1. Descriptive Spatial Analysis
Definition of Crime Mapping
Single Symbol Mapping
Buffers
Chart Mapping
Graduated Mapping
Hotspot Analysis
Practical Examples
The purpose of this section is to review methods of descriptive spatial analysis, the process of using maps to spatially describe a data set. This section includes several examples to illustrate when it is appropriate to use the various types of descriptive mapping methods such as single symbol, chart mapping, etc.

2. Definition of Crime Mapping
Crime analysis is …
A geographic information system (GIS) is a set of computer-based tools that allow a person to modify, visualize, query, and analyze geographic and tabular data.
Consequently, computerized crime mapping is the process of using a geographic information system in combination with crime analysis techniques to focus on the spatial context of criminal and other police activity.
It is important to remember that using a GIS to analyze crime is not just the act of placing incidents on a map but also of analysis.
Source: Boba, R. (Forthcoming). Crime mapping. In Encyclopedia of criminology. Chicago: Fitzroy Dearborn Publishers.

3. Single Symbol Mapping
Uses individual symbols to represent point, line, and polygon features.
Allows for a detailed analysis of small amounts of data.
“Similar to the wall maps and push pins that have historically been used by police agencies to map crime, single symbol maps use individual symbols to represent point features such as the locations of crime or traffic accidents, line features such as streets or pathways, and polygon features such as land parcels or police districts. Single symbol maps allow for a detailed analysis, and they are used quite frequently in policing to depict incident locations for small amounts of data. A drawback to using single symbol mapping is that if two or more incidents share a geographic attribute such as the same address, subsequent symbols are placed on top of the original. Thus, it is difficult and time-consuming to determine if more than one incident is occurring at the same address. Additionally, maps of large data sets can become cluttered if too many features are added.”
Source: Velasco, M. & Boba, R. (2000, November). Manual of crime analysis map production. Washington, DC: Office of Community Oriented Policing Services.

4. Example: Too Much Data
This single symbol map is not a useful analytical tool since too much data are present on the map. Better methods for displaying a large amount of burglary data are shown later in this section.

5. Example: Tabular Data
This map is useful since it allows for a detailed analysis of a small amount of data. The number of burglaries is shown in the legend so that viewers know that each point represents only one incident.

6. Example: Geographic Data
Single symbol mapping is usually acceptable for geographic data sources such as buildings, rivers, and police beats.

7. Example: Geographic Data
Unlike the points used to depict school locations in the preceding slide, the use of polygons (parcels) allows viewers to determine the edges of a school’s campus. Parcels can be extremely useful for buffer mapping, discussed on the following slides.

8. Buffers A buffer is a zone of a specified distance around a feature.
Points, lines, and polygons can be buffered.
Buffers are useful for proximity analysis and can be designated at one or many intervals (e.g., 500 feet, 1,000 feet, 1 mile).
Buffers allow you to analyze activity occurring around a geographic feature; for example, assault arrests occurring within 200 feet of bars.

9. Buffers: Point Example
As shown in this example, buffers can be drawn around bus stops to determine whether there are safety issues in the area. Additional geographic locations that may be useful to buffer include transit stations, street lights, and intersections.

10. Buffers: Line Example
Recall the discussion of “awareness space” in the Theory section of this training course. As shown in this example, pathways can be buffered to determine an individual’s awareness space (locations/areas with which an individual has some level of knowledge).

11. Buffers: Polygon Example
In this example, parcels are buffered at 1000 and 2000 feet; buffers can be useful for determining if drug or weapons violations occurred within proximity of a school campus. Other types of polygon data that can be buffered are buildings.

12. Chart Mapping
A chart map allows for the display of the values of many data attributes at once with either a pie or a bar chart.
The mapping program takes the values for numerous variables and displays them in a pie or a bar chart on the designated location on the map.
Chart mapping is used less frequently than single symbol and graduated mapping, but it can be helpful for administrative crime analysis; that is, conveying information in a visual, easy-to-understand format.

13. Chart Mapping: Pie Chart Example
This map depicts the relative frequencies of four types of incident reports taken at middle schools. Note that the size of the pie charts can be altered; in this example, larger charts represent schools with a higher number of incidents while smaller charts depict schools with fewer incidents.

