Introduction

The relationship between poverty levels and crime rates is one that is debated by a number of sociologists, economists, and criminologists today. Some argue that poverty has an “intimate” relationship with crime because people below the poverty line are less likely to be educated, are generally more stressed, and are willing to do anything to get the basic possessions they need to survive. Others point at the most recent recession and note how crime rates actually went down during that period, suggesting that there is no simple relationship between poverty levels and crime rates. Our hypothesis is that as poverty levels increase, crime rates will as well. We believe this because poorer people are less likely to be educated, are likely to be more desperate for money, and may even turn to drugs, which would lead to an increase in the crime rate.

Method and Results

Shown below is the code we used to read in our data from the Internet and assign column names to it:

library(ggplot2)
setInternet2(use = TRUE)
housing <- read.table("https://archive.ics.uci.edu/ml/machine-learning-databases/housing/housing.data", header = FALSE)
names(housing) = c("CRIM","ZN","INDUS","CHAS","NOX","RM","AGE","DIS","RAD","TAX","PTRATIO","B","LSTAT","MEDV")

Conditions:

L: From the scatterplot shown above, it appears that there is a moderately strong, linear relationship between poverty levels and crime rates in different neighborhoods.

I: The observations in this study were neighborhoods in Boston in 1978. It seems likely that neighborhoods in the same area would affect each other’s crime rates, as they might share school districts and share the same police department.

N: According to the scatterplot, the crime rate does not appear to vary according to a Normal distribution, as most of the observations seem to be concentrated at lower crime rates. We will have to proceed with caution.

E: The standard deviation of the crime rates appears to be much lower at poverty levels below 10% than they are at poverty rates greater than 10%. The variances of the crime rate do not appear to be equal at every poverty level. We will have to be cautious of this when coming to conclusions about this data. There also appear to be several extremely high outliers in the crime rates among the neighborhoods in the data set.

R: This data set was collect by the U.S. Census Service, and therefore is not a random sample.

Shown below are the results of a test of significance on the slope of the LSRL relating crime rates to poverty levels testing whether the slope is greater than zero at an alpha level of 0.01.

housing.lm = lm(formula = CRIM~LSTAT, data = housing)
summary(housing.lm)
## 
## Call:
## lm(formula = CRIM ~ LSTAT, data = housing)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -13.925  -2.822  -0.664   1.079  82.862 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -3.33054    0.69376  -4.801 2.09e-06 ***
## LSTAT        0.54880    0.04776  11.491  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 7.664 on 504 degrees of freedom
## Multiple R-squared:  0.2076, Adjusted R-squared:  0.206 
## F-statistic:   132 on 1 and 504 DF,  p-value: < 2.2e-16

Since the p value is much lower than 0.01, there is very strong evidence to conclude that the slope of the LSRL, relating crime rates to poverty levels, for the population is greater than 0.

Conclusion

Even though the significance test shows that the slope of the LSRL relating crime rates to poverty levels is greater than zero, there are a number of issues with our data that make this conclusion less reliable. First and foremost, the data is a census of neighborhoods in Boston instead of a random sample of neighborhoods around the U.S.. This means that the results of this test cannot be generalized to the rest of the U.S., and only apply to Boston. Another major issue was how the crime rates were not Normally distributed around the LSRL. This is shown by the graphic below:

Since the slope of the LSRL was 0.5488, the ratio of crime rate to the percentage of the population should be approximately Normally distributed around that value. However, the distribution of the ratio of crime rate to the percentage of the population in poverty is clearly skewed, with the vast majority of the values falling close to zero.

In the future, it may be interesting to examine a random sample of neighborhoods or towns around the U.S. so that we can make a more valid conclusion about whether there is a relationship between poverty levels and crime rates in the U.S..

Sources:

http://www.newrepublic.com/article/80316/relationship-poverty-crime-rates-economic-conditions

http://economics.fundamentalfinance.com/povertycrime.php

http://www.nationaldialoguenetwork.org/poverty-and-crime/

http://www.poverties.org/poverty-and-crime.html