Outdoor Lighting and Crime - Amper

eventually in overall crime rates intermediate between the day rate and Curve E. If these
points are plotted on a graph of absolute overall crime rate against the respective ambient light
levels at night, clearly the resulting curve will have a shape like Curve E but flatter. The same
curve would result if each of several identical cities were each given a single light reduction,
different in each case. In the real world, cities are not identical, and social factors related to
time of day do affect crime. The effect would be to add a ‘noise’ term to the data points,
displacing them up or down from positions on a smooth curve.
The ordinates in the plots of crime against light energy loss per unit area are the crime rates
for individual cities. The values are the observed equivalent of the theoretical prediction plus
an idiosyncratic error term. The abscissas are quantities roughly related to mean luminance or
illuminance of each city at night. Actual illuminances for streets are likely to lie within the
range indicated by line A in Figure 6, giving a clue to the mean constant of proportionality
between the satellite measures and the corresponding street illuminances. An ideal measure
would be proportional to just the ambient illuminance, but many factors could introduce
variations, such as mix of lamp types and proportion or number of upwardly aimed
floodlights. The horizontal position of each city’s data point is therefore also subject to some
possible error term that is not directly connected with the hypothesis.
If the hypothesis is correct, then the actual plot of crime rate against mean light energy loss
per unit area for cities within a given country should be something like Curve E, with
individual points subject to vertical and horizontal displacement from unrelated influences.
Bear in mind also that non-lighting effects are likely to make up part of the vertical ordinates
of both the observed data plot and the theoretical form of Curve E. As mentioned in Section
5.2.3.7, two of the actual plots for USA appear to be consistent with the shape of Curve E in
parts above Line A. The varying slope of the theoretical curve is approximated by the actual
linear regression line, or better approximated when the light energy loss data are transformed
logarithmically. Curve F is not supported and Curve C is rejected by the USA results.
Similar conclusions apply to the results for England, and possibly for Canada.
Depending on which part of a Curve E is represented by the actual light energy loss
measurements, it can be seen that the slope of the regression line might well end up with a
negative intercept on the vertical axis without necessarily devaluing the predictive power of
the regression line in the illuminance region it applies to.
An unduly small or negative intercept could arise if the slope is too large for reasons such as
data errors or unknown influences. This is checked now in the case of Figure 13. The range
in the satellite measures shown on Figure 13 and in Table 8 is a factor of 2.25 or 0.35 log unit,
short 68 in comparison with the 5 log units covered by Line A in Figure 6. It is not even as
large as Line B in Figure 6, the mean increase of 3.375 in light levels in the relighting
experiments included in the Farrington and Welsh review and meta-analysis. (Even that
range was criticised in Part 1 for being too small for accurate determination of the effect on
68 This is not surprising for two reasons: firstly the selection of cities for light energy loss
measurement appears to have been mostly on the basis of apparent brightness detected by the
satellite, and secondly, the uniform application of national standards for street lighting would
tend to limit the variations introduced by other sources such as lit advertising signs and
decorative floodlighting.
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