Prospective crime mapping in operational context Final report

2. Testing the generalisability of prospectivemappingAs discussed above, research concerned with geographical hotspots of crime demonstratesthat over a given period of time crime is spatially concentrated (see, for example, Eck andWeisburd 1995). Other research (e.g. Farrell and Pease, 1994) demonstrates that within aspecific geographical region, crime also exhibits temporal clustering, with incidence ratesincreasing with the onset of the winter, and diminishing around the spring. However, unlessthe risk of victimisation is communicable, one would expect these spatial and temporalclusters to be independent of each other, with the incidence of new series of crime eventsfailing to exhibit localised spatial and temporal increases. Simply put, the communicability ofburglary risk may be demonstrated only by showing that burglary clusters in both space andtime. Conformity to this pattern would be evident if houses near the burgled home werevictimised shortly afterwards more than would be expected on the basis of chance. Thosereaders not concerned with technical details on the demonstration of clustering should skip tothe beginning of the next chapter at this point.Empirical research concerned with the space-time clustering of events was first conducted byKnox (1964) to study epidemics of leukaemia. The rationale underlying the Knox test is todetermine whether there are more events that occur close in space and time than would beexpected on the basis of a random distribution. To do this, each event is compared with everyother and the distance and time between them recorded. For n cases, this generates ½n (n-1) pairings. A contingency table, such as shown in Table 2.1, with i columns and j rows isthen populated. The spatial and temporal increments (or bandwidths) used in the rows andcolumns can be arbitrary, although they should be so defined as to allow specific hypothesesinformed by the underlying theory to be tested. For instance, in the case of crime the questionconcerns the distance over which crime has an impact and for how long? The bandwidthsselected should have relevance to operational policing.Table 2.1: Knox contingency table example1 month 2 months 3 months …………..100m n 11 n 21 n 31200m n 12 n 22 N 32300m n 13 n 23 N 33400mn 14 n 24 n 34……..……..Note: The mathematical notation n ij refers to the observed frequency for the cell occurring in column i and row j.Thus, n 11 refers to the cell in column 1, row 1.The contingency table generated can be compared with a chance distribution. Onecomplication is that the assumption of independence of observations, a criterion for mostinferential statistical methods, is violated. However, Knox suggested that in the absence of aspace-time interaction, the statistical distribution of the expected values for the cells of thecontingency table would conform to a Poisson distribution and could be computed in thesame way as a Chi-Square test, using the marginal totals of the table. Thus,4