Assignment 3

Introduction:
An independent research consortium hired me to study the geography of foreclosures in Dane County, Wisconsin. From 2011 to 2012, there was an increase of foreclosures that left county officials concerned. Since I was hired, I had been given the addresses of all the foreclosures in Dane County for the years 2011 and 2012. With this information, I was able to analyze these foreclosures spatially, but just keeping in mind that I won't be able to find the cause of the foreclosures. My main focus was to evaluate the spatial differences between the two years and use this information to try and predict foreclosures in 2013. I also looked at three Tracts specifically as well: Tract 108, 25, and 120.01. By using Z-Scores and Probability, I was be able to provide useful information on the number of foreclosures for all of Dane County that will exceed 10% of the time and 80% of the time.

Key Terms:

I will first define and explain some key terms that will help with better understanding of the methods.

Z-Scores: Z-Scores are used to help indicate the number of standard deviations an observation is below or above the mean. This is also referred to as a standard score of a given value. To find the Z-Score, one must use a specific formula (Figure 1).  A breakdown of the formula: Zi: Z-Score, Xi: observation, U: mean of data, S: standard deviation of data.

Figure 1

Probability: The likelihood of something to occur, represented by a percentage. Z-Scores help to find  the probability, based on a normal distribution. Once the Z-Score is found, that score is used to find the probability by using a specialized chart (Figure 2). 

Figure 2

Data: The data I used for this study was foreclosure data from Dane County, Wisconsin; specifically the years 2011 and 2012.  

Methods:

First of all, I created a map (Figure 3) to show the basics of the Dane County Tracts and to highlight Tract 25, 108 and 120.01 so I was aware of the location of these Tracts in the county. There is also an inset map included to show where Dane County is located in Wisconsin. 

Figure 3

Next, I created a map (Figure 4) that displays the differences of foreclosures in Dane County between the years 2011 and 2012 which is represented by the standard deviation classification. To do this, I added a field in the attribute table and subtracted the 2012 values from the 2011 values. 

Then, I was asked to calculate by hand the Z-Scores of the three selected Tracks for both 2011 and 2012, which left me with a total of 6 scores. I was able to calculate the Z-Scores by using the mean and standard deviation from each year. I added all of the necessary information along with the results onto a spreadsheet to show the bigger picture (Figure 5). 

Figure 5

Results:

By looking at Figure 4, which is the map that shows the differences in foreclosures from 2011 to 2012, we can see that darker blues represent the increase of foreclosures in 2012. Whereas the darker brown colors represent a decrease in foreclosures since 2011. We can also see the that the center of Dane County does not show much change but the Tracts on the outer edge of the county do. An important concept to know about the center of Dane County is that is where the capital of Wisconsin is located. Another aspect to notice is that Tract 120.01 is the darkest blue color which is >2.5 Standard Deviation. 

Figure 4

To better analyze the differences, I created a map of just the 2011 (Figure 6) and just the 2012 (Figure 7) foreclosures in Dane County. First looking at Figure 6, this map also represents the standard deviation classification which was to help with calculating the Z-Scores. By looking at each of the three selected tracts individually again, it looks like Track 120.01 and 108 were greater than 1.5 standard deviation from the mean. This means that they had higher amount of foreclosures than the average during 2011. Tract 25 however, had less than the average foreclosures in 2011 because it was <-0.50 standard deviations. 

Figure 6

Now looking at Figure 7, the only Tract that displayed a change was 108, which ended up having foreclosures in the average range for the year 2012. Analyzing both Figure 6 and Figure 7, the maps show that the Tracts clustered around the center of Dane County, which we know is where the Capital of Wisconsin is placed, mostly fall <-0.50 standard deviations below the mean that represents that this area of the county has less than average foreclosures in both years. This reinforces Figure 4 showing the changes between 2011 and 2012 because that map shows that the center tracks didn't have much change between both years. 

Figure 7

Lastly, after I created each of these maps to analyze the spatial differences between the foreclosures in 2011 and 2012, I could then make my prediction for 2013 using Probability. Just to refresh, the goal was to use Probability to determine the number of foreclosures for all of Dane County that will exceed 10% of the time and 80% of the time. So, the number of foreclosures that will likely occur 80% of the time, if the patterns continue into 2013, will be 3.98 or more realistically 4 to round up to a whole foreclosure. And the number of foreclosures that will only likely occur 10% of the time will be 24.98, or once again round to 25 to for a whole foreclosure. 

Conclusions:

To tie everything together, we reviewed the differences of foreclosures in Dane County, Wisconsin in the years 2011 and 2012 with an emphasis of Tracts 108, 25, and 120.01. This showed that Tract 120.01 had the most change compared to the other two. There is a map (Figure 4) to show the difference of foreclosures between both years represented by standard deviation. We observed that the biggest changes occurred around the borders on the county and the least amount of changes in the center where the Capitol of Wisconsin in located. There are two separate maps (Figure 6 &7) that show just the foreclosures in 2011 and just 2012, also represented by the standard deviation classification. These maps were useful also with analyzing the foreclosures because another important piece of information we noticed was that the Tracts that were located in the center of Dane County were mostly <-0.50 standard deviations below the mean for both years which again ties in with Figure 4 because that map shows that the center Tracks don't have much change between both years. Lastly, using Z-Scores and Probability, we predicted foreclosures for 2013 finding that at least 4 foreclosures will likely occur 80% of the time and up to 25 foreclosures will only likely occur 10% of the time. The implications with the results is that these findings can help us with locating foreclosures spatially, however they do not tell us the cause for them. Also, these are just predictions and do not indicate that any increases or decreases will absolutely occur at all. My recommendation would be to use this information as reference on making decisions however not having it be your sole source of data.