Assignment 3

Introduction

                Dane County is interested in understanding the spatial pattern of the increase of home foreclosures in 2011 and 2012 as well knowing if the trend will continue through 2013. Addresses in the county have been geocoded into the various census tracts in Dane County so that an analysis can be conducted at the census tract level.

Methodology

                To complete my analysis, ArcMap was used display the census tracts for Dane County. Then a statistical analysis was completed using mean, standard deviation, z-scores and mean center. Standard deviation is the measure of the dispersion (how spread apart) a particular set of data and how the mean (average) accurately depicts the data. In this case, the mean was calculated by the average number of foreclosures per census tract. A z-score explains the position of a particular number and where in lands on the standard deviation curve (figure. 1) and can be used to find the probability of a particular occurrence taking place. For example, a negative z-score means that the likelihood of that observation is higher than 50 percent and if a z-score is positive than its probability is less than 50 percent. Also the larger the z-score the closer to the tails of the distribution the observation will be. Mean Center shows the spatial center of a set of data that can be weighted by statistics that can help display a specific spatial pattern in a data set. 

Figure. 1 Standard Deviation Curve 

Results

                When looking at the foreclosure data for Dane County (figure 2.) there was an increase in the number of foreclosures between 2011 and 2012 of 97 foreclosures for the county as a whole, with an increase of nearly an additional foreclosure per census tract on average. For this analysis three specific census tracts, 120.01, 108, and 25 (figure 3.). For each of aforementioned census tracts, their z-score were calculated to see how these different census tracts compared to the other census tracts in Dane County. When looking at z-scores for the 2012, a couple of patterns stick out. Census tract 120.01 has a very high z-score meaning that it has far more foreclosures than the county average and census tract 25 has a much smaller z-score and therefore falls to the bottom of the distribution. To place these results in the context of probability, for 2012 the number of 3.974 foreclosures will be surpassed about 80 percent of the time (z-score of -0.84) and a number of 24.962 foreclosures will only be surpassed 10 percent of the time (z-score of 1.28).

                When looking at the map for 2011 (figure 4.) there were fewer foreclosures in the center of the county with the largest number of foreclosures being found in the northern section of the county. In 2012 (figure 5.), the census tracts that surround census tract 120.01 had less foreclosures than in 2011. Looking at the differences between 2011 and 2012 (figure 6.) the most dramatic increases came about on the eastern and western borders of the county. Also, when looking at the Weighted Mean Center amongst the three maps below (figures 4,5, and 6),  it is evident that it has shifted towards the west and means that the spatial distribution of foreclosures has moved more so to the west.  Based upon the statistics provided (figures 2 and 3) and the maps below (figure 4,5 and 6) a trend of increased foreclosures especially the eastern and western borders were the greatest increase from 2011 and 2012 can be expected in 2013.

Figure 2. Shows the statistics for Dane County in 2011 and 2012

Figure 3. The chart above displays the statistics for census tracts 120.01, 108, and 25 for 2011 and 2012

Figure 4. The map above shows the number of foreclosures by census tract in 2011

Figure 5. The map above shows the number of foreclosures by census tract in 2012

Figure 6. The map above shows the difference in foreclosures between 2011 and 2012

Conclusion

                Based upon the information presented above, it can be inferred that an increase in the total number of foreclosures should continue. This is especially true for the census tracts located in the eastern and western sections of the county as the areas in the center of the county have been fairly stable in comparison. It is important to note that without further background information about the economic situation of Dane County, this study is fairly limited in the amount of information that can be interpreted. However there are important spatial trends that can be seen and that can aid county officials in their assessments of the foreclosure issue in Dane County going forward.

Sources
http://www.muelaner.com/wp-content/uploads/2013/07/Standard_deviation_diagram.png