situations where, apparently as a result of the failure to recognize that absolute differences between rates and relative differences between rates can (or typically do in the case of discipline disparities) change in opposite directions as discipline rates decline generally. Very likely, all the situations discussed in the prior paragraph where general reductions in discipline rates were accompanied by increased relative differences in discipline rates, the absolute difference declined. See my January 29, 2019 email to the editors of School Psychology Review regarding the failure of editors of that journal to recognize that it is possible for relative and absolute differences in adverse discipline outcome to change in opposite direction, much less that they do most of the time.
In October 2017, a Virginia organization named the Legal and Justice Center issued a report titled “Suspended Progress 2017: An update of the state of exclusionary discipline in Virginia’s public schools” discussing disparities in adverse discipline outcomes by race and disability in Virginia. The report appraised demographic differences means of a comparison between the proportion a group made up of students and the proportion it made up of disciplined students, the ratio of the disadvantaged group’s discipline rate to that the advantaged group’s discipline rate, and the absolute differences between rates.
Like virtually all other work on discipline disparities, it showed no understanding that generally reducing discipline rates by PBIS and other means tend to increase (a) the differences between the proportion blacks make up of students and the proportion they make up of disciplined students (whether measured in absolute or relative terms) and (b) the ratio of the black suspension rate to the white suspension rate.
As discussed in the prefatory note, however, generally reducing discipline rates does tend to reduce the absolutely difference between black and white rates. And the Legal and Justice Center report principally relied on the absolute difference between rates to measure disparities, though also referenced other measures.
Table 1 below is based on data on the report’s Figure 3 (at 4)[i] on rates at which black and white students received one or more short-term out-of-school suspensions (STOSS) from the 2011-12 to the 2015-16 school years, along with the absolute difference between rates, the ratio of the black rate to the white rate, and the estimated effect size (which is the measure of difference I discuss in “Race and Mortality Revisited,” Society (July/Aug. 2014).
The table shows alternative figures for the 2015-16 year, because the report elsewhere gives a different figure for whites in that year (3.4% versus 3.3%) in the Figure 3 that appears on page 3. The 3.4% figure, which is also shown for Hispanics, comports with the 3.8 ratio black the black rate to the white and Hispanic rates the report mentions on page 3.
I limit the data in the Table to blacks and whites both because that is usually the most useful information and because the Figure 3 of page 4 gives year-by-year figure only for blacks and whites. The black and Hispanic figures would be the same as the black and white figures in the final column.
Discussing the data, the report noted that the absolute difference ranged between 9.8 and 8.9 percentage points. This would pertain to the 2011-12 and the 2013-14 school years, between which there occurred a general reduction in discipline rates, which, as commonly happens, was accompanied by a reduction in the absolute difference but an increase in the black-white ratio. The EES indicates that the difference in the strength of the forces causing black and white rates to differ can be measured, increased very slightly. Thereafter, there occurred increases in the black rate but no increase for whites (which necessarily means an increase in the EES) or a very slight one, as shown in the bottom row of the table.
Table 1: Black and white short-term suspension rates from the 2011012 to the 2015-16 school years with measures of difference.
In October 2018, the organization issued a new version of the report with data on the 2016-17 school year. In that version the report highlighted that the following information (at 1; original emphasis):
Perhaps most disturbing in the 2016-17 data is an increase in the already astonishing rate that Virginia schools continue to disproportionately suspend Black students. The suspension rate for Black students was 4.5 times higher than for Hispanic and white students—up from 3.8 times higher in 2015-16.
An increase in the black-white ratio (or the black to white and Hispanic ratio) to 4.5 would be remarkable absent a very large general reductions in suspensions (which seems not be the case). But the origin of the 4.5 figure is not evident. It is repeated on page 6, which also has a chart showing short-term suspension rates of 12.5% for blacks, 3.6% for Hispanics, and 3.3% for whites. According to these figures, the black/Hispanic ratio is 3.47 and the black/white ratio is 3.63.[ii]
On the other hand, one can derive the ratio of one group’s rate to another group’s rate from figures on the proportion the group’s make up of students and the proportion they make up of suspended students. That method – which gives the same results as the ratio of one rate to another – shows a black-white ratio of 4.51 for the 2016-17 school year. But the information would yield a ratio of 4.46 for the 2015-16 school year.[iii]
This method shows that Hispanic and white rates were essentially the same in both the 2015-16 and 2016-17 school years. That is the Hispanic-white ratio was .98 in the former year and 1.01 in the latter year, which (allowing for rounding) would indicate that the white and Hispanic figures were the approximately the same in both years. In any case, there seems to be some inconsistency in the figures in the report (unless I have misinterpreted something). But it is very unlikely that the black-white ratio increased from 3.8 to 4.5 between the 2015-16 and 2016-17 school years.
As discussed in the email to the editors of School Psychology Review mentioned in the Prefatory Note, for most states, Department of Education data on black and white rates of one or more suspension and multiple suspensions for the 2013-14 school year illustrate the way that reducing suspensions by eliminating what would otherwise be first suspensions will tend to increase relative differences in one or more suspension while reducing absolute differences between rates or one or more suspensions. Virginia is one of those states. According to these data (which differ slightly from the one or more suspension figures for the 2013-14 year in the Legal and Justice Center 2017 report), black and white rates were 12.16% and 3.66% for one or more suspensions (a ratio of 3.43 and an absolute difference of 8.99 percentage points) and 5.65% and 1.34% for multiple suspensions (a ratio of 4.2 and an absolute difference of 4.31 percentage points). Thus, as in the great majority of states, eliminating what would otherwise be first suspensions in Virginia will tend to increase the black-white ratio but reduce the absolute difference between rates.
Technical Note: The following is a technical point that applies to analyses of demographic differences in (a) in-school suspension, (b) short-term out-of-school suspensions, (c) long-term out-of-school suspensions, and (d) expulsions. The (a), (b), and (c) categories are each intermediate categories in a hierarchy of discipline severity. For reasons discussed on my Intermediate Outcomes page, one cannot effectively analyze rates of experiencing in (a) or (b) or (c), but one can effectively analyze rates of (a) combined with (b) through (d), (b) combined with (c) and (d), and (c) combined with (d), or (d) alone – just as one cannot effectively analyze rates of receiving grades of B, C, or D, though one can analyze rates of B or below, C or below, D or below, or F. But there are sufficiently few long-term out-of-school suspensions and expulsions compared with short-term out-of-school suspensions analyses of rates of out-of-school short-term suspensions probably gives a fair picture of the situation. See also the Discipline Disparities page.
[i] The report has two charts identified as Figure 3, one on page 3 and one on page 4.
[ii]Both of the reports invariably use “times higher” or “times larger” when they actually mean “times as high” or “times as large.” That is, a ratio of 3.0 means one figure is three times as high (200% greater) than another, not three times higher (300% greater) than another. The misusage predominates even in scientific journals with the exception of the New England Journal of Medicine. See the Times Higher subpage of my Vignettes page. Though ProPublica’s analyses of demographic differences are invariably undermined by failure to recognize the ways measures tend to be affected by the prevalence of an outcome, perhaps due to the influence of Philip Meyer’s Precision Journalism, the organization appears to be very careful on this point.