Assignment_2 GEOG_510 Spatial Analysis_Spring 2016 Prof. Christopher Bone | GTF: Christina Appleby Student: Isabel Rivera Introduction: The city of Chicago has been known for a long history of organized crime and well as famously home to the American mafia figure Al Capone.i Even today, Chicago is still categorized as high criminal city in the US, particularly by the media. In 2012, Chicago had a murder rate of 18.5 per 100,000 residents, ranking 16th among cities with 100,000 people or more.ii Over the last years, many cities in the US have seeing an increment of violence after many years of decline. This is the case of Chicago, that sow a significant declined from the years 1990's to 2000's. A rate went from 943 murders in 1992 to 415 in 2013, which created a significant decline in murders. iii This can also be evidence in the graph from Chicago tribune.com web site; figure 1, in which the constant curve of violent crimes from 2006 to the present have drop. In 2008 violent crime report show 3,542 to a 2,036 in 2016. It is important then to identify the causes of why there is an increment of this crimes rather than just alarming societies for such rise, has many media have done in present and pass. It is hard to determine the specific factors that can create an increment or rise of crime, since is context related for each individual city. But for many cities the causes are about "rivalries among organized street gangs, often over drug turf, and the availability of guns are cited as major factors in some cities, including Chicago. But more commonly, many top police officials say they are seeing a growing willingness among disenchanted young men in poor neighborhoods to use violence to settle ordinary disputes." iv Therefore is important to determine the causes of the rise of crime, particularly if these are related to specific neighborhoods or ethnic groups, which can help, understand their local situations and problems that can contribute to these events. Understanding the causes may allow proposing solutions for those problems, which can result in decline of crime for many cities, particularly Chicago. The objective of this study is to utilize crime and census data to describe the spatial distribution of homicide events in Chicago and to determine if the probability of homicide is higher in neighborhoods with specific racial compositions. The study aims to answer the following questions in order to determine to establish an answer and also as a way to find a methodology of statistical and spatial analysis:

• What is the probability of at least n homicides occurring each day in the City of Chicago?

• What is the probability of exactly n homicides occurring each day in the City of Chicago?

• What is the binomial distribution of homicides occurring from 0 to 10 days in the City of Chicago?

• What is the frequency of homicides occurring in each neighborhood in Chicago?

• What is the probability of a homicide occurring in a neighborhood that has various proportions of individuals who are black or white?

Figure 1: From the Chicago tribune.com, Crime in Chicago by month from 2006 to 2016. Methods: The study is concentrate in the city of Chicago as shown in figure 2, highlighted by the metropolitan area in gray. The site is limited on to the North and East by the Lake Michigan and at the West, South and Northwest by the suburban development. In figure 3 shows the 77 community areas of the city of Chicago, which were subdivided in 1920's by the sociologist at the University of Chicago, "which can be further be subdivided into over 200 informally defined neighborhoods.v The data use for this study was taken from:

• Chicago Police Department's Crime Data Portal. In which the file that was used was the homicide report that occurred in 2015.

• U.S. Census Bureau's American Fact Finder. The file access was the Census tracts in Cook County, Illinois (in which Chicago is located), and the variable selected was race, for American Community Survey "ACS" of 5 years estimates.

• U.S. Census Bureau's Maps and Data. Data selected was the cartographic boundary shapefiles with the Census Tracts for Illinois.

• City of Chicago's Data Portal. The file access was the city limit boundary for Chicago.

 

 

 Figure 2: Boundaries - City of Chicago © City of Chicago Data Portal  

Figure 3: Chicago Community Areas, Data compiled using the Chicago Community Areas List numbered 1-77 and 'Sides' descriptions © Alissa Pumpvi

 

