whereabouts. Since is no standard pattern in terms of geography and time exists, I have
chosen to divide the data into the following periods:
A. Time of the day/week:
i. At work, Weekdays from 8 am to 5 pm ii. Off work, Weekdays from 5pm to 8 am iii. Weekend
B. Time of the year:
i. Winter (December, January and February) ii. Spring (March, April and May)
iii. Summer (June, July and August)
iv. Fall (September, October and November)
Of course many other periods could have been used. Taking the late hours, when people sleep into, consideration could be an option. The choice of the periods is based on the assumption that if there is a significant difference in geographic occurrence of accidents, it would prove most significant when comparing the periods above.
10.4 Comparing Spatial Distributions
This section will discuss the problems of comparing geographically distributed data, i.e.
spatial distributions.
10.4.1 Unbiased Comparison
The first problem is to introduce an unbiased measure that can be used to compare two different time periods with a different amount of accidents. Table 3 shows that there are big differences in the number of accidents, hours and accidents per hour in the data available.
Which complies well with the results from Figure 17.
Time period # Days # Hours # Accidents # Accidents
Table 3. Data from time periods.
The number of accidents in a given period as such is not interesting to project, since it is not the objective to determine an overall resource allocation strategy, but to deal with the
resources at hand as well as possible. Hence a reasonable measure seems to be the number of accidents assigned to a cell point as a fraction of the total number of accidents for the entire period or simply as an index. An index could be:
number of accidents within cell
number of accidents in period * number of accidents per year = new cell value This would also render the index more meaningful. Each cell value would then represent the number of accidents per year in that cell just as if accidents happened through an entire year as they do in the actual period. The number of accidents per year is set to 30.000 (on Funen).
10.4.2 How to Compare
The second problem is how to compare the various time periods, or rather how to determine when there is a significant geographic difference: One way of comparing the data is simply by visualizing it using the GIS software and see if there appears to be a difference and preferably finding an explanation of why. Another way could be to use statistics to verify the results.
However, it has not been possible to develop or find a model that suits this problem.
The statistical models dealing with spatial problems are, to this author’s knowledge, mostly used in geology and fields dealing with sample data and then trying to interpolate what have not been measured. Models such as Inverse Distance Weighted (IDW) and Kriging [SAM p.
92] are not designed to deal with discrete events like accidents, or entire populations as in this project, but to interpolate a surface from a minor set of measurements. An alternative could be to use a classical homogeni/chi^2 test, but these tests are normally used to compare small samples from a large section of a population, and not an entire population like in this project.
Since all data, or at least what could be geocoded, is used in this project we know the distribution and we also know that there is a difference, the question therefore is: “Does the difference matter when placing ambulances?” or in other words “Is the difference so big that it should be taken into consideration?” Of course, it could be a case of an underlying
distribution of accidents, and then the more traditional statistical methods could be used. But what defines the underlying distribution, does such a distribution make sense?
Alternatively, two time periods can be compared by comparing the optimal solutions for placing ambulances, or rather calculating the difference i.e. using the optimal solution found to the one problem on the other problem, and then calculating the new solution value.
Nevertheless since the number of ambulances vary, i.e. for each number of ambulances there is a new comparison, and since finding optimal solutions for large number of ambulances is more or less impossible (chapter 11: “Models”), this method does not seem to be applicable.
I have chosen to rely mostly on the visual inspection of data, for the pure reason that if the difference is so small that it cannot be visualized, it is probably also so small that it will be of no significance, and it will be difficult to convince anyone that a difference is actually present.
10.4.3 Which to Compare
With 12 different time periods the number of possible comparisons are 66, and using visual inspection to compare the periods, it may be an advantage to establish which periods are expected to be different and then compare those first to test if the method works at all.
The major problem is that what we are looking for are “large” geographical changes. Such changes could of course be calculated when comparing the difference between various divisions of Funen, such as residential, industrial and commercial divisions or divided into municipalities. The residential, industrial and commercial divisions seem to be the most reasonable choice, however such divisions are seldom so unique that they comprise only one type of activity, especially commercial and residential areas tend to mix in the cities. That there should be a difference between municipalities in the given periods does not seem obvious, a difference would probably be difficult to explain as anything else than random variation.
A completely different way is to divide Funen into a grid and then sum up the absolute difference over all the cells between each of the time periods. The ones with the highest difference might be worth investigating. An alternative is to use the same grid division, but simply pick the periods, which are expected to have the biggest difference.
The result of the “sum of absolute difference” method is shown in “Appendix II” The one with the highest score was “summer at weekends” compared with “fall at work”. The subjective guess is that there is a big difference between “summer at weekends” and “winter at weekends”, based on the assumption that people will be attracted to different areas, such as beaches and nature in general during summer, whereas during winter they are more prone to stay indoors.