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Some datarelated issuesAs stated in the introductory section, the MoJ in Britain has, since 1992, published information on the ethnicity of persons in contact with the CJS. The data for the 12 (financial) year periods, 200607 to 201718, which are used in this chapter require amplification on several points. Stops under the PACE, CJPO, and Terrorism ActsThe MoJ data present information, by ethnicity of the detainee, on the stops of persons, and any vehicles in which they may have been travelling, undertaken in each of 42 Areas, under three separate pieces of legislation: section 1 of the PACE Act 1984, section 60 of the CJPO Act 1994, and section 44 of the Terrorism Act 2000. Since the number of persons stopped under the CJPO and the Terrorism Acts was small, compared to those stopped under PACE (370,454 stops under PACE and 13,175 under CJPO for E&W for The benchmark populationThe MoJ does not provide information for stops under the PACE and CJPO Acts on whether the detainee was a pedestrian or a motorist.^{9} This is an important point because it relates to the appropriate benchmark for measuring racial disparity in stops. Farrell and McDevitt (2010) set out the pros and cons of several possible benchmarks. The easiest benchmark to use is local census data. These data could be used either in terms of the racial demographics of the resident population, or the resident driving population, of an area. This distinction is significant: if, compared to pedestrians, it is motorists who are largely stopped, then it is the driving population which is the appropriate benchmark.^{10} However, in general, local census data suffer from the flaw that they take no account of persons passing through the area whether as pedestrians or motorists; so, while an area may be characterised by a high level of stops these may be of transients rather than residents.^{11} For reasons set out in the following, this chapter uses the racial demographics of the resident population in the Areas of E&W as the benchmark for measuring racial disparity.
The decomposition of stop rates by AreaSuppose there are N persons in a country, M of whom were stopped by the police. Then a = (M/N) x 1,000 is defined as the stop rate of that country per 1,000 of its population. Now if the N persons can be subdivided into К mutually exclusive groups, indexed k = 1, K, with N_{k} persons and M_{k} stopped persons in each group, where f^N_{k} = N and M_{k} = M, then k=1 k=l the country’s stop rate can be written as the weighted average of the groups’ stop rates, a_{k} the weights being n_{k}, the shares of each group in the overall population: If there are R police areas in the country, indexed r = 1, R, such that N[ is the number of persons and M_{k} is the number of persons stopped, from group k in area r, then the stop rate of group k, a_{k} = M_{k}/N_{k}, can be written as the weighted average of the groups’ stop rate in each area, the weights being the area shares in the overall population of the group: where Now the stop rate of group k (k = 1,... ,K) in area r, a[ = M_{k}/N_{k}, can be decomposed as follows: к к The termsM^{r} = and N^{r} = in equation (5.3) represent, respec t=l к. 1 tively, the total number of persons stopped and the total number of persons in area r,(r=l,..., R); the terms A and B, respectively, МЦМ^{Г} and N^{r}k/N^{r}, represent the share of group k in, respectively, the total number of persons stopped Ю and the total number of persons (0_{k}) in area r; the term C represents the overall stop rate of the area with a^{r} = M^{r}/N^{r} being the number of stopped persons in that area per 1,000 persons; so, from equation (5.3), ceteris paribus, the higher the stop rate of area r, cf, the higher will be the stop rates of all the groups in area r. Substituting equation (5.3) into equation (5.2) yields the expression for the stop rate of group k for the country in its entirety as follows: Equation (5.4) shows that three forces will shape a_{k}, the stop rate of persons from group k. The first is the distribution of the members of a group between the various regions as represented by n[. The greater the proportion of persons from the group living in areas with high stop rates (i.e.,n[ is high in regions with high cf) the higher will be a_{k}. In other words, equation (5.4) demonstrates that the stop rate of a group can change for the worse as its members migrate from low to high stop areas. Second, a rising rate in an area will lift all boats  as the stop rate of a region (cf) rises, so will the stop rate of all the groups located within it. Finally, notwithstanding distribution shifts between areas, and changes in the stop rate of areas, a group’s stop rate will also depend on racial bias. This is captured in equation (5.4) by the term a_{k}/P'_{k}, the ratio of the group’s share in the total of stops in an area (a£) to its share in the area’s population (fil). This ratio measures the disproportionality between a group’s share of the area’s stops and of its population. The greater this disproportionality, the greater the degree of bias against, or in favour of, the groups: the higher/ lower the stop rate of a group in area r, the larger/smaller the ratio a^{r}k/(3^{r}k. 
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