Summary: The eect of `ignoring the pairing' on the
distribution of the log crossratio
P.M.E.Altham, Statistical Laboratory, University of Cambridge,
May 26, 2004
This short note was produced in response to the paper (2004) by Marchant, who criticises the
statistical analyses in recent work by Farrington and others.
a) The crime prevalence comparisons
For example, Painter and Farrington (1999) show their Table 2 `Changes in the prevalence of Crime'
and use the log crossratio to examine the eect of the `Treatment': in this case improved street light-
ing, on reduction in particular types of crime. We wish to compare data from the `Experimental'
households with corresponding data from the `Control' households, by means of the log-crossratios of
A diĘculty for Painter and Farrington was that when the time came to analyse their data, the infor-
mation on the exact pairing of the households was unavailable. Thus, for example, although in the
Experimental group, 431 households were measured before the `treatment', and 372 households were
measured after the `treatment', we do not know the pairing for the 372 households which were quite
possibly observed both before and after. We compare the reduction in crime rate for the `Experimen-
tal' group with the corresponding reduction for the `Control' by looking at the dierence between log
crossratios for the 2 groups, and its estimated variance in the 2 cases.