were expelled” obviously was intended to mean that 56.6% of expelled students were Latino. But the statement nevertheless reflects both the view that one would expect such proportion to decline for more susceptible groups when there occur general reductions in expulsions and that in fact, at least for blacks, the proportion increased.
From the figures cited in the complaint properly understood, and the proportions three identified groups made up students – 62% Latino, 6 % African American, and 25% white in 2013-14, given at page 15 of the complaint – one can calculate rate ratios for expulsions in 2009-10 and 2012-13. The formula would be ((a) proportion more susceptible group makes up of students/(b) proportion more susceptible group makes up of persons experiencing the outcome)/ ((c) proportion less susceptible group makes up of students/(d) proportion less susceptible group makes up of persons experiencing the outcome.
(I use the proportion the various groups made up of students in 2013-14 as a proxy for the proportions they made up of students in the 2009-10 and 2012-13. The proportions in those periods probably differ only slightly from the proportions for 2013-14 and differences are unlikely to materially affect the points that follow.)
The ratio of the black rate to the white rate increased from 2.66 to 5.10 and the ratio of the Latino rate to the white rates increased from 1.07 to 1.28. The ratio of the black rate to the Hispanic rate also increased from 2.50 to 4.0.
Thus, we have the usual pattern whereby general reductions in the prevalence of an outcome were accompanied by increases in relative differences between rates at which more and less susceptible groups experience the outcome.
The Kern County situation, which involves more than two groups, differs from the situation of a universe of two groups that I use in many examples in a number of respects. First, in Kern County, even though the Latino rate is higher than the white rate in both periods, the Latino rate is lower than the rate for all non-Latino persons and thus Latinos make up a smaller proportion of expelled students than they make up of all students. Thus, according to the way some school districts would examine the matter Latinos would be underrepresented among expelled students. Second, even though the relative difference between the Latino rate and the white rate increased between the two periods, the proportion Latinos made up of expelled students declined.
Patterns like these are reasons it is always better to make comparisons between two groups at a time. The IDEA Data Center Disproportionality Guide subpage of the Discipline Disparities page of jpscanlan.com mentions this issue in the context of explain the reasons why one should never analyze a disparities issue on the basis of the difference between the proportion a group makes up of persons potentially experiencing an outcome and the proportion it makes up of persons actually experiencing the outcome.