Analytical methods. From the data acquired for this study, the first analytical methods was to determined the probability of a least n homicides that could occurred each day in the City of Chicago. The elaboration of a histogram was developed to determine the frequency of the number of homicides for one day in 2015. This was carried out with the file access from Chicago Police Department's Crime Data Portal, called: Crimes_-_2001_to_present.csv. Which later was save under Homicides.csv. From this is was determined by the function in "R" lenght(unique(Date)) the count of events that occurred by each day to determined the number of day that n homicides occurred and maximum number of homicides that happened in one day. Also the location of homicides was address by plotting them in a location homicide graph, in which the location was given by the longitude and latitude with the value of homicides per location. A Choropleth map was develop in order to determine spatially the location of homicides with respect to population group (in this case white and black) for the city of Chicago that took place in each census track. The data use to develop this map was from census tract and city boundary shapefiles, from U.S. Census Bureau's Maps and Data, file: cd_2014_17_track_500k.shp. Together with the city limit boundary for Chicago, from City of Chicago's Data Portal. File name: geo_export_13774959-a9ad-48d4-848b-f0775cb9570f.shp. This two files were intersected and overlay with the race data for American Community Survey "ACS", file: ACS_14_5YR_B02001_with_ann.csv, in order to generate the two population groups (black and white). With the creation of two choropleth maps, we can determine the spatial location of homicides in the city of Chicago for black and white population groups. Finally the calculations of probability of homicide occurring in a neighborhood that has the following proportion of population of white and black were determined through the following range <10%; 10-20%; 30-40%; 40-50%; 50-60%; 70-80%; 80-90%; 90-100%, with the file shape file: Illinois_Race.shp.

Graphics Results: Statistical Graphs and Spatial Analysis Maps of the study

 

Figure 5: Graph the shows the number of homicide per location (Latitude and Longitude) within the City of Chicago in one day in 2015.  

 

Figure 4: Histogram Graph from R, displaying the frequency of the number of homicides in one day in 2015 in the City of Chicago.  

 Figure 6: Choropleth map, that shows the location of homicides in red dots with density of African American in the census tract.  

 Figure 7: Choropleth map, that shows the location of homicides in red dots with density of White in the census tract.  

Statistical Results: From the study it was determine that the probability of a least one homicide occurring each day for a period of one year was of 255 days being 255/365 = 69 %, and by breaking it down into the probability of n homicides per day, we have the following results:

n (# daily homicides)

Probability in %

1 69% 2 38% 3 15.6% 4 5.2% 5 2.2% 6 0.9% 7 0.4% 8 0.2% 9 0.2%

10 0.2% In the other hand the probability of exactly n homicides occurring each day in the City of Chicago was as follow depending on the number of homicides events. The maximum numbers of homicides register in 2015 for one day was 10 homicides.

 Figure 8: Choropleth map, that shows the location of homicides, circle area of homicides concentration.  

Within R functions it was also calculated the mean of frequency of the total homicides with a value of 1.92, and a standard deviation of 1.19. The total number of homicides during 2015 in the City of Chicago was 491. The binomial distribution of least one homicide occurring in 10 days in the City of Chicago was determine as fallows:

The variables use where: n= 10 days (number of trials) x= 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 (number of times given outcome occurs with the n trials, = 10 max homicides) p= 255/365 = .69 (probability of the given outcome in a single trial) q = (1-p) = 0.31 (probability of the other outcome in a single trial) n! = 10! (or 3,628,800) n factorial: 10!= [(10)(9)(8)(7)(6)(5)(4)(3)(2)(1)]

P(X)= n!pxqn-x

X!(n-X)!

Number of Homicide

Total days frequency count

Probability in %

1 115 31.5% 2 82 22.4% 3 38 10.4% 4 11 3.0% 5 5 1.3% 6 2 0.5% 7 1 0.2% 8 0 0.0% 9 0 0.0%

10 1 0.2%

When x=1 P(X) = (3,628,800)(0.691)(0.319) (1!)(9!) P(X) = (3,628,800)(0.69)(0.0000264) 362,880 P(1) = 0.00001824

When x=2 P(X) = (3,628,800)(0.692)(0.318) (2!)(8!) P(X) = (3,628,800)(0.476)(0.00008528) 80,640 P(2) = 0.0018268

When x=3 P(X) = (3,628,800)(0.693)(0.317) (3!)(7!) P(X) = (3,628,800)(0.328509)(0.0002751) 30240 P(3) = 0.01084

When x=4 P(X) = (3,628,800)(0.694)(0.316) (4!)(6!) P(X) = (3,628,800)(0.22667)(0.00008528) 17280 P(4) = 0.042245

When x=5 P(X) = (3,628,800)(0.695)(0.315) (5!)(5!) P(X) = (3,628,800)(0.156403)(0.0028629151) 14400 P(3) = 0.11283

When x=6 P(X) = (3,628,800)(0.696)(0.314) (6!)(4!) P(X) = (3,628,800)(0.107918)(0.00923521) 17280 P(4) = 0.20929

When x=7 P(X) = (3,628,800)(0.697)(0.313) (7!)(3!) P(X) = (3,628,800)(0.0744635)(0.029791) 14400 P(7) = 0.2662011

