Introduction:
So far 2016 has been a hard year for Chicago. This year has had the highest murder rate in the last two decades and its only April. As of April 10th there has already been 156 reported homicides in 2016 (Chicago Tribune). As reported in an article titled The root cause of Chicago’s glut of murders by Steve Bogira, states that the issue of high homicide rates in Chicago has been ongoing for the last 40 years, with poor neighborhoods having much higher rates of homicide. The prevailing cause of this stems from poor neighborhoods lack of police protection and the cities racial and economic segregation (Bogira). The goal of this report is to answer the question of how race influences the probability of someone being the victim of a homicide in Chicago. By using crime and census data from 2015 this report will look at the spatial distribution of homicides and use statistical analysis to describe the data. This report will find the probability of the number of homicides occurring each day, the binomial distribution of homicides from 0 to 10 days and the frequency of homicides in each neighborhood. As well the report will find the probability of homicide occurring in neighborhoods of different racial composition.
Methods:
This report covers the area within the city limits of Chicago. Using the City of Chicago data portal a city boundary shapefile was obtained in order to create a boundary for the crime and census data. The crime data was obtained from the Chicago Police Department’s crime data portal and using the filter options a data set contained all of the homicides in 2015 was obtained. The census data was obtained using the American Fact Finder website and we collected census tract data for Cook County, Illinois with the race variable selected. This information comes from the American Community Survey (ACS) which creates population, demographic and housing estimates of the U.S. population. For this report the 2010-2014 5-Year Estimates are used. This data has the largest sample size of the ACS estimates which means it is generally more reliable and useful for the scope of this report. This gave us our dataset of the racial composition of Chicago’s census tracts. As well as the race data, a cartographic boundary shapefile of the census tracts for Illinois was downloaded from TIGER products geographic database. TIGER stands for Topologically Integrated Geographic Encoding and Referencing and are the spatial products from the Census Bureau’s geodatabase. These are very useful for mapping, and the cartographic boundary shapefile we downloaded is specifically designed for small scale thematic mapping (Census Bureau). This data was then imported into R in order to be used for our analysis. The first step was to edit the crime data so that the Date and Time variables are stored in two different columns rather than the same one. This was done in order to get information on the number of homicides occurring each day. Next a frequency table was created to show the number of homicides for each date. Using this frequency table a histogram was also created to show the frequency of homicides in one day in 2015. DISCUSS BINOMIAL DIST HERE A plot of the locations with symbol size scaled by the frequency was also created. With the crime data prepared we used R to format the ACS data and get the information on demographics of each neighborhood. A choropleth map was then created using this data to show population information of Chicago. The final step was to merge the number of homicides with the population data in order to calculate the probabilities of homicide in neighborhoods of different racial composition. This was done by calculate the proportion of the neighborhood population that is black, and the proportion that is white. Then we calculated the probability homicide occurring for black and white proportions of less than 10%, 10-20%, 30-40%, 40-50%, 50-60%, 70-80%, and 90-100%. By comparing how the probabilities of homicide differ between the two races we can see how race composition affects the homicide rate in Chicago neighborhoods.
Results:
This frequency plot shows the number of days in which at least n homicides occurred where n is represented on the y axis, and number of dates is on the x axis. From the frequency table used to create the above graphic we know that there are 115 days out of the year in which one homicide occurred, and 255 days where one or more homicides occurred. This also shows us that the maximum amount of homicides that occurred in one day is 10. Therefore the probability of at least n homicides occurring each day is the number of days at least one homicide occurred divided by the total number of days. In this case it is 255/365= 0.699 which is 69.9%. In order to create the exact probability of n homicides occurring each day I have compiled the following table showing the exact probability for number of homicides each day ending at 10 homicides because that is the most that occurred in one day.
