Is Capital Punishment a Deterrent? Murder Rates Compared with Execution Rates in Texas, and on a National Level

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IB Math Studies IA
Is Capital Punishment a Deterrent? |
Murder Rates compared with Execution Rates in Texas, and on a National Level|

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The United States of America is one of the only democratic countries that still use capital punishment. This has raised a rather extensive debate, especially over the last 4 decades. I became interested in this issue in 2011 after the controversy surrounding the execution of Troy Davis, and the issue has remained. In my research, one argument in favor of the use of capital punishment has always stood out as the most solid: that it serves as a crime deterrent and will save more lives than we kill. On the other hand, people from the opposing side state that if the death penalty really did act as a deterrent, states that implement it should have much lower murder rates than states that do not, and that is simply not the case. I decided to further investigate the issue by comparing the yearly murder rates and execution rates of the state that has accounted for almost 40% of executions in the country: Texas, and to use Pearson’s Correlation Coefficient to determine if there is any correlation between the two. Question: What kinds of correlations exist between murder rates and execution rates in Texas?

Variables: Yearly number of executions in Texas.
Yearly number of murders per 1000 people in Texas

Hypothesis: There will be no correlation between murder rates and execution rates.

The first thing I did was collect the data. For the state of Texas, I took the total number of murders each year starting in 1977, the year after the reinstatement of the death penalty that resulted from the Supreme Court case of Gregg vs. Georgia. The source I found (http://www.disastercenter.com/crime/txcrime.htm) only accounted for murders up to 2011, as the 2012 murder statistics hadn’t been released yet. I found a yearly record of executions in Texas at (http://www.txexecutions.org/stats.asp). In the interest of saving space, I entered all data in Table 1 in intervals of 5 years. Table 1: Texas Murder and Execution Statistics 1977-2011| Year| 1977-1981| 1982-1986| 1987-1991| 1992-1996| 1997-2001| 2002-2006| 2007-2011| Number of Executions | 0| 20| 22| 65| 149| 123| 98| Number of Murders (per 1000 people)| 10.6| 11.2| 11.1| 9.55| 6.46| 6.89| 6.49| Pearson’s Correlation Coefficient:

Pearson’s Correlation Coefficient:

I decided to use the Pearson correlation coefficient in order to find out what sort of correlations exist, if any, between executions and murder rates in Texas. The results should be able to show what kind of relationship exists between the two variables, if capital punishment actually has any effect on murder rates and can act as a deterrent.
Where our x value is the yearly number of executions, our y value is the yearly murder rate in Texas and n is the sample size. The first step in the equation is to substitute the variables with data values, which I calculated as shown by Table 2:

Table 2: Texas Murder and Execution Statistics Processed for use with Pierson's Correlation Coefficient| |

Year| 1977-1981| 1982-1986| 1987-1991| 1992-1996| 1997-2001| 2002-2006| 2007-2011| Σ Σ
|
Number of Executions (x)| 0| 20| 22| 65| 149| 123| 98| 477| Number of Murders per 1000 people (y)| 10.6| 11.2| 11.1| 9.55| 6.46| 6.89| 6.49| 62.29| xy| 0| 224| 244.2| 620.75| 962.54| 847.47| 636.02| 3534.98| x2| 0| 400| 484| 4225| 22201| 15129| 9604| 52043|

y2| 112.36| 125.44| 123.21| 91.2| 41.73| 47.47| 42.12| 583.53|

Σx =477
Σy=62.29
Σxy=3534.98
Σx2= 52043
Σy2=583.53
n=7 (7 intervals of 5 years...
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