Assignment 3

Introduction:
There has been concern among county officials about the increase in foreclosures in Dane County, WI from 2011 to 2012.  Looking at the foreclosures geographically, one can analyze spatial patterns of how the foreclosures have changed from one year to the next.  To analyze, the z scores of 3 census tracts within the county for each year were found.  The research will explain patterns of foreclosure and predictions using Z scores about the foreclosure patterns in the following year, 2013.  It will also answer questions about the chances of increase in foreclosure and be visualized with the aid of maps.  Specifically, what the number of foreclosures will be exceed 70% and 20% of the time in the future, 2013. 

Methodology:
Data was used from the U.S. Census for Dane County in 2011 and 2012.  For the first part of the issue at hand, a map of the differences of observation of foreclosures at each track between the years 2011 and 2012 was made.  To do this, a field was added to the attribute table of the census track data in ArcMap by subtracting the differences in the 2012 field from the 2011 field.  A graduated symbols map was then made based off of standard deviations of this new field of differences (map 1).  The standard deviations show how tightly the differences values in each track are clustered around the mean of foreclosures.  Standard deviations farther from zero mean that those tracks have greater outlier numbers of foreclosures, either much higher or much lower differences between the two years, than the average of the differences.  The next part of the assignment involved calculating z scores for three tracks from each year of data using the z score equation.  The Z score shows the number of deviations on a standard deviation chart a foreclosure observation is above or below the mean.  The Z scores can then be used to find probability of future foreclosure patterns by using a z score chart probability chart.  To predict foreclosures for 2013, the differences field was added to 2012 track field to estimate foreclosure numbers in 2013 if current trends like those between 2011 and 2012 continue.  Working the z score equation in reverse after finding the z score which aligned with the percentage on the z score chart for the tracks in 2013 estimate field, the observation number which the tracks had to be over to exceed either 70% or 20% of the time was found. 

Results:
As indicated in map 1 below, most county track differences (all but 4 tracks) between 2011 and 2012 fell between -2.5 and 2.5 standard deviations above or below the mean.  This means that these tracks had greater or lesser difference values than the average number of differences between the years 2011 and 2012.  The tracks deviating most from the average seemed to occur along the outside of the county.  The inner square area of the county had the most tracks with -.5 to .5 deviations.  The results obtained from z score calculations using the mean and standard deviation for all tracks in both the 2011 and 2012 fields are as follows:
Tracks in 2011:
122.01: z score of -.61
31: z score of 1.44
144.01: z score of 2.35
Tracks in 2012:
122.01: z score of -.63
31: z score of .57
114.01 z score of 2.69
These indicated the placement of each tracks distance above or below the average on the standard deviation curve.  The deviation in each of these particular tracks from the average number of foreclosures can be determined.  Track 144.01 deviates the most and has a greater number of foreclosures than the others.  Also, tracks 144.01 and 31 had the greatest amount of difference between the two study years, indicating that the deviation from the average number of foreclosures in track 31 decreased and the increased in track 114.01.  The mean also increased from 11.39 in 2011 to 12.29 in 2012.  Using the patterns in 2012, the number of foreclosures estimated in 2013 to exceed 70% need to be above 6.23.  As shown in map 2, this included about half of all tracks, found mainly in the northern part of the county.  The number of foreclosures to be exceeded 20% of the time, needed to be above 20.61, and included fewer tracks.  A map was made by selecting for counties with greater numbers than 7.14 or 20.61.

Map 1



Map 2

Conclusions:
The results show that the concern for an increase in foreclosures in Dane County is valid.  As map 2 shows, the number of foreclosures can be exceeded in the following year the majority of the time.  For example, 70% of the time in 2013, there are many tracks in the country that will exceed the number of observations given.  This is a fairly high amount.