14. Chart Mapping: Bar Chart Example
Bar charts illustrate relative frequency levels, versus relative percentages. In this example, bar charts are used to depict data attributes of a geographic polygon feature (block groups). Note the high population of 18 to 29 year olds in the left block group – what might this mean?

15. Graduated Size Mapping
Data are summarized so that symbols (point or line features) are altered in size to reflect the frequencies in the data.
Reflect more incidents at a given location with a larger symbol or a thicker line.
“In a graduated size map, data are summarized so that symbols (point or line features) are altered in size to reflect the frequencies in the data (see next section for classification methods). A graduated size point map reflects more incidents at an individual location with a larger symbol. A graduated size line map reflects more incidents along that line segment with a thicker line. Graduated size maps are valuable for depicting multiple events of the same type at the same location, such as traffic accidents. However, it is difficult to use graduated size maps to depict different types of incidents, e.g. burglaries and thefts, as they too are placed directly on top of one another. In addition, graduated size maps become cluttered if a large number of incidents are mapped, and oftentimes, larger symbols may conceal smaller ones, depending on the map’s scale.”
Source: Velasco, M. & Boba, R. (2000, November). Manual of crime analysis map production. Washington, DC: Office of Community Oriented Policing Services.

16. Example: Too Much Data
Similar to the single symbol map on slide 4, too much data are depicted in this example. Also note that the symbol sizes should be differentiated more so that the frequencies are easier to distinguish.

17. Graduated Size Point Mapping Example
A smaller amount of data are used in this example, making the robbery locations easier to distinguish. Also note that the symbol sizes are altered so it is easier to determine the frequencies associated with each point.

18. Graduated Size Line Mapping Example
In this example, thicker street segments represent higher frequencies of drug incidents. Similar examples are victimizations per student pathway, traffic accidents by street segment, etc.

19. Graduated Color Mapping
Point, line, or polygon features are shaded according to a statistical formula, custom setting, or unique value. Also called choropleth mapping.
Most Commonly Used: Unique Value, Natural Breaks (default), Custom.
Others: Quantile, Equal Area, Equal Interval, Standard Deviation.
“In a graduated color map, either point, line, or polygon features are shaded according to a statistical formula, custom setting, or unique value. There are several approaches to classifying, or grouping information when creating graduated color maps. (Note: these classifications are also used to produce graduated size maps described above.) Each classification method is briefly described below:
Natural breaks: Identifies natural breakpoints inherent in the data by using a statistical formula.
Equal area: Finds breakpoints between polygon features so that the total area of the features in each classification range is roughly the same.
Equal interval: Divides the entire range of values into classifications based on equal sized sub-ranges.
Quantile: Divides each class into the same number of features.
Standard deviation: Identifies the mean value and classifies values above or below the mean based on the standard deviation.
Custom: Classes are determined by the user.
Unique Value: Classes are based on unique values in the data.
With the exception of custom ranges, which are determined by the user, all of these classification methods are dependent upon the data; that is, for each data set, the values in the ranges will be different depending on the distribution and values within the data.
A graduated color map of polygon features such as police beats or census tracts is referred to as a choropleth map. Choropleth maps are used regularly in policing and are most useful for representing large data sets, such as annual calls for service by police reporting area or crime rate per population.”
Source: Velasco, M. & Boba, R. (2000, November). Manual of crime analysis map production. Washington, DC: Office of Community Oriented Policing Services.

20. Points Shaded by Unique Value: Geographic Data
With unique value, the classifications are based on unique values selected by the user; in this example, schools are shaded by type.

21. Points Shaded by Unique Value: Geographic Data
This is a simple example with shading used to illustrate the absence or presence of public restrooms, which can affect the type of activities that take place at the park.

22. Points Shaded by Unique Value: Tabular Data
Unique value classification should be used cautiously with tabular data. For example, if the user wants to shade burglary locations by type of entry method, there is no way to distinguish between two incidents with different methods of entry that occurred at the same location. If used with tabular data, unique value classification should only be used with single symbol data, not graduated size or color.

23. Points Shaded by Unique Value: Tabular Data
In this example, graduated color is used to depict the sequence of events.

