I commonly illustrate the pertinent statistical pattern by showing that lowering a test cutoff, while tending also to reduce relative differences in test pass rates, tends to increase relative differences in test failure rates, as in Table 1 of my “Race and Mortality Revisited,” Society (July/Aug. 2014) and Table 1 of my December 8, 2017 testimony before the U.S. Civil Rights Commission. The pattern can also be illustrated by suspension data showing that the ratio of the black rate to the white rate is almost always larger for multiple suspensions than for on-or-more suspensions. Thus, if all persons are given alternative punishments to what would otherwise be the first suspensions, the ratio of the black ratio of one or more suspensions to the white rate of one or more suspensions, will tend to go up, as recently discussed in my “Maryland Discipline Study Shows Usual – But Misunderstood – Effects of Policies on Measures of Racial Disparity,” Gunpowder Gazette (Dec. 16, 2019). That point may be compared to the illustration in the Tables 4 and 5 of the Commission on Civil Rights testimony, which presents the matter in terms of the proportion blacks and boys make up of students with one or more suspensions and students with multiple suspensions (i.e., the latter is larger than the former).
Truancy data is also useful for illustrating the point. Table 1 below is based on data from a 2016 article on truancy in Los Angeles (Nadra Nittle, “Truancy, suspension rates drop in greater Los Angeles area schools,” LA School Report (Mar. 7, 2016). The table shows the proportion of blacks and whites falling into various increasingly severe levels of truancy. As the level of truancy increases and the proportions of both blacks and whites falling into that level declines, the ratio of the black rate to the white increases. Thus, as schools increasingly limit sanctions for truancy to only the more extreme cases of truancy, the ratio of the black sanction rate white rate sanction rate will tend to increase.
Table 1. Black and white rates of reaching various levels of truancy and ratio of the black rate to the white rate
Ratio of Black Rate
to White Rate
More than twice
More than a few times
More than monthly
More than weekly
Table 1 in the body of this subpage presents rates experiencing any truancy and rates of experiencing more than the level truancy indicated in the second to fifth rows. The data are based on the data in the second table in the Nittle article. That table actually showed the rates of falling within each of five discrete categories as in Appendix Table 1 below.
Appendix Table 1. Black and white rates of experiencing certain discrete categories of truancy and ratio of the black rate to the white rate
1 to 2 times
A few times
Once a month
Once a week
More than once a week
For reasons discussed on the Intermediate Outcomes subpage the Scanlan’s Rule page of jpscanlan.com, even with a sound measure it is not possible to analyze demographic differences in rates of falling into discrete categories of outcome severity, save for the most severe. That is why it was necessary to aggregate the rates shown into rates of experiencing any truancy and rates of experiencing more than a particular level of truancy.