Geography 370 Assignment 3
Introduction
This lab introduces the ideas of calculating z-scores and probability and showing the results with ArcMap. A research consortium has provided data about foreclosure rates for Dane County, Wisconsin, between 2011 and 2012. The issue found is that the county's foreclosure rates are increasing and that even more will occur in 2013. Creating a probability scenario using county tract data will give a better insight to this issue at hand. Spatial patterns can be detected with this map, but it is impossible to understand the reasons behind the patterns without further data.
Methodology
The research consortium has provided census tract data from the US Census Bureau. Once this data was geocoded and joined in ArcMap, the software can calculate z scores about the county. The difference found between two years was done by adding two z score fields for each year in the existing data in ArcGIS. Then, adding another to calculate the difference between the two, the map then shows the difference in z scores from 2011 to 2012. A z score is calculated by subtracted the mean from an observation, and dividing that value by the standard deviation of all of the data. When calculating a standard deviation, it is not precise on where that value is located on a normal distribution curve. A z score will more accurately reflect where the value stands on that curve. For this lab, the foreclosure z-scores were calculated and then used to measure the probability that the census tracts will exceed the mean of the data. The probability that foreclosures in Dane County will be exceeded 70% of the time and whether they will be exceeded 20% of the time are both calculated. These probabilities are calculated assuming the patterns in 2013 are the same as those in 2012.
Results & Conclusions
A few foreclosure counties were studied individually to look at calculations within this study. These areas are included in the table below. Results of the county's total mean and standard deviations of each year are below the table.
This lab introduces the ideas of calculating z-scores and probability and showing the results with ArcMap. A research consortium has provided data about foreclosure rates for Dane County, Wisconsin, between 2011 and 2012. The issue found is that the county's foreclosure rates are increasing and that even more will occur in 2013. Creating a probability scenario using county tract data will give a better insight to this issue at hand. Spatial patterns can be detected with this map, but it is impossible to understand the reasons behind the patterns without further data.
Methodology
The research consortium has provided census tract data from the US Census Bureau. Once this data was geocoded and joined in ArcMap, the software can calculate z scores about the county. The difference found between two years was done by adding two z score fields for each year in the existing data in ArcGIS. Then, adding another to calculate the difference between the two, the map then shows the difference in z scores from 2011 to 2012. A z score is calculated by subtracted the mean from an observation, and dividing that value by the standard deviation of all of the data. When calculating a standard deviation, it is not precise on where that value is located on a normal distribution curve. A z score will more accurately reflect where the value stands on that curve. For this lab, the foreclosure z-scores were calculated and then used to measure the probability that the census tracts will exceed the mean of the data. The probability that foreclosures in Dane County will be exceeded 70% of the time and whether they will be exceeded 20% of the time are both calculated. These probabilities are calculated assuming the patterns in 2013 are the same as those in 2012.
Results & Conclusions
A few foreclosure counties were studied individually to look at calculations within this study. These areas are included in the table below. Results of the county's total mean and standard deviations of each year are below the table.
2011 Mean: 11.39
2011 Standard Deviation: 8.776
2012 Mean: 12.299
2012 Standard Deviation: 9.906
Using a z score chart, for a 70% probability that the county's foreclosures will exceed the mean, the z score must equal -.52. Showing the calculations below using 2012 data and assuming they are the same in 2013, the probability is 7.85. This means that there is a 70% chance that the county will have at least 7.85 foreclosures, if not more. As far as a 20% likelihood to exceed, the z score must be .84. After calculating this out, there is a 20% chance that Dane County will have 20.62 foreclosures or more across the county.
After looking at the results of the map, it is clear there is a wide range of foreclosures each year. The darker, negatively numbered tracts have larger differences and changes in foreclosures, while the lighter and positive numbers have fewer. In the core of the county there seems to be little change from the average amount of foreclosures. It would appear that the 70% chance that the county will have 7.85 or more foreclosures will most likely be apparent in is on this inner core (lighter colors), where less variation from the mean is occurring. The 20% chance that there will be at least 20.62 foreclosures will most likely happen in the outer parts of the county (darker values), where the variation and z scores are further away from the average number of foreclosures. Those that are varying more from the average are more likely to encourage the upward trend of foreclosures happening from 2011-2012. Hopefully, by incorporating more information into this study, the county can approach potential solutions to the areas with increasing foreclosures. One concept that could be introduced is setting up different agreements within these areas and the banks around them. Tax credits or exemptions could be encouraged for different kinds of behaviors to help the people living in these homes. With help from different businesses and corporations, these homeowners can be given grants towards their mortgages in exchange for other services. Continuing this study should involve the reasons behind these patterns, with more insight as to how the homeowners can be assisted.
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