24. Natural Breaks The default classification method in most GIS programs.
Identifies natural break points between classes using a statistical formula.
Graduated Polygon Example
The natural breaks classification is based on each unique data set; the GIS finds the best fit based on the number of class breaks selected by the user. This classification is the default in most GIS programs and is used most frequently by crime analysts. It is most useful for exploratory or descriptive analysis, not for making comparisons across time.

25. Custom
Ranges can be determined by the user and are not based on the data.
Important for comparing the same type of data over time.
Graduated Polygon Example
With custom classifications, the user manually sets the ranges based on the data. Custom ranges allow for comparisons among different data sets using a common scale. In order to determine appropriate custom ranges, it is useful to create a natural breaks map first to get an idea of the distribution of the data set.

26. Quantile
Each class contains the same number of features (data points).
Graduated Polygon Example
While most classifications are based on values in the data, quantile is concerned with the number of cases. First the data are sorted by frequency, then they are broken into classes containing an equal number of cases based on the number of classification ranges. It may be useful to illustrate this classification method with a simple example. To follow is a list of frequencies, if we use five classification ranges, then each class will have two cases.
Frequency 1 3 -- 6 24 25 32 38 44 59
112

27. Equal Interval
Divides the range of attribute values into equal sized sub-ranges.
Features are then classified based on the sub-ranges.
Graduated Polygon Example
The equal interval classification is fairly straightforward. In the example above, the highest value is 18, So if there are five classification ranges, the GIS will simply divide 18,871.7 by 5, which equals 3, Therefore, each class is equally divided into ranges of 3, The application of equal interval is limited since it doesn’t account for the shape of the distribution and can be greatly influenced by outliers, as shown above.

28. Standard Deviation
The GIS determines the mean value and then places class breaks above and below the mean based on the standard deviation.
Graduated Polygon Example
The calculation of standard deviation is similar to the process discussed in the Statistics section of this training course, then each polygon is shaded according to where it stands relative to the mean. This method can also be useful for identifying outliers in a data set. Note that there is usually no area that is shaded the color of the mean (as it is a statistical product and may not exist in reality, such as 4.57 crimes in a beat).

29. Use of Classifications
Classifications are the descriptive statistics of spatial analysis. Thus, they should be controlled by the analyst and carefully applied.
A danger is that the GIS has defaults (natural breaks into five categories) and analysts do not change them.
Guidelines:
Use most, if not all, of the classifications in the beginning of the analysis to determine the nature of the data and its distribution.
Experiment with number of categories and classifications to see how the maps change.
Determine the purpose of the analysis and choose the best classification.
Analysts are encouraged to experiment with the different classification ranges in order to fully understand how they are calculated and can be used. However, some of the methods (e.g., equal area) probably do not have any relevance for analysis in policing and should not be used. The most frequently used methods are natural breaks, custom, and unique value.

30. Exercise Scenario: How much data? Which unit of analysis?
You are a member of a problem-solving team tasked with addressing an ongoing robbery problem in the city. You have been asked to bring an analysis of robbery to the first meeting. What type of map would you bring?
How much data?
Which unit of analysis?
Which classification?
Discuss this scenario with the class before advancing to the next slides.
Obviously, one would also do analysis other than what can be done with mapping. However, for this exercise, focus the conversation on mapping.
How much data: most current, but enough to see seasonal effects. One year would be enough…not a tactical analysis.
Which unit of analysis? Depends on how much data. The next slide shows graduated size points, but graduated color should probably be used since one year is too much data for points.
Which classification: for a one-time, exploratory analysis such as this, the natural breaks classification may be most useful.

31. Graduated Points
Note that the type of classification is stated in the legend, it is good practice to add this information to every graduated map so that users understand what the data represent and so that, if necessary, the map can be recreated.
Clearly, one year of robbery data is too much information to display through a graduated size point map.

32. Graduated Color Polygons: Natural Breaks
While this map is general, it may be the most useful for scanning purposes; that is, determining the size and locations of the city’s robbery problem. This map is a starting point for further analysis.
Note the difference between slide 31 and 32 and the really dark maroon area on slide 32. The slide depicts the whole dark area as a problem whereas on slide 31 we see specific points. Many times officers see this and they will assume the whole area is bad when in fact in reality it is not.

33. Graduated Color Polygons: Standard Deviation
Standard deviation is also useful in that it allows users to identify relatively higher areas that may be most in need of police attention. One note about the legend: some analysts replace the labels above with nominal labels such as lower than average, average, higher than average, etc. so that the maps are easier for a variety of users to understand.

