Assignment 3
GEOG 370
9 March 2017
For this assignment, I have been hired by an independent research consortium to study the geography of foreclosures in Dane County, Wisconsin. County officials are worried about the increase in foreclosures from 2011 to 2012. As an independent researcher I have been given the addresses of all foreclosures in Dane County for 2011 and 2012. My goal is to explain the patterns and provide some understanding to the trends in the foreclosures.
The following are calculations of the Z scores of three separate Census Tracts. Each Tract has a calculation based on the Count2011 data and a calculation based on the Count 2012 data. To make the calculation, the mean and standard deviation of the Count2011 and Count2012 data is needed. To find these I went under symbology then to Quantities and clicked on Classify. Once I clicked on Classify a box under Classification Statistics displays the Mean, and Standard Deviation. The last thing needed is the Xi value of the 3 census tracts. These can be located in the attribute table. Once all of the values are found, the following equation is used to calculate the Z scores: Zi=(Xi-μ)/S where Zi=Z-score, Xi=Observation of I, μ= Mean of the data, S= Standard deviation of the data.
For Count2011 mean 11.39 Standard deviation 8.776
Calculation three tracts:
Census Tract 122.01: Xi=6 (6-11.39)/8.776 Zi= -0.6141
Census Tract 31: Xi=24 (24-11.39)/8.776 Zi= 1.437
Census Tract 114.01: Xi=32 (32-11.39)/8.776 Zi= 2.348
For Count2012 mean 12.30 Standard deviation 9.906
Calculation three tracts:
Census Tract 122.01: Xi=6 (6-12.30)/9.906 Zi= -0.6360
Census Tract 31: Xi=18 (18-12.30)/9.906 Zi= 0.5754
Census Tract 114.01: Xi=39 (39-12.30)/9.906 Zi= 2.695
The Z-score calculations show how many standard deviations away from the mean each tract is. Tract 114.01 is the furthest from the mean and tract 31 is closest.
The map below shows changes in foreclosures from 2011 to 2012. Positive numbers indicate more foreclosures in 2012 than 2011. Negative numbers indicate more foreclosures in 2011 than 2012.
To solve this I look at the z-score chart to determine the z-score for 70%. The z-score is -0.52.
I can then enter this in the Count 2012 equation to determine the Xi value then evaluate potential Census Tracts that have this value.
(Xi-12.30)/9.906=-0.52 Xi=7.149
This result means that, based on the 2012 data, 70% of the time, a county track will have more than 7.149 foreclosures.
What number of foreclosures for all of Dane County will be Exceeded only 20% of the time?
Z Score 0.84
(Xi-12.30)/9.906=.84 Xi=20.62
This result means that 20% of the time, based on the 2012 data, a county track will have more than 20.62 foreclosures.
The map above is good for illustrating the areas in Dane County that have the most amount of foreclosures. These are the pink areas.
Conclusion:
It is clear to see that there are big spatial patterns involving foreclosure in Dane County. It appears that in 2012 the highest number of foreclosures are the bigger sections not in the center or in the southern parts. The lowest number of foreclosures are the smaller sections in the center of the county, and just a couple outside the center.
It is also clear to see big change in the number of foreclosures from 2011 to 2012. This can be observed in the first map. The lightest and darkest colors indicate this change. Based on the first map and the increased mean from 2011 to 2012, if the same trend continues, I believe that there will be even more foreclosures in 2013 than in 2012.
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