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Jim Kompanek
Introduction
Lesson 7 furthers the examination of crime pattern data for Philadelphia using burglaries as an example. Custom color schemes and patterns were used to portray the same data in different ways.
Custom Color Schemes
Figure 1 consists of burglary data (rates) for census tracts within the city of Philadelphia. It uses a custom color scheme which ranges from light green to dark blue. It is symbolized using an equal interval classification scheme. With equal interval classification, the data is distributed within equally sized classes. In the case of Figure 1, this data is grouped in roughly 0.29 percent increments. This classification scheme works well with rectangular distribution, with generally equal rates throughout the dataset. As can be seen in Figure 1a, the data is slightly skewed with very few observations between 0.87 and 1.45 percent. The majority of readings are within the first two classes (0 - 0.29 and 0.29 - 0.87 percent) and Figure 1 does a generally poor job at displaying this lower level of variation. Though the lower crime classes seem to make up the majority of the census tracts, the highest crime tracts do stick out with this scheme (north of Center City, along Broad St.).
Figures 2 and 3 both use a diverging color scheme of brown/white to light/dark purple. A diverging scheme combines two sequential schemes together that diverge from a common light color. This scheme is generally used for making comparisons from a base value. In the case of Figure 2, the 0.58 - 0.87 percent class is the median class in the equal interval classification and is symbolized with a white color. From the white median class, the colors diverge with brown hues indicating below-median and purple hues indicating above median burglary rates. Again, Figure 2 does a good job at indicating the tracts with the highest burglary rate, it does a poor job at differentiating the areas with below median-crime.
Figure 3 uses the same diverging color scheme but uses a standard deviation classification scheme. This scheme determines classes based on how far they deviate from the mean. This classification scheme is generally more useful when looking at the given data, as it indicates how the tracts deviate from a mean burglary level (where, presumably the average-burglary rate tracts are of less interest). Figure 3 gives a more realistic portrayal of where burglaries are happening throughout the city with the highest crime tracts indicated in purple. Because this is based on the mean burglary rate, the outliers (the few very high crime tracts) do not impact the distribution the way Figures 1 or 2 do.
Figure 1. City of Philadelphia crime data using equal interval classification scheme.
Figure 1a. City of Philadelphia crime data chart displayed with equal interval classification scheme.
Figure 2. City of Philadelphia crime data using equal interval classification with diverging color scheme.
Figure
Figure 3. City of Philadelphia crime data using standard deviation
classification with diverging color scheme.
Symbolization Methods
Figures 1, 2, 3 (see above) are all choropleth maps which map the rate of burglaries throughout the city. The following figures (Figures 4-9) all map raw counts of burglaries. Choropleth maps are generally not used when it is desired to map raw counts; as such, graduated and proportional symbols do a better job portraying the raw data.
Figure 4 is a map of the raw count of burglaries by census tract in Philadelphia using a graduated symbolization scheme. Because the few very high burglary census tracts generally painted a distorted view of crime distribution (see Figures 1 and 2), the following figures use a Natural Breaks (Jenks) classification scheme. This classification method uses a calculation that "creates class breaks inherent within the data by maximizing the differences between classes" (Figure 4a) (Gruver 2007). This method seems most-important because it minimizes the number of classes devoted to the lack of variation within the higher burglary tracts. The graduated symbols are represented by purple circles (on a light purple background) which vary in size with small circles representing a low number of burglaries and large circles representing a high raw number of burglaries. With a graduated or proportional symbolization, circles, squares, and triangles best portray variations of data to the map reader. The dark purple circles were chosen because they contrasted the light purple (which was of a similar hue) background and were the focal point of the map. Clusters of high burglary areas are visible along Broad and Market Streets, as well as near I-95 to the east. Because only the raw count of burglaries are mapped, this data is not corrected for areas of high population. It also appears that the larger tracts, in general, have lower overall burglary counts, but this could also be because the larger tracts have a lower overall population.
Figure 4. City of Philadelphia crime data using a graduated symbolization scheme.
Figure 4a. City of Philadelphia crime data chart displayed with Natural Breaks (Jenks) classification scheme.
Figure 5 represents the same data as above (again, with four classes and Natural Breaks (Jenks) classification) but uses a proportional symbolization scheme. In Figure 4 (see above), the ratio of circles sizes is arbitrary, with the higher counts simply being larger than that of the smaller. The proportional scheme depicts the symbols as proportional in size based on the actual counts, i.e. the 10 circle depicts a count 10x higher than the 1 circle. The biggest obstacle I faced with this type of map was minimizing the obstruction caused by the circles. Unfortunately, this was the biggest challenge of using a proportional symbolization scheme. Again, I chose a color scheme of the same hue but with the circles being darker than the background. Although, the same clusters are generally visible in Figure 5 that were seen in Figure 4, this map is generally too obstructed to be of much use. I also attempted to shrink the smallest class to a size of 1 but that only managed to make the smallest classes indecipherable and did not dramatically shrink the largest symbol.
