Z scores, Mean Center, and Standard Distance

Introduction:

This assignment focused on locating the Mean Center and Weighted Mean Centers for the data from 2003 and 2009.  We also found the Standard Distance and Standard Deviation for the same years.  The question we are looking at focuses on the areas of Eau Claire where there are a high number of arrests for disorderly conduct.  The investigation includes analyzing data from each of the years, 2003 and 2009 to see if there is a difference in the two years or how similar they are.  I am looking the information for both years to see if there is a particular part of Eau Claire where most of these arrest occur or the most likely places for it.  I will be looking at the 2003 and 2009 arrests data for disorderly conduct and locating the Mean Center, the Weighted Mean Center, Standard Deviation and Standard Distance. I will use these to try to narrow down an area in Eau Claire that is the most affected by these arrests.  I will also analyze the data to see if there is a difference between 2003 and 2009 or if they are similar.  I will also use the Eau Claire bars to see if there is any correlation with the distance to a bar. 

Methodology:

First I am using the Mean Center which is a spatial measure of central attached to a Cartesian plane (x,y) or (latitude, longitude), constructed from the average of x and y values.  The center point is a point from the average x and y values for the input feature, the input features are grouped according to the case field values and mean center is calculated from the average x and y values for the centroids in each group.  In this case I used the arc tool box and mean center tool to calculate it.  I also used the Weighted Mean Center which is a little different, it is calculated by using the Mean Center but adding value associated with each point.  Such as in this case it was weighted to Join with the map and a count.  This adds a little more information about the arrests and their location to a bar. 

Map 1:  This map represents the arrests for 2003 and the Mean Center in red and Weighted Mean Center in green.  Notice that the Weighted Mean Center is slightly south west of the Mean Center.  The big blue dots are locations in which 13-30 arrests have occurred which is the highest number, many of the larger blue dots are somewhat close to the Mean Center and the Weighted Mean Center.  There is a large blue dot indicating that there were a large number of arrests but there is no information in this map to indicate the reason for this.   

Map 2:  All the information in the previous map is the same but this is for the year 2009 instead.  If you notice the Mean Center and the Weighted Mean Center are both in close to the same place and the large green dot northeast of the Mean is also a place of concern for this year. 

 

Map 3:  From 2003 to 2009 there is not much difference in the Mean Center and the Weighted Mean for each of these years.  They are so similar that it was difficult to find colors for this map that you could see well due to overlap.  The area with the most arrests is basically the same in both years.  In 2009 there is a new development that is not in the 2003 data, the large pink dot to the left of the Mean and the Mean Center is much larger in the 2009 data.  Perhaps there was a bar that was added within that 6 year span. 

 

Next we are looking at the Standard Distance. The Standard Distance is the spatial equivalent to the standard deviations.  It measures the degree to which features are concentrated or dispersed around the points.  It provides a single summary measure of the feature distributions around any given point.  It is expressed as a radius or a circle.  Using the Weighted Standard Distance, it is used in connection with Weighted Mean Centers.  This is also done by using Arc Map and choosing the Arc Tool Box and Spatial Statistics Tools- Measuring Geographic Distributions and choosing the Standard Distance, and in the input box you can chose to Weight it by the location of the arrests in 2003.  Each are using 1 Standard Deviation above the mean.

Map 4:  This map for 2003 shows that the Weighted Standard Distance is slightly smaller and slightly more south as shown in pink,  The Standard Distance in blue is slightly larger and somewhat more northern. Maybe this has to do with the large blue square that has appeared to be a high place for arrest on all the maps so far.  There were just as many arrests in the northern most larger square as all of the other larger squares in the Standard Distance. 
 

Map 5: This map is of 2009 shows very little if almost no change from 2003.  The areas are very similar and the areas of concern are still very close if not the same.  There is a small difference in the 2003 and the 2009 maps, on the right most part between the two circles, there is a group of larger pink circle indicating more arrests there and these places are not as prevalent in2003.

Map 6:  This map shows the Weighted Standard Distance for 2003 and 2009.  As discussed in the previous maps there is very little difference between the years.  The arrests and the distance from the bars is still concentrated in the same areas. 
 

Results:

I am using map 7 which shows the relationship of arrests for Disorderly Conduct with the locations of Eau Claire bars.  I found there to be a strong correlation to the location of bars and the amount of arrests in the particular area near bars in the Mean Center.  As indicated below, the areas in red show a high amount of arrests in the area of the Eau Claire Blocks that is located on or near Water St.  This area is known to be frequented by many college kids and has many bars located in a short distance from the college and from each other.  The information in the previous maps shows that this is an area of concern.  In Map 1, 2, 3, 4, 5, 6 show the concentration of bars in and the concentration of arrests in the same areas.  A large amount of the bars are located near the bars Mean Center labeled with a black asterisk. There is still the large amount of arrests in the northern part of Maps 1-6 that has not been addressed.  My best explanation is as follows, there are only two bars in that particular area, either one or both bars may be places that a lot of drinking occurs to cause so many arrests.  Due to the amount of arrests in that particular area for both years, there must be something that is not known through this analysis.   

Map 7:  This map shows the location of the Eau Claire bars and the Standard Deviation of how many arrests per Block Group.  It has much of the same information as the other maps.  It show the locations of the maps in relation to the Mean Center of the bars which is coincidentally the same areas of many arrests.  The red blocks are associated with many bars being in close proximity to them.  The red area is more than 2.5 standard deviations from the mean which means that there are large number of arrests near these particular bars.  The dark orange area is also in close proximity but the lighter orange block in the lower right side of map only has a few bars on its border but no bars inside of its perimeters.  Further information would be needed to know the reason for this. 

Figure 1:  This figure shows the PolyID of particular Block Groups and the number of arrests there.  I have calculated the z-scores for them to indicate the distance from the mean. Block 41 is not very far off the mean, 46 is much higher than the mean, one would assume it is one of the dark red areas on Map 7 while 57 is located in the light green which is <0.50 stdv.

If this pattern holds next year in Eau Claire, based on this Data, what number of Disorderly Conducts in Eau Claire will be exceeded 70% of the time? 

Figure 2:  This is the calculation of the probability that the number of arrests will be exceed 1.29 70% of the time.

Figure 3: This calculation shows the probability that the number of arrests will be exceed 11.92 arrests 20% of the time.  

Conclusion:

The overall results show that there are many more arrests for the years 2003 and 2009 near bars and even more so where there are multiple bars in a small area.  There is a specific area near and on Water Street that has a cause for concern.  I think the implications of this is huge.  If these results could end up in the hands of someone who really cared about the situation, they could have more strict guidelines for the bars and how much alcohol they can serve.  If the bar owners were to come together to have better regulations on when to cut someone off this could prevent over drinking which could prevent disorderly conduct arrests.  The bar owners would lose money doing this so in turn it takes you right back to where you were previously with young college students drinking past their limits.  This is not what all the results say but the Mean Center for bars and the Mean Center for arrests is basically the same spot.  Recommendations, more police patrol, more security in the bars.  This is not just about Disorderly Conduct, this is about the possibility of drinking and driving too which is I am sure a whole analysis of its own.  These results should prove that there is a problem but problems are not usually solved when the solution causes loss of revenue.