Lab 4 - Correlation and Spatial Autocorrelation

Part 1: Correlation
1.

Correlation Chart

When looking at a set of data that focuses on distance and sound level one might get curious as to how they correlate to one another. Using tools such as Excel and SPSS calculating and visualizing the correlation between the two becomes much easier.

The null hypothesis would be that there is no linear association between distance (ft) and sound level (db). The alternate hypothesis is there is a linear association between distance and sound level.

Looking at the Correlation chart you can see the correlation for the two is -.896. Being that .896 is close to 1 tells us the variables have a strong correlation and the fact it is a - tells us that as the scatter plot shows us as distance increases the sound level decreases.

The null hypothesis is rejected.

2. Correlation matrices can also be created using SPSS. A correlation matrix is all the variables compared to one another. The following matrix is based on Detroit Census data.
Looking at the matrix, you can see that a strong correlation exists.
White and having a Bachelor Degree (+)
White and Black residents (-)
 Median Household Income and Median Home Value (+)
White and Retail Employee (+)

3. Introduction:
     The Texas Election Commission or (TEC) wants to evaluate the elections in Texas through analyzing patterns and voter turnout in counties. The TEC has provided voter data from the 1980 and 2012 Presidential Elections. Through the examination of spatial auto-correlation and correlation the TEC will have a better idea of what the voter breakdown and turnout is across the state.

Methodology:
     Unfortunately the TEC did not provide enough data alone to analyze and come to any conclusions. Luckily, the U.S. Census Bureau website has a database including demographic data needed.  Once downloaded the data can be joined together using the 'join' tool in ArcMap and exported as a shape file. Once exported the data could be opened in GeoDa, a freeware program and analyzed.

     GeoDa is able to run spatial auto-correlation tests and this is essential in determining information for the TEC. Because the tests are weighted the settings remained default when looking at the Poly ID.
     Spatial Auto-correlation is relevant because it looks at each individual counties and evaluates them based on counties touching each other and in each direction, (side to side, below and above).
A Moran's I test was done as well as a LISA map created to represent the results on a per county basis.
     This was done 5 times covering, Hispanic Population percent in 2010, Voter Turnout in both 1980 and 2012 and also Democratic Vote % in 1980 and again in 2012.
The Moran's I test is done to measure the degree of spatial auto-correlation. This is represented by a value between -1 and +1. A value close to -1 indicates a strong negative pattern, a value close to 0 represents a lack of spatial pattern and a +1 indicates a strong positive pattern.
The LISA maps help create a visually friendly representation the significance difference at a county level.

Results:

Figure 1 - 2012 Democratic Vote Percent

Figure 2 - Moran's I chart for 2012 Democratic Vote Percent

     Looking at the map (Figure 1) and Moran's I chart (Figure 2) regarding the 2012 Democratic Vote Percent in Texas, we can see a significant number of High (red) counties in the south/west part of the state and Low (blue) counties in the North. Looking at the Moran's I chart you can see see it has a value of .6959 which is a positive correlation. The data is grouped in the lower area and spread widely in the high area. 

Figure 3 - 1980 Democratic Vote Percent

Figure 4 - Moran's I chart for 1980 Democratic Vote Percent

      This LISA map (Figure 3) shows a larger variation in voting pattern for the 1980 election. The Moran's I chart (Figure 4) shows a spread as well and has a value of .5752 which equates to medium, positive correlation.

Figure 5 - 2012 voter turnout

Figure 6 - 2012 voter turnout Moran's I chart

     The LISA map (Figure 5) shows the 2012 voter turnout was high in only a few counties while low in the southern counties nearest to the border. The Moran's I chart (Figure 6) represents a weak trend with much variation but still is slightly positive with a value of .3359.

Figure 7 - 1980 voter turnout

Figure 8 - Moran's I chart for 1980 voter turnout

     In 1980 the LISA map (Figure 7) shows a few more high turnout counties while the south even then had a very low turnout. The Moran's I chart  (Figure 8) presents a low yet positive trend at .4681.

Figure 9 - 2010 Hispanic Population Percent

Figure 10 - Moran's I chart for 2010 Hispanic Population Percent

     The last map (Figure 9) represents the Hispanic % throughout Texas. The South/Western counties have a very high percent while the North Eastern counties are generally low except for one county which sits at High-Low. The Moran's I chart (Figure 10) shows a significant positive trend and has a value of .7787 which happens to be the closest to +1 of all of our values. 

Figure 11 - Correlation Matrix

This Correlation matrix (Figure 11) shows there is a very high confidence level. At 99% it shows that each variable relates to one another. 

Conclusion:

     Looking at the maps and charts one can see there is an apparent relationship between the percent of Hispanic Population and percent of Democratic votes. It appears that in the counties with the highest percent of Hispanic population there is also a very low voter turnout. It makes sense there is a higher Hispanic population percentage in the southern part of the state as it is closest to the border of Mexico. Using this information and visuals the TEC and the Governor can see that voter turnout has ever so slightly changed the last 30+ years. Key areas to be considered are counties with higher Hispanic populations as these counties are less likely to turnout and vote but perhaps with the right campaigning these results could be changed depending on the messaged projected to those populations.