| Probability of Exactly n Homicides Occurring | |
| n | Probability |
| 0 | 0.301369863 |
| 1 | 0.315068493 |
| 2 | 0.224657534 |
| 3 | 0.104109589 |
| 4 | 0.030136986 |
| 5 | 0.01369863 |
| 6 | 0.005479452 |
| 7 | 0.002739726 |
| 8 | 0 |
| 9 | 0 |
| 10 | 0.002739726 |
In order to calculate the binomial distribution of homicides occurring between 0 to 10 days a few critical pieces of information are required. First is number of events (n), in this case 10 days, next the probability of a homicide occurring on any day (p) is 255/365=0.699, and the probability of a homicide not occurring (q) is 1-p=0.301. Finally our given outcome values (X) is the range of days 0-10. I created the following table and chart by calculating the binomial distribution of each X value in order to show the distribution occurring between 0 to 10 days.
| Number of Days | Binomial Probability |
| 0 | 6.10471E-06 |
| 1 | 0.000141767 |
| 2 | 0.00148149 |
| 3 | 0.009174412 |
| 4 | 0.037284384 |
| 5 | 0.103900801 |
| 6 | 0.201070488 |
| 7 | 0.266821587 |
| 8 | 0.232360826 |
| 9 | 0.119911567 |
| 10 | 0.027846573 |
This data shows the binomial distribution of homicides over a 10 day period. This shows us that every 7 days there is the 26.6% chance of a homicide occurring in the city of Chicago.
The above map shows the spatial distribution of homicide locations by neighborhood. The neighborhoods are shaded so that darker green represents higher proportions of black population.
This graphic by comparison shows the same locations but weighted by the number of homicides in each location. This helps understand the frequency distribution of homicide locations in Chicago.
The final piece of information is the probability of homicide occurring in neighborhoods based on their racial compositions. The table below shows the differences in homicide probability between black and white neighborhoods.
| Homicide Probabilities | |||
| Proportion | Black | White | |
| <10% | 0.15451 | 0.67382 | |
| 10-20% | 0.03648 | 0.03219 | |
| 30-40% | 0.02146 | 0.03863 | |
| 40-50% | 0.03433 | 0.06009 | |
| 50-60% | 0.0279 | 0.04506 | |
| 70-80% | 0.02575 | 0.03863 | |
| 80-90% | 0.06438 | 0.0279 | |
| 90-100% | 0.54721 | 0 | |
Discussion:
The data from this report shows a clear pattern between race and the probability of a homicide occurring. The data shows us that on any given day there is a 69.9% chance of at least one murder occurring in Chicago, this is a massive percent but when we look at the spatial distribution of homicides another more troubling pattern emerges. From the choropleth map created with the data its possible to see that the majority of homicides occur in neighborhoods with a higher black population. The homicide probability table confirms this visual pattern by informing us that the higher the percentage of black population in a neighborhood the higher the probability of a homicide occurring. To me the most notable shift is in the 90-100% black communities where the probability of a homicide is 54.7% where as white neighborhoods of 90-100% have a 0% probability. What this tells us is that the homicides happening in Chicago are unevenly distributed between neighborhoods, and neighborhoods of color have a significantly higher homicide rate. This evidence backs up the theory that the number of homicides in neighborhoods is directly linked to the racial segregation that has occurred in Chicago. This data shows that there is indeed a significant correlation between predominantly black neighborhoods and high homicide rates. This is a symptom of systemic injustice happening in Chicago and backs up the assertions made by Bogira that the root cause of Chicago’s murders are the racial and economic segregation of neighborhoods.
References:
“Crime in Chicago — Chicago Tribune.” Crime in Chicagoland. Web. 10 Apr. 2016. <http://crime.chicagotribune.com/chicago/homicides>.
Bogira, Steve. “The Root Cause of Chicago’s Glut of Murders.” Chicago Reader. Web. 10 Apr. 2016. <http://www.chicagoreader.com/Bleader/archives/2012/07/10/the-root-cause-of-chicagos-glut-of-murders>.