RACE AND THE ENFORCEMENT OF DRUG DELIVERY LAWS IN ...

whites engaging in the same behavior in the same geographic area. 106 This calculation
likely understates the actual disparity between black involvement in drug
delivery and black representation among arrestees because the observational
study includes only those who deliver drugs outdoors and because some of the
arrestees classified by SPD officers as white were likely Latino/Hispanic. Still, if
the 33 percent figure is treated as the “benchmark” against which arrest statistics
are compared, very large racial disparities remain after race differences in
involvement in drug delivery are taken into account.
In what follows, the statistical significance of the difference between the share of
downtown deliverers who are black or white and the share of delivery arrestees
who are black or white is evaluated. Tests of statistical significance allow us to
assess whether, for example, the fact that the proportion of arrestees who are
black is greater than the proportion of deliverers who are black may be due to
the fact that we only have samples of these two groups. Social scientists conclude
that an observed difference between two sample proportions is statistically
significant if it is very unlikely to be the result of chance. Conventionally, social
scientists consider a difference between two proportions to be statistically
significant if there is a 5 percent or smaller probability that the observed
difference is the result of chance.
In this case, we are comparing the estimated proportion of observed downtown
deliverers who are black or white with the proportion of purposeful downtown
delivery arrestees who are black or white. 107 To measure the statistical
significance of such differences, researchers calculate a Z score that can be
translated into a probability. 108 Z scores with an absolute value of 2 or more are
106 Whites were 9.3 percent of those arrested, but 49.5 percent of those observed delivering
drugs. Dividing the former by the latter yields a ratio of .187. Conversely, blacks were 85.3
percent of those arrested, but 33.3 percent of those observed delivering drugs, a ratio of 2.56.
The result of dividing 2.56 divided by .187 is 13.6 equals 13.6.
107 Insofar as some Latinos/Hispanics are classified as whites, tests of the statistical significance
of white under-representation among arrestees will be based on an inflated estimate of white
representation among arrestees and are therefore conservative. Conversely, any tests of the
significance of Latino under-representation among arrestees would rest on deflated
estimates of Latino representation among arrestees, and would therefore exaggerate Latino
under-representation. Z scores are therefore not used to test the significance of Latino underrepresented
among arrestees.
108
The Z score for each comparison is calculated according to the following formula:
( ˆ π ˆ
2
−π1)
z =
ˆ
σ π
π
ˆ2 − ˆ1
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