Assignment 3

Foreclosures in Dane County, Wisconsin

Introduction:

In this research question I will be investigating the changes in foreclosures in Dane County, Wisconsin from the years 2011 to 2012. I can not determine the reason behind this change spatially as there are a lot of reasons behind foreclosures, but I will be looking at the change from a spatial point of view. This information could possibly be helpful to others for instance families looking to by a house, relaters, and people in political offices. I am researching this question specifically because it has been a topic of concern among County Officials as to why this number has gone up, and if it will continue to do so. I will with my question be finding the patterns from one year to the next to see if I will be able to provide a prediction for the next year (2013).

Methodology:

To answer my research questions I will have to use a couple of different methods on the way.
First to find the change in the years 2011 to 2012 I had to add a field to my attribute table. I did this by adding a blank field add calculating it using the fields Count2011 and Count2012 and subtracting the year 2012 from 2011 to get the changes in house foreclosures.

Another method I used was calculating the Z-Score specifically of a certain Census Tract in the County. Z-Score is figured by taking your X like in this instance the number of foreclosures in a certain census tract and subtract that from your mean of the year and divide that by your standard deviation of that year. This equation is shown in Figure 1 below.
A method that relates to this is how I found the mean and standard deviation for the certain years I did this simply by going into the symbology part of Arcmaps and going to classify. This is represented by Figure 2.

2011:
Mean=11.39
Standard Deviation=8.78
2012:
Mean=12.30
Standard Deviation= 9.91

Figure 1: Z-Score

Figure 2: Standard Deviation and Mean

Along with Z-Score another method used was finding an X-value from probability. To do this you first use Figure 3 to find you percent probability and that from there you find the Z-Score found in the first row and column. When you have your Z-Score you can then use the Figure 1 equation to get the X value. I used this specifically to find the number of foreclosures that would be exceeded a percentage of the time. Which will become more clear further in the blog.

The data that I am using for these methods comes from the foreclosure data by the Census for the years 2011 and 2012 by individual house.

Figure 3: Standard Statistical Table

Results:

First for results I have the Map (Figure 1) that covered the change in foreclosures from the years 2011 to 2012 that I discussed in my methodology section. This showed that there was a more substantial change in an increase in foreclosures in 2012.

Figure 1: Map of Change form 2011 to 2012

My next results were that of the Z-Scores from 2011 and 2012 for three specific Census Tract areas of the county. I found from my results that in two of the areas (108 and 25) the Z-scores go up a small amount, but in the other one (120.02) it goes up a substantial amount. This goes along with my previous findings that the number of foreclosures goes up over the year. It also correlates to Figures 1 and 2 by the standard deviation and how it is correct with the up and down shown by what I calculated the Z-Scores as for those three Census Tracts.

Z-Scores:

Figure 2: Standard Deviation of 2011

2011: 

Census Tract 108 

Z-Score= 2.01

Census Tract 120.01

Z-Score= -.614

Census Tract 25

Z-Score= 1.78

Figure 3: Standard Deviation of 2012

2012:

Census Tract 108

Z-Score= 1.48

Census Tract 120.01

Z-Score= 2.99

Census Tract 25

Z-Score= -.938

Probability:

I found that the probability that the patterns from 2012 will stay the same into the next year:
From the data the number of foreclosures that will be exceeded 80% of the time is 3.98, and that will be exceeded 10% of the time is 24.98. If found this like I explained in the methodology section by using the Figure 3 in that section to find the Z-Score and then algebraically finding the X value which in this case is the number of house foreclosures. This shows that by the pattern the foreclosure numbers should increase the same spatially in 2013. Spatially I think it is also most likely to happen in the up and coming suburbs of Madison like Sun Prairie (which is on the northeast middle side of the county. From the map it shows more outer Census Tracts to be the locations of foreclosures so I believe the patterns will continue there.

