Quantitative Methods Assignment 3: Z scores and Probability

The purpose of this assignment is to study the geography of foreclosures in Dane County, Wisconsin. To do so, foreclosures in the area from 2011 and 2012 were spatially analyzed. A map was created to analyze the spatial patterns of the foreclosures, and answer the question of what the chance of foreclosures looks like for Dane County in 2013. In order to answer this question, data was placed in ArcGIS and manipulated with various tools in order to project the spatial patterns that the 2011 and 2012 Census Tracts data contain, and make predictions about foreclosures possibilities for Dane County in 2013.

 
Two different calculations were used when spatially analyzing the data set, z-score and probability. Z scores are based on a normal distribution and can be used to find the probability of something. A z-score can be used to determine how often patterns are occurring in a data set. As a z-score increases, so does probability. Probability is the ratio between the absolute frequency for an outcome and the frequency of all outcomes in an event. In this assignment, the data being analyzed is from county officials in Dane County, the addresses of foreclosures in the area were given and then geocoded and added to the Census Tracts for Dane County. The foreclosure data years were 2011 and 2012. The data from these two years of foreclosures will be used to predict the chance for foreclosures in the county in 2013.
The z-score was calculated for three census tracts in this assignment, tracts 122.01, 31, and 114.01. These calculations were completed for the 2011 and 2012 data sets. (See Figure 1 below) Two maps were also created that depict the pattern of house foreclosures in Dane County in 2011 and 2012 (Figure 2).

Figure 1:
Tract 122.01 Z Score-2011: Mean: 11.392523
Standard Deviation: 8.77303
Z-score: -0.614671
2012: Same z score of -0.614671

Tract 31 Z Score-2011: 1.43072
2012 Z Score: 0.753158


Tract 114.01 Z Score-2011: 2.348958
2012 Z Score: 3.146858

Figure 2:

The results of this assignment show the shift in where house foreclosures in Dane County were most concentrated in 2011 and 2012. In 2011, the concentration of house foreclosures is located in the northern part of the county, this pattern can be seen in the map on the left in Figure 2. The dark maroon color indicates where the most house foreclosures were located in the county. In 2012, this high concentration shifted to the right, and then was located on the east side of the county. This shift can be seen directly when looking at Figure 2 by comparing the two maps and locating the clockwise shift that this high concentration area experienced. The z score values calculated for tract 122.01 for 2011 and 2012 came out to be the same value, indicating no change in the pattern of house foreclosures for this specific census tract. The z score values that were calculated for tract 31 ended up being the two scores that were closest to the mean in this data set. The z score in 2011 for tract 31 was 1.43, and this value went down to 0.75 in 2012, meaning that the number of house foreclosures within this tract in 2012 was much closer to the mean of 11.39, which also indicates the high probability of this being a recurring pattern for this tract within Dane County. The z scores that were calculated for tract 114.01 were both quite high values, in 2011 it was 2.35 and this increased to 3.15 in 2012. This indicates that the house foreclosures located within this census tract are father away from the mean than any of the other 5 z scores that were calculated in this assignment. The probability for the two z scores for tract 122.01 is 0.7291. The probability for the z score value for tract 31 in 2011 is 0.9236, and for 2012 it is 0.7734. The probability for the z score for tract 114.01 in 2011 is 0.9906, and for 2012 it is 0.9991. If the patterns that are seen in 2012 for Dane County hold, the z score values for tract 122.01 2011 and 2012, along with the 2012 calculation for tract 31
would be exceeded 70% of the time. 20% of the time, the z score values for tract 31 in 2011, along with both z scores for tract 114.01 would be exceeded because they have a much higher probability than the other z scores.

The results of the assignment indicate a shift in the house foreclosures concentration in Dane County, Wisconsin in 2011 and 2012. This is a shift to the right or clockwise, and the high concentration area of foreclosures shifts from the north part of the county in 2011, to the east part of the county in 2012. This spatial pattern can be seen when looking at figure 2 and comparing the two maps that were created in the assignment. The patterns of 2012 along with the high z score calculations indicate that this high concentration of house foreclosures in the county will most likely continue to shift clockwise around the county, this may be because when foreclosures happen one year in a county, many residents move to a new part of town during this time, making the new part of town more populated and leaving behind house foreclosures. I think that the overall high z score values found for 2012 census tracts and the high z scores found in 2011 and 2012 for tract 114.01 are significant and helped in my prediction of what 2013 will look like. The information gathered in this assignment will be useful to the county officials of Dane County because seeing the 2011 to 2012 shift will be essential to estimating what the 2013 spatial pattern will look like. The z score calculations and probabilities that were found in this assignment can also be applied to further research on the movement of the high concentration area of house foreclosures in Dane County. One recommendation that I have is for county officials to be prepared for the house foreclosures to begin being more concentrated in the southern area of the county. Based on the spatial patterns seen in 2011 and 2012, it is likely that the foreclosures will continue to shift clockwise. Another suggestion I have would be to keep an eye on census tract areas like 114.01, because of the high z score values which indicate that the outcome seen in this tract will likely reoccur.