Assignment 5

Assignment 5: Correlation

Part 1

A) Correlation: Distance vs Sound Level 
Given the chart below (Figure 1) shows the relationship between distance in feet vs sound levels in decibels. A correlation matrix, that displays correlation and significance levels, was created in SPSS (Figure 2). Based on the results in both the graph (Figure 3) and the chart. Looking at the chart, there is a strong negative correlation between distance and sound levels. This can be explained by the correlation being almost -1 as the value is -.896. This indicates that there is a strong negative correlation between the two variables. Meaning as distance increases, sound levels decreases. This trend can be seen in the graph below (Figure 3). There is also a significance level of zero and this means there is an sufficient statistical difference between the two variables meaning that there is a linear relationship between distance and sound.

Figure 1. Chart displaying distance and sounds levels

Figure 2. Correlation Matrix for Figure 1

Figure 3. Displays the relationship between sound level and distance

B) Detroit Population Statistic Matrix

Given an excel file showing different social statistics by race, education, different employment types, home value and income, I  created another correlation matrix (Figure 4). When looking at the table a few different trends are evident. First, when looking at the bachelor degrees by race there is a moderate positive correlation to Whites (.698) and Asians (.559) and bachelor degrees obtained. Looking at employment statistics, there were no significant correlations between the different races and different occupations. There was however, high correlations between bachelor degrees and median household income as well as median home value with both correlations being at .754. The was also low negative correlation between Blacks and median household income at - .408. 

Figure 4 Detroit Census Tract Matrix

Part 2: Texas Voting Statistics 

Introduction
The Texas Election Commission (TEC) was interested to see if voter patterns have changed between 1980 and 2012. They would also like to see if there are any clustering patterns for these variables. To complete the analysis TEC provide voter turnout and percent Democratic vote information for both 1980 and 2012. Hispanic population statistics for 2010 from the United States were also included to see if this particular demographic has an effect of voter turnout and Democratic voting percentage. 


Methodology
To complete the analysis Moran's I, LISA maps, statistical correlations and choropleth maps. Moran's I is a spatial correlation tool that shows how a set of data is clustered (areas of similar characteristics such as high values surrounded by other high values and vise versa), dispersed or neither. LISA maps allows for data clusters to be shown on a map by running statistics on areas bordering regions to see if there are similarities between the data and if there are spatial patterns. Moran's I and LISA maps were conducted in Geoda, correlations were created in SPSS and choropleth maps were created using ArcMap.

Results 
To begin the analysis, voter turnout in 1980 statistics were run through Moran's I (Figure 5). The Moran's I value was .468 which means that the data was not very clustered with most of the data being found in the middle and being dispersed fairly evenly across the different quadrant in the chart. This pattern can also be seen in the LISA map (Figure 6) with most of the values being grey (not clustered. Areas on the map that are blue are areas of low voter turnout surrounded by other areas of lower voter turnout. Areas in the red are the inverse, being areas of high voter turnout surrounded by other areas of high voter turnout. Looking at the bottom left quadrant (Figure 5), the data points found towards the bottom represent the strongest cluster of being areas that are very low in voter turnout surround by others of similar value. On the map these are the blue areas located south Texas. Again, the inverse can be said for the red areas found in north Texas.

Figure 5 Moran's I for Voter Turnout in 1980

Figure 6 LISA Map showing clusters in voter turnout in 1980

Looking at the 2012 voter turnout data in the same formats, the data presents a small decrease in the amount of clustering trends. Looking at figure 7, the Moran's I value was .335. Again this means that the data was not very clustered and similar trends appear. There is a cluster of lower voter turnout in south Texas. There is also less clusters of areas with high voter turnout.

Figure 7 Moran's I for voter turnout in 2012

Figure 8 LISA map for voter turnout in 2012

After looking at voter turnout statistics, Democratic voting percentages were analysed. Looking Democratic votes 1980 there are clusters in both high Democratic voting areas as well as areas of low Democratic values.With high Democratic votes being located in southern and eastern parts of the state and low democratic votes being located in northern parts of the state.

Figure 9 Moran's I for Democratic voting percentages in 1980

Figure 10 LISA map for Democratic voting percentages in 1980

Democratic Voting numbers in 2012 show that there is an increase in the strength of clustering in areas of high democratic voeing percentages and decrease in the strength of the clustering for areas of low Democratic voting percentage (Figure 11). Geographically there are more clusters of low Democratic voting percentages in the northern part of the state, these areas are represented in blue in figure 12. Clusters of areas of high democratic vote, along with becoming strong also appear to be spreading in the southern portions of the state (red areas in figure 12). The eastern portion of state present an interesting trend being that there are no clusters. This means that voting trends in this area are more dispersed. These trends also align with the choropleth map below (Figure 13).

Figure 11 Moran's I for Democratic voting percentages in 2012

Figure 12 LISA map for Democratic voting percentages in 2012

Figure 13 Democratic voting percentages in 2012

Looking at Hispanic population percentages in 2010 bring about interesting trends in regards to Democratic voting percentages and voter turnout percentages. The correlation matrix below (Figure 14), there is a high positive correlation of .718 between areas with high Hispanic populations areas and areas with high democratic voting percentages. This particularly interesting when looking at the distribution of Hispanic populations in 2010 (Figure 15) and Democratic voting percentages in figure 12 as they both highly concentrated in the southern regions of the state. Combined with the increased evidence of a high correlation between the two variables, it can be assumed that high Hispanic populations have a large effect of the Democratic voting trends in the state as areas with low Hispanic populations tend to have low Democratic voting percentages. Voter turnout percentages also has a high correlation in regard to Hispanic population percentages. However, where Hispanic percentages and Democratic voting percentages are positive, Hispanic percentages and voter turnout is a negative correlation. This also matches the trends set in the previous figure 8 and in figure 14 where areas of high Hispanic populations are in the same areas as areas of low voter turnout.

Figure 14 Correlations matrix for Hispanic populations and Democratic voting percentages and voter turnout in 2012

Figure 15 Hispanic population percentages in 2010

Conclusions 
Based upon the results above, I have concluded that voting trends in Texas have become more clustered in regards to Democratic voting percetages. There has been increases of areas of low Democratic voting areas in the northern and central parts of Texas and increases of areas of high Democratic voting percentages in the southern parts of the state. This is highly connected to Hispanic population percentages as Hispanic populations have a high positive correlation with Democratic voting percentages. These areas of high Hispanic populations and high Democratic voting percentages are also areas that have low voter turnout. This could mean that Hispanic populations in the southern and western regions of Texas may be an area of high interest in coming elections for Democrats as it may significantly help their total percentages as there is a large number of nonparticipating voters who are very likily to vote Democrat in the southern part of Texas.