Conclusions:

First I would like to restate my research question that is to find spatially the change in house foreclosures from the years of 2011 to 2012 in Dane County. A long with from these patterns will there also be an increase in the year 2013.
A summary of my results showed that at least one of my z-scores showed an increase in change, and that from Figure 1 of my results section the overall number went up from 2011 to 2012. Although comparing the mean and standard deviations of the two years the are only slightly different in numbers shown in my methodology section under Z-scores. The numbers match accurately with my results, but it is not as great of a difference as it seems to show on the map. In my conclusion of the results spatially, I believe that the increase happened more on the outer edges of the county and the suburbs of the main city of Madison in Dane County. This pattern is shown on all of the figures in the results section of the blog. The probability section made more sense of the patterns of the change and to if they it were to make sense for the same change to occur in 2013. It shows that 80 percent of the time for 2013 there will be rounding up to an increase of 4 houses more that will be foreclosed on. Although not a large number it still backs up the hypothesis.

Assignment 2

Part I:

Range: Range just refers to the greatest number in a group of observations minus the smallest number in that same group. It shows the disperses of the set of observations.

Mean: Mean refers to all the numbers in a group of observations added up divided by the total number of observations made. This is showing what number the observed group is more tending to out of all the numbers.

Median: Median is the number that is in the exact middle of a group of numerically ordered observations. Usually works best with a group that has an even number of observations, if there is an odd number of numbers then you take the difference between the even two.

Mode: Mode is the number that appears the most out of all the numbers in the group of observations.

Kurtosis: Kurtosis is shown on the graphed observations as steepness or the lack there of. This steepness is referring to the distribution of numbers away from the mean. There are two types flat or peaked. Peaked would be a lesser number distributed to that side and flat would be a greater number.

Skewness: Skewness is defined as how much the shape of the observations graphed is shifted from the one side of the mean of the group. It can either be a negative or positive skewness depending on if more observations fall below or above the mean.

Standard Deviation: This can be defined as how close or far away an observation is to the mean or the most common observation. It shows how far an observation "deviates" from the normal.

In past studies the highest score for standardized tests have always been higher at Eau Claire Memorial than Eau Claire North. This has led to a questioning in the staff at North. I will be looking to see if the top score is an accurate betrayal of the teachings at North. The test score max is 200 for this test and the highest score at North is 194 and at Memorial 198. I will be looking at more than the highest score, and instead the range, mean, median, mode, kurtosis, skewness, and standard deviation to tell the differences between the success of the students at the differing schools.

Eau Claire North:
Range= 83
Mean=160.92
Median=164.5
Mode=170
Kurtosis= -.55723
Skewness= -.5791

Standard Deviation:24.48

Eau Claire Memorial:
Range= 91
Mean=158.54
Median=159.5
Mode=120
Kurtosis= -1.17435
Skewness= -.1848

Standard Deviation: 27.58

These are the results I was able to compute of the two high schools. It turns out that in almost all categories North comes out on top of Memorial. Norths median and mean scores are higher than Memorials, but Memorials skewness is more negative than north which is better for scores. I don't think North teachers should be concerned about the performance of their students because over all they are testing about equal and even a little higher than Memorial based on the mean score. Mean score is in my opinion the best way to represent this data because it is the most fair way of averaging the students scores.

Part II:

Geographic or Spatial Mean Center: In my own words spatial mean center is where the push and pull of the land area (or latitude and longitude) ends up. It is the exact center of the area of a given place.

Weighted Mean Center: Weighted Mean takes in account other factors. You can do the weighted mean of a group of observations and it will be in the middle of where the greatest number of observations are pulling it.

This map is of the geographic mean (so unweighted) of the state of Wisconsin. This is where spatial the mean or center of the state is. It also shows two weighted means. One is the mean center of the population of the state in 2000 and the other is of the mean center of the population in 2015. The weighted mean centers make sense because it is relatively low in the state because of the pull from Madison and Milwaukee, but even though there is more land north of the center it is far less populated. You can tell by the graph that there was a shift from 2000 to 2015 in population. It has shifted southwest of where it was in 2000. This shows that it is moving in the direction of Dane County which is were Madison is which makes a lot of sense. Madison is the second biggest city in Wisconsin, and it is a very hip place for young people to move especially with it being a big college town.