Assignment 5

Assignment 5

Correlation and Spatial Auto-correlation 

Part I: Correlation 

Definitions:

Correlation= Measures the association between pairs of variables, but does not imply causation

-There is two factors that go into correlation, one is strength and the other is direction

Strength= The strength between two variables ranges from a positive to a negative one where positive one is the strongest.

Direction= The relationship can either be positive, null (no difference), or negative. 

Co-variation= the measure of how two variables change together

Hypothesis Testing with Correlation= To determine if an association exists between two variables 

Spatial Auto-correlation= Correlation of a variable with its self through space. So if neighboring areas are more a like it is a positive and negative if unalike. 

Moran's I: A chart of 4 quadrants of comparison ranging between positive and negative 1 showing the strength of the auto correlation. High, High = (+,+), High, Low = (+,-), Low, High = (-,+), Low, Low = (-,-). 

LISA map: The purpose of these maps is show a spatial component of the spatial auto-correlation. 4 categories of color that correlate with the strength of the relationships described in Moran's I. Red related to high and blue related to low. 

1. Using the data in Image 1, create a scatter-plot and place a trend line on that scatter-plot in Excel. The scatter-plot created is seen in Image 2. To find the Pearson correlation use SPSS which is shown in Image 3. 

-Null Hypothesis= There is no significant difference between distance and sound level

-Alternative Hypothesis= This is a significant difference between distance and sound level

Image 1: Scatter-plot Data

Image 2: Scatter-plot

Image 3: Correlation

Results Summary: From Image 2 and Image 3 you will find that there is a significant (because of the two asterisks) strong relationship because of the Pearson Correlation being -.896 along with the direction being negative because of the -.896 as well. The Sig 2-tailed test is .000, so that means that you reject the null hypothesis which is there is no significant difference between distance and sound level. 

2. Census Tracts and Population in Detroit, Mi

Results:
From this correlation matrix of Detroit there are a lot of things to infer. There are only two categorizes for whites that were not significant and that was the manufacturing and Finance categories. Looking at there sig 2-tailed test they both failed to reject the null  hypothesis which make sense then. For the black population all the categories have significant relationships besides that of the number of Finance Employees. For the Asian population all the relationships are significant besides with the Hispanic population category. With the Hispanic population there were five categorizes that were not significant with it. The categories were Asians, number of Bachelor's Degrees, number of manufacturing employees, number of retail employees, and number of Finance employees. There are certain correlations that stand out in terms of strength and direction. There is the strongest positive relationship between Asians and number of Retail employees, and Blacks had the strongest negative relationship. So, the probability you will see Asians being employed in retail is far higher than Blacks in Detroit.

Part II: Spatial Auto-correlation

Introduction: Given data of the percent Democratic votes and voter turnout from the Texas Election Commission for the years 1980 and 2012 Presidential Elections has there been any clustering patterns of these two values over the last 32 years? Using SPSS and GeoDa to answer this question and report the findings for the Texas Election Commission. Also, by using the online Census Data compare this to Hispanic population of Texas counties in 2010. This will all help to determine if there is a spatial auto-correlations for each of the elections with voting and voting turnout.

Method: To start off with this task for the TEC first you download the shape-file of Texas and the data of Hispanic Population 2010 from the online U.S. Census. For the Hispanic Data only the population percent is necessary so deleting row A2 and the rest of the columns is an important step to take once you have the excel spreadsheet of the data opened. In ArcMaps, open the shape-file of Texas downloaded from the Census, and join the Hispanic data along with the Texas voting patterns data provided by TEC to that Texas shape-file. While doing this make sure to use Geo_ID for joining. After joining export that shape-file with the data as a new shape-file so it is ready to use in GeoDa. Open GeoDa and click on "New Project From" and open this new Texas shape-file. You then have to create something refereed to as a "Spatial Weight".To do this go to tools, then create weight manager and ADD ID VARIABLE. Then under contiguity weight select Rook contiguity, and then hit create. After this is done begin to create Moran's I charts along with LISA cluster maps(make sure they are Uni-variate for both Moran's and LISA) for percent votes in 1980 and 2012 along with voter turnout in 1980 and 2012. Do this as well for Hispanic Voters, along with make a weights matrix's for this as well.

Results: Below are each of the Moran's I charts and each of the LISA cluster maps for voting and voter turnouts. There is also provided a Moran's I chart and LISA cluster map for Hispanic population. The last thing included is a weights matrix's for all of the categories.

Image 4: LISA map of Percent Democratic vote for 1980

Image 5: Moran's I chart of percent Democratic Vote for 1980

Image 6: LISA map percent Democratic Vote for 2012

Image 7: Moran's I chart of percent Democratic Vote for 2012

Image 8: LISA map of Voter Turnout for 1980

Image 9: Moran's map of Voter Turnout for 1980

Image 10: LISA map of Voter Turnout in 2012

Image 11: Moran's I chart of Voter Turnout in 2012

Image 12: LISA map of Percent Hispanic Population

Image 13: Moran's I chart of percent Hispanic Population

Conclusion:
There was a lower democratic vote increase over the past 32 years in northern and mid Texas, and an increase in Democratic vote in Southern Texas along the boarder. On the Moran's I charts in 2012 percent Democratic vote was much more clustered negatively than in 1980 which was much more spread out. There was still a higher number of Low-Low counties in 2012 as there were in 1980 just an increase in Low-Low in 2012. Voter turnout isn't clustered very tightly, but in 2012 there seems to be more of a cluster in High-High than there was in 1980. Comparing Democratic Vote to Voter turnout, in the areas of Democratic Voting High-High there is a voter turnout of Low-Low. This connects to the chart and map of Hispanic population because that is the area of High-High. Not much changed in voter turnout from 1980 to 2012 besides an increase in High-High in the northern tip counties along with a transition the most east part of the state from Low-Low to white. This means more people showed up to the poles in northern Texas along with in West Texas. There was a change from High-Low to Low-Low voter turnout in southern Texas from 1980 to 2012, so less people showed up to vote correlating to less Hispanics showing up to vote. Spatially there was not much change in voter turnout over 32 years, but for percent Democratic vote the area as to which were high and low didn't change but became more dense and gained surrounding counties.