Assignment 3

Intro

In this assignment, the goal is too study the geography of foreclosures in Dane County Wisconsin. There has been an increase in foreclosures from 2011 to 2012, this is a problem in any county. Therefore County officials are worried, and as an independent researcher my goal is to analyze spatially the pattern of these foreclosures between 2011 and 2012, and provide understanding as to the chance foreclosures will increase in 2013. Although it is not possible to determine the reasons for foreclosures occurring, it is possible to perform a spatial analysis and determine the odds that foreclosures will increase again in 2013. In order to understand the spatial analysis of Dane County Wisconsin Foreclosures Z-scores, Probability, and Standard Deviation will be used to analyze the 2011 and 2012 census tract data.

Z-score
Z-score is the exact number of standard deviation that an observation is away from the mean. For example, if an observation falls between 2 and 3 deviations from the mean, the z score will tell you that it is exactly at say 2.54.

Figure 1: This image shows the z-score equation that is used. 

Probability
Probability is the frequency that an outcome will occur based on a z-score that is calculated for specific observations. This tells the likelihood of an outcome based on a percentage.

Figure 2: This image shows the probability chart that is used to determine the percent of an outcome using z-score.

Standard Deviation

Standard Deviation is a measurement that tells how the numbers in a data set are spread out from the mean. the numbers fall either one two or three deviations from the mean to the right or left, the right being positive and the left being negative. 

Figure 3: This image shows a normal distribution curve with the standard deviation break down.

Methodology

To begin to analyze the foreclosure differences between 2011 and 2012 in Dane County Wisconsin I began by creating a new field in ArcMap which showed the change in the number of foreclosures between 2011 and 2012. With this new field a map was created showing the standard deviation of change between 2011 and 2012 (Figure 4). This new field provided a sense of the increase in foreclosures between these two years. After creating this new field, three predetermined tracts were selected and the z-scores were calculated for these three specific tracts (Figure 6). After determining the z-scores, the pattern in 2012 was tested to determine what number of foreclosures will be exceeded 80% of the time, and exceeded only 10% of the time (Figure 6). This was done by using the probability chart (Figure 2) and determining what percent of the time these increases will occur. After determining the probabilities, then a series of maps were created by mapping the standard deviation by census tract in 2011 and 2012 (Figure 5). Then an analysis of the different maps was done to determine the pattern of change between the two years.

Results

The trend that is seen in foreclosures in Dane County, Wisconsin between 2011 and 2012 is that there is an increase in the number of foreclosures. This trend is shown in figure 4 showing darker green colors which mean they have seen an increase in foreclosures in those tracts, where the darker brown colors show a decrease in foreclosures. For example the eastern side and north western side of Dane county have experienced a higher number of foreclosures compared to the southern and central north side of the county. A spatial trend is seen here by mapping the standard deviation, but there is some internal factor that can not be determined by this type of analysis that causes these specific areas to experience greater or less foreclosures, these could be due to factors like income level.

Figure 4: This image shows the Foreclosure change between 2011 and 2012 using the standard deviation of the Change field which was created to show the difference in the amount of foreclosures. 

A map of standard deviation was produced for both 2011 foreclosures and 2012 foreclosures. These maps show the magnitude of the number of foreclosures in specific census tracts. In 2011 there were less outliers on the negative side of the standard deviation histogram of the data which causes the data to show more foreclosures occurring more closely to the mean. This means that there was a more reasonable number of foreclosures. Compared to the 2012 standard deviation map of foreclosures which has a greater number of outliers on the positive side of the standard deviation  histogram, this means that a majority of census tracts have a higher number of foreclosures in relation to the mean. When comparing these two standard deviation maps it emphasizes the trend that there is an increase in foreclosures from 2011 to 2012.     

Figure 5: This map shows both 2011 and 2012 foreclosures mapped by standard deviation. 

When Focusing on the three specific tracts 108, 25, and 120.01 six Z-scores were calculated three for each tract in 2011 and three for each tract in 2012. It is shown in Tract 108 in 2011 the number of foreclosures in this specific tract was farther on the positive side of the mean in comparison to 2012 where it was not as high, however with a difference in the mean being only roughly 1 more foreclosure these numbers seem more closely related.

Figure 6: This chart shows the results of the Z-score calculations from the three predetermined tracts from 2011 and 2012. this chart also shows the mean median and standard deviation which was used to calculate the z- scores.

The number of total foreclosures that exceed 80% of the time is 3.98, and the number of foreclosures that only exceed 10% of the time is 24.98. To determine the number that exceeds 80% a z-score of -.84 was used  which means that 80% of the time the foreclosures for a tract will exceed roughly 4. And the number of foreclosures using a z-score of 1.28 means 10% of the time a tract will exceed about 25 foreclosures.

Conclusions

After performing a spatial analysis of foreclosures in Dane County Wisconsin between 2011 and 2012, an estimate can be made that the trend will continue into 2013 causing a greater number of foreclosures, although we can not pin point this for sure because the underlying cause of these foreclosures is not known, we can understand that if the trend continues 2013 will have a greater number of foreclosures. This is because we see an increase in the number of foreclosures in different tracts based on how far they fall in the positive direction of the mean based on the standard deviation analysis. I have found that with an increase in foreclosures on the outer edges of the center of Dane county, this means more rural areas that are not as heavily populated have a greater chance of having foreclosures. This could be due to potential increases in home value and a possible downward trend in income for these home owners, but this would require a further investigation into the lives of the people who live in these rural areas.