Presumably, in a crime map, the areas with the highest levels of crime would be of most interest; as such, in Figure 6 I experimented with excluding tracts with the lowest burglary levels and thereby lowering the proportion between the highest and lowest tracts, which decreased the size of the largest symbols. Again, I used the same color scheme but substituted triangles for circles. Figure 6 appears to do a better job at portraying patterns of higher burglaries in Philadelphia. These crime patterns appear to be consistent with what was observed in Figure 4.
Figure 5. City of Philadelphia crime data using a proportional symbolization scheme.
Figure 6. City of Philadelphia crime data using a proportional (with exclusions) symbolization scheme.
Like Figures 5 and 6, Figure 7 uses a proportional classification scheme. Instead of using an arbitrary shape, it uses a pictograph of a ski mask representing a burglars face. In this map, I used a gray background and proportional black pictographs to represent the crime data. Clusters of high burglary tracts are clearly visible in the same patterning as the previous figures. Although some areas of the map are overly crowded, this map does a better job of portraying crime patterning than Figure 5. This may be because the holes in the symbols give a less crowded "feel" to the map.
Figure
Figure 7. City of Philadelphia crime data using a pictograph symbolization
scheme.
Figure 8 depicts discrete burglary data for Philadelphia using a dot density map. In this case, each dot represents one burglary. Each dot is randomly placed with in the tract. Although this map does an excellent job at portraying the data as it is not nearly as cluttered as the previous figures, the small dot size implies a specific location of a burglary. As with the previous figures, a complimenting color scheme was uses (light purple background and dark purple symbols) with the symbols being darker as they are the focal point for the map.
To further examine crime data with dot maps, a multivariate dot map was produced in Figure 9. A similar color scheme was employed, with a range in purple hues used to represent burglary data from 1998 until 2003. Darker hues were used for the more recent data, as presumably, they would be most relevant. Because so much more data is portrayed in Figure 9, it was impossible to represent one burglary with one dot. In this instance, ten burglaries were represented by each dot. It should be noted that if this map was actually produced, this ratio of burglaries-to-dots would need to be mentioned in the legend. Ultimately, too much data is presented in the figure and no patterns of burglary counts could be seen between years. Removing the middle years and focusing on the earliest and the latest may ultimately provide for better results.
Figure 8. City of Philadelphia crime data using a dot density symbolization scheme.
Figure 9. City of Philadelphia crime data using a multivariate dot density symbolization scheme.
Discussion
In this lesson, burglary data was examined using two separate methods: choropleth and symbolization methods. The choropleth maps produced in Figures 1 to 3 mapped the burglary rates of each census tract and the subsequent features mapped the raw count of burglaries. In general, the same patterns of high-burglary tracts were visible in all of the figures, and the dot density and choropleth maps did the best job of portraying this data without obscuring the underlying tract boundaries and roads. The graduated and proportional symbolization schemes obstructed much of their underlying features but portrayed similar crime trends.
In all of the maps, I attempted to use the same principles when choosing color schemes. The background was generally lighter but within the same hue as the symbols. The symbols used darker colors to make them stick out on the map. Diverging color schemes were most appropriate for the Figures 1 and 2 because they portrayed changes in rates and a graduated color scheme was used in Figure 3 because it represented the standard deviation which diverged from zero.
The choice of classification schemes also played an important role in the resulting maps. The use of an Equal Interval classification resulted in nearly empty classes because of the relatively few high crime tracts, while the Standard Deviations did a acceptible job at showing the extremes (both high and low burglary tracts). Ultimately, I used a Natural Breaks (Jenks) classification method because it grouped the highest crime tracts together, instead of creating nearly empty classes like the Equal Interval classification scheme.
The only map which portrayed time was Figure 9. Ultimately, too much data is presented to actually see any trends over the course of six years. By removing the middle years or every-other year's data, the resulting maps may have been clearer. To give a general comparison of burglary counts between years (although outside of the scope of this lesson), pie charts were used in the following figure. Although the charts don't allow for comparison of burglary counts between tracts, they do indicate an overall decrease in burglaries over the course of six years.
Figure 10. City of Philadelphia crime data using pie charts.
References
Gruver, Adrienne
2007 Multiple Classifications and Multiple Representations, Lesson 8. The Pennsylvania State University World Campus Certificate Program in GIS. Accessed 28 May 2007
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