Statistics
Winter Math Reflection
The most interesting mathematical challenge that I have met so far this year presented itself within the Mini Correlation project. For this project we were asked to choose two different things we wanted to find a correlation between. For example, race and incarceration or homicides and gun ownership. By doing this it will allow us to find correlations between bigger things and possibly make changes based on what we find from correlations made. After we chose our topics we measured the correlation between the two and did the math using computations and explained our findings.
For my project I chose to focus on incarceration vs. race. I found the correlation between the percent of African Americans in each state and the incarceration rate per 100,000 people in each state. The first measurement was the percent of African Americans in each state (all 50 states, n) and the second was incarceration rate per 100,000 people within each state. The data I found and used was from Wikipedia and consisted of the percent of African Americans within each state, and the number of people incarcerated within each state. The data was last updated in 2010. To look at my data spreadsheet click here. The link leads to a data spreadsheet that is not just my own research findings, but coincides with class data as well. Based on my research, I found that there was a 0.60 correlation between the amount of African Americans in each state and the number of people incarcerated in each state, thus resulting in a positive correlation.
Since the correlation between the two measurements was found to be 0.60, it is safe to say that it is a rather strong correlation. Therefore, when the number of african americans go up in each state, incarceration rates go up. The percentage of one variable being explained by the other is my r^2 which is .36. 36% of the variation in incarceration can be explained by the number of African Americans in each state.
From doing this I learned the limitations of correlations. Meaning even if there is a correlation between something, it is not necessarily the causation. Through this process I learned how to identify if my results were statistically significant and whether or not the significance of the correlation led to being the causation or not being the causation. My result proved to be statistically significant (more than 99% significant) due to the fact that I had enough data to show that it was not just chance but an actual fact. The size of my data and correlation result showed the strength of the connection between my two research points.
In order to find a correlation and prove that it was mathematically correct, we did the following computations.
n=50
r=0.60
r^2=.36
t=5.19 (more than 99% significant)
These computations showed the likelihood of my results being chance was exceedingly low if not, non existent. Based on my results, it was easy to see the correlation between the percentage of African Americans within each state and the number of people incarcerated within each state. The data showed that in states that have higher percentages of African Americans, there is a higher incarceration rate. The correlation is significantly high and basically proves that there are far more African Americans incarcerated than Whites, Hispanics or other.
My conclusion revealed that based on the data results and the correlation found, in the states that have a higher percentage of African Americans, there is a higher incarceration rate. This result points to a number of different possibilities when looking at this matter. For example, race causes incarceration rates to go up. This makes sense because the amount of African Americans incarcerated is far greater than the amount of any other race. Meaning that we have an racist and unequal society.
This project helped me gain certain mathematical skills that I did not have before. It was challenging because I did not understand all of the content nor how to do it and apply it to what I was researching. It taught me to ask questions and make sure I understood the content by asking for help. From this project I will take forward the new mathematical skills I learned and the ability to advocate for myself in order to produce a project I will be proud of.