34. Exercise
Scenario:
As part of an impact evaluation for a problem analysis project to reduce commercial burglary, you are asked to prepare a map that compares before and after (same amount of time) the response by block group.
How would you present this in two maps?
In one map?
Discuss this scenario with the class before advancing to the next slides.
Remember that custom classifications are typically required for making accurate comparisons between two maps.
This exercise is to get the class to think about the classifications we just discussed.
In two maps you would use custom. In one you would present the differences.

35. First of two maps
Note the use of a custom classification range…

36. Second of two maps
Note the use of a custom classification range…

37. In one map: Difference between Pre and Post
This custom range allows for the display of change over time in one map. Bar charts could also be used to illustrate change, although the study area would have to be smaller. A paired samples t-test can also be used to show a statistical difference (versus a visual difference seen here); see the Statistics section of this training course for more information about this method.

38. Exercise
Scenario:
The chief asks you to examine aggravated assault and simple assault in the city to see if there are differences in the relative frequencies by block group (or other polygon). That is, are there some areas that are higher in aggravated assault than others and are those the same that are higher in simple assault?
Discuss this scenario with the class before advancing to the next slides.
There are two classifications that allow us to compare two unlike distributions…

39. Using Standard Deviation: Aggravated Assault
Standard deviation is useful in that it allows users to identify problem areas for aggravated assault. These areas can be compared with the following map of simple assault.

40. Using Standard Deviation: Simple Assault
Note that the problem areas for simple assault are similar to those for aggravated assault; however, we do not know the frequency of the problem – does simple assault occur more frequently than aggravated assault?
This map focuses more on comparing the means.

41. Using Quantile: Aggravated Assault
With the quantile classification, each class contains the same number of data points. In this example, one-fourth of the block groups fall into each category. This map is useful in that it shows the values of aggravated assault per block group.

42. Using Quantile: Simple Assault
With the quantile classification, each class contains the same number of data points. In this example, one-fourth of the block groups fall into each category. This map is useful in that it shows the values of simple assault per block group.

43. Hotspot Analysis
In this context, the term hotspots refers to concentrations of events confined to a particular geographic area that occur over a specific time period. Hotspots are also referred to as clusters or concentrations.
Methods for determining hotspots…
Graduated color maps
Map grids
Ellipses
Kernel density interpolation
Hotspot analysis is another method of descriptive spatial analysis. The following section describes four methods of hotspot mapping, outlining the strengths and weaknesses of each. Hotspot mapping is also discussed in the Spatial Statistics section of this training course.
In a discussion about calls for service and redistricting the following phenomenon was discussed.
Some cities have a high daytime population and a low night population and in other cases it is the reverse (e.g., Wisconsin).

44. Hotspot Analysis Graduated Color Maps
Point, line, or polygon features are shaded according to a statistical formula, custom setting, or unique value.
In this example, census groups are shaded by the number of incidents.
Note: incidents are placed on the map at their address location for reference.
Graduated color maps are relatively easy to produce since most analysts have access to geographic data sources such as census tracts or block groups which can be used to aggregate point data. However, these land units may be arbitrary and the shading does not reflect the actual locations of the incidents. For example, note in the map above that many of the incidents occur at the boundaries of the census tracts.

45. Hotspot Analysis Map grids
Each grid cell is shaded according to the number of incidents.
Unlike the preceding graduated color map, this method allows for smaller search areas.
However, the grids are arbitrary and may not depict realistic separation of land areas.
The creation of a grid allows the analyst to control the size of the land units; however, grids are also arbitrary and may not account for actual land features such as streets and lakes.

46. Hotspot Analysis Ellipses
Ellipses are drawn around the most dense concentrations of activity.
Software such as S.T.A.C. (Spatial and Temporal Analysis of Crime), developed by the Illinois Criminal Justice Information Authority (ICJIA), uses a statistical method to find clusters.
2nd order cluster
1st order clusters
More information about the STAC program can be obtained on the Illinois Criminal Justice Information Authority’s Web site at:

47. Hotspot Analysis Kernel Density Method
A grid is applied to the map, and a “score” is derived based on the number of incidents within each grid cell as well as the distance to other incidents.
Cell size and search radius can be dictated by the user.
The density method is explained in detail in the Spatial Statistics section of this training course. With this method, hotspots are identified by overlaying a grid and searching for dense concentrations of activity.