When x=8 P(X) = (3,628,800)(0.698)(0.312) (8!)(2!) P(X) = (3,628,800)(0.051379)(0.0961) 80640 P(8) = 0.222188

When x=9 P(X) = (3,628,800)(0.699)(0.311) (9!)(1!) P(X) = (3,628,800)(0.035452)(0.029791) 14400 P(7) = 0.010561

When x=10 P(X) = (3,628,800)(0.6910)(0.310) (10!)(0!) P(X) = (3,628,800)(0.024461)(1) 80640 P(8) = 0.0244619

The total sum of binomial probability is 0.900 and its distribution represented in figure 9.

For the frequency of homicides occurring in each neighborhood in Chicago, from the census tract files the following image abstracted from R, determines the relationship between the 873 neighborhoods with its individual frequency of homicides occurring.

Finally the calculations of probability of homicide occurring in a neighborhood that has the following proportion of population of white and african-american were determined through the following range <10%; 10-20%; 30-40%; 40-50%; 50-60%; 70-80%; 80-90%; 90-100%, as describe in the following tables (1, and 2).

At least N of homicides Probability

1 0.00001824 2 0.0018268 3 0.01084 4 0.042245 5 0.11283 6 0.20929 7 0.2662011 8 0.222188 9 0.010561

10 0.0244619 Total 0.90046204

 Figure 9: distribution of least one homicide occurring in 10 days in the City of Chicago  

 

Figure 10: Frequency of homicide per neighborhood. In the red square shows 4 neighborhoods, with a frequency of 2 homicides for one of them.  

Discussion: Through this study by the use of crime and census data we were able to spatial graph and calculate with statistics the distribution of homicide events in Chicago and to determine the probability of homicide being higher in neighborhoods with specific racial compositions. From the analysis we can conclude that there is a higher probability for a higher concentration of African American population group for a homicide to occur. In the other hand for a higher white population the probability of a homicide to occur is very low to none for a range of 90 to 100% of population. In regards of the frequency of homicide occurring in one day, from the histogram figure 4, it can be inferred that 1 to 2 homicides per day are more frequent per day than those with higher count, such as 10 homicides in one day. From the figure 5 we can determine the number of homicide per location and in figure 6 and 7 Choropleth map the location of homicides in red dots with density of African American and White in the census tract. The main neighborhoods that concentrate higher values of homicides are located in the neighborhoods in the Westside, Southwest and Southside and south side of the city respectably. The probability of a least one homicide occurring in the city of Chicago is a 69%, and exactly values of 1 and 2 homicides with a probability of 53.9%. Therefore it can be concluded that there is a higher probability of one to two homicides occurring per day in the city of Chicago. It can be implied that there is a higher probability of homicide occurring in neighborhoods with specific racial compositions. Although this study only addresses two racial groups (white and black) further investigation and analysis should be done with other racial groups in order to have a more objective data analysis. This future work could also be expanded into other cities in the US, with the same methodology to compare a make an objective conclusion. Right now is only base on the statistical data from this city and from those special groups.

   

Table 1:   Table 2:  

References: Brunsdon, C. and L. Comber 2015. An Introduction to R for Spatial Analysis and Mapping. SAGE Publications Ltd. McGrew Jr, J. C., & Monroe, C. B. (2000). An Introduction to Statistical Problem Solving in Geography. Waveland Press.                                                                                                                i Wikipedia contributors, "Timeline of organized crime in Chicago," Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/w/index.php?title=Timeline_of_organized_crime_in_Chicago&oldid=711407550 (accessed April 10, 2016) ii Fenton, Justin (June 3, 2013). "Baltimore ranked 6th in murder rate in 2012". The Baltimore Sun. Retrieved April 8, 2016. iii Zorn (July 26, 2013). "Wrongly Accused". Chicago Tribune (Section 1). p. 23. "Police: Chicago Reports 415 Murders In 2013, Lowest Since 1965". Retrieved April 8, 2016. iv Davey, Monica and Smith, Mitch (August 23, 2015). Murder Rates Rising Sharply in Many U.S. Cities. The New York Times. Retrieved April 10, 2016. v "Community Areas Map" (PDF). City of Chicago. June 2010. Retrieved 11 April 10, 2016. vi Wikipedia contributors, "Community areas in Chicago," Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/w/index.php?title=Community_areas_in_Chicago&oldid=712893849 (accessed April 11, 2016)