48. Hotspot Analysis Factors to consider:
Definition of a hotspot
Choice of variables
Number of hotspots
Scale
Grid size and search area
Visual display
Comparisons
There are many different methods of hotspot analysis, and each technique will reveal different groupings and patterns within the groups.
Factors to consider:
Must points belong to a cluster or can they be isolated? Can points belong to multiple clusters?
Whether other variables are used to weight similarities among points.
Whether users can define the number of clusters to be found.
Whether clusters are defined by small or large areas.
What is the total search area for clusters? How is it defined?
Whether clusters are mathematically or user-defined.
How the clusters are drawn.

49. Practical Examples of Descriptive Mapping
The following examples are based on work conducted by the Police Foundation’s Crime Mapping Laboratory and are meant to illustrate the methods of descriptive mapping discussed in this section.

50. To assist in resource allocation of ATF agents: analysis of gun tracing incidents per county for numerous states.
This is a simple graduated color map with a custom legend.
This map is only an example. The data used to make this map are not real.

51. To assist in resource allocation of ATF agents: analysis of number of agents per county for numerous states.
This is a simple graduated color map with a custom legend.
This map is only an example. The data used to make this map are not real.

52. To assist in resource allocation of ATF agents: analysis of gun tracing incidents and number of agents per county for numerous states.
This standard deviation map can be used to determine areas in need of more or fewer ATF resources.
This map is only an example. The data used to make this map are not real.

53. Problem Analysis Project Discussion
Discuss various types of descriptive analysis that could be done.

54. Local Level Risk Assessment for Homeland Security
Various geographic data are used in combination to assign a score to an area. The score is a combination of values (weighted) that can be based on either the presence/absence of features.
The result is a thematic shading of polygons with the darkest (highest score) implying a higher risk. (Note that there is no probability assigned, only a score.)
This method can be used for other types of crime (e.g., risk of auto theft, robbery, etc.)
The homeland security risk assessment discussed on the following slides allows for the prioritization of targets and more effective allocation of police resources. It draws upon work done by Bryan Hill of the Glendale, AZ, Police Department.

55. Features to Consider Nuclear power plants
Ammonium nitrate repositories
Airports
Amtrak
Mass transit lines
Amusement parks
Malls
Hydro Plants
Landmarks
Research laboratories
Dams
Petroleum refineries
Ports
Government buildings
Interstates
Rivers
Population levels
Major utility lines
Etc.
These are several data sources that may be useful to consider when preparing a homeland security threat assessment. It may be helpful to ask students to list features to consider for a sample problem such as robbery and motor vehicle theft.

56. Example
This map depicts several selected data sources: research facilities, rivers, schools, railroads, and government buildings. The following slides depict one method for combining these data sources to create a risk assessment.

57. Zones containing some part of a government building or property (note polygons).
The selection of adjoining zones is a subjective decision based on the analyst’s knowledge that a high volume of activity at a government facility would have a substantial impact on the surrounding areas.

58. Zones through which rivers flow.

59. Zones that border railroads.

60. Zones that contain schools.

61. All Zones within ½ mile of major research facilities (weighted).

62. Total Risk Assessment
This determination of risk is based on the presence of potential terrorist targets, but similar profiles can be created for crimes such as robbery and auto theft. Risk profiles allow police to focus their crime reduction efforts at high-risk locations.

63. Alternative method: Using arbitrary grids (same sized area).
This map represents an alternative method of determining risk using an arbitrary grid rather than zones.

64. Caution
This method is not tested, and many decisions are subjective (e.g., what data to include, values given to the variables).
Also…
What should the unit of analysis be? Beat? Grid?
If an arbitrary grid, what should the grid area be? What should the grid cell size be?
Which of the many types of data available should be included and when? (Different jurisdictions will include different types of data.)
How should the variables be scored in relation to one another? For example, should nuclear facilities be weighted more than malls?
It is important to consider these questions when preparing a risk assessment.

65. Problem Analysis Project Discussion
Discuss what variables would be considered in a risk assessment of commercial burglary for the sample jurisdiction.