Lab 3: Significance Testing

Part 1: T & Z Tests

Below are some terms and operations that are crucial to understand what was done later in the lab. Calculations of the data and terminology is crucial to determine the differences between Northern and Southern Wisconsin.

	Interval Type	Confidence Level	n	Sig. Level	z or t	z or t value
A	Two Tailed	90	45	0.05	Z	pos or neg 1.65
B	Two Tailed	95	12	0.05	T	pos or neg 2.201
C	One Tailed	95	36	0.05	Z	1.65
D	Two Tailed	99	180	0.01	Z	pos or neg 2.58
E	One Tailed	80	60	0.2	Z	2.06
F	One Tailed	99	23	0.01	T	2.5
G	Two Tailed	99	15	0.01	T	pos or neg 2.997

A Department of Agriculture and Live Stock Development organization in Kenya estimate that yields in a certain district should approach the following amounts in metric tons (averages based on data from the whole country) per hectare: groundnuts. 0.5; cassava, 3.70; and beans, 0.30.  A survey of 100 farmers had the following results:

 μ          σ

            Ground Nuts   0.40     1.07

            Cassava            3.4       1.42

            Beans              0.33     0.14

a.       Test the hypothesis for each of these products.  Assume that each are 2 tailed with a Confidence Level of 95% *Use the appropriate test

b.      Be sure to present the null and alternative hypotheses for each as well as conclusions

c.       What are the probabilities values for each crop? 

d.      What are the similarities and differences in the results

A.    Z-Score= Sample Mean – Country Mean/ (Standard Deviation/Sqrt(n))

Ground Nuts= -.9346

Fail to Reject

Cassava= -2.1127

Reject

Beans- 2.1429

Reject

B.     The Null hypothesis is that at a 95% confidence interval there is no difference between the averages of Kenya’s crop production in comparison to the other 100 sampled farmers. (ground nuts, cassava, beans)

The alternative hypothesis at a 95% confidence interval says there is a difference between the 100 sample farmer and the average crop production of Kenya.  (ground nuts, cassava, beans)

C.     Ground Nuts: -.9346 (No difference)

Cassava: -2.1127 (Difference)

Beans: 2.1429 (Difference)

D.    There are two similar things that I noticed when looking at the data that I calculated. Two out of the three data sets fell outside of the range that would have classified a difference. As far as Z- scores go the numbers varied more, -2.1127 was 2 standard deviations below the county average. Then -.9346 is also almost one standard deviation below the county average.  The final value of 2.1429 is over two standard deviations over the county average. Hence the differences that I spoke about in the opening sentence.

An exhaustive survey of all users of a wilderness park taken in 1960 revealed that the average number of persons per party was 2.8.  In a random sample of 25 parties in 1985, the average was 3.7 persons with a standard deviation of 1.45 (one tailed test, 95% Con. Level) (5 pts)

a.       Test the hypothesis that the number of people per party has changed in the intervening years.  (State null and alternative hypotheses)

b.      What is the corresponding probability value

A.    The Null hypothesis at a 95% confidence interval is that there is not a difference in the average number of people per party in 1960 in comparison to the 1985 sample.

The Alternative hypothesis at 95% confidence is that there is a difference in the number of people per party in 1960 in comparison to the 1985 sample.

B.     1960=2.8

Sample in 1985=3.7

Standard Deviation of 1.45

N(1985)=25

The corresponding probability value of 1.711 and the T-score of 3.1034 would lead us to reject the null hypothesis. What these numbers tell us is that there is a difference between the whole number of park users in 1960 compared to the 985 sample.

Part 2: What and Where is up North?

Introduction

      In this Lab we were tasked with determining what separates the north from the south in Wisconsin. I am sure my opinion of up north is much different than others. For the purpose of this assignment I used Highway 29 as my divider between north and south. The objective of this assignment is to learn how to calculate Chi-Square and then understand how it relates back to hypothesis testing. Next it was also important to understand how to relate a spatial output to the Chi- Square statistics and then to relate that all back to the real world. Then finally we have to make sense of all the numbers and calculation to relate this all back to geography. No matter where I looked there is no clear cut definition of Up North. Each individual persons perspective influences what they think is up north. To determine where up north is in Wisconsin I used three different data sets. I chose to use Non- Resident Gun licenses sold per county, Acres of Lake Per County and Non- Resident Fishing License sold per county.

Methods

      I first went onto the US Census site and brought in the Wisconsin counties. After the 72 counties were displayed in ArcMap I began to select all the counties that were north of highway 29 and all the counties south of Highway 29. If counties had 29 going through them, I separated them to the category that had the majority of the county. When looking at counties and trying to separate it my data may vary from others but I found 28 counties north of Highway 29 and 44 counties south of Highway 29. The counties north of 29 are a light shade of red while the counties south of 29 are a baby blue. Each of the other 3 variables that I used are represented by various numbers, for the counties they are just 1-4. It is sort of backwards in the aspect that 4 is the least and 1 is the most. We were provided SCORP DATA on the Q drive which was there to give us options into the data we wanted to map. Once we decided which ones we wanted to use, 3 separate joins were performed.

The Map above simply illustrates how I split the state for this lab. Red is Northern Wisconsin and Blue is Southern Wisconsin.

The Map above is a representation of the amount of non resident fishing licenses sold per county in the state of Wisconsin. The darker the green the more licenses sold in that county, then the lighter the color the less licenses sold. It is easy to see the cluster of dark green counties in the North West portion of the state and the again slightly East. I believe the reasoning behind this is that there is simply more species of fish such as walleye. Also fish number are higher, less pressured and generally speaking bigger. So this makes it an obvious attraction for out of county residents.

The Map above is a Map of the amount of Non Resident gun deer licenses sold per county in the State of Wisconsin. Very similar to the map of the non resident fishing licenses we see a similar pattern here. The NorthWest corner of the state is sell more tags than any other area. I believe this is because there is an immense amount of public land in that area. The Nicolet National Forest is close by, also many people own cabins up north for other recreational activities along with hunting.

The Map above is a Map of the amount of Acres of inland lakes that each county in the state of Wisconsin has. Here we see a slightly different trend than the previous two maps. the north doesn't necessarily dominate the map.

Assignment 2: Disorderly Contuct

Nathaniel Krueger

Geography 370

Quantitative Methods

Introduction

When people think of college towns, they think of loud music, drinking and out of control behavior. The same goes for the citizens of Eau Claire, whom frequently make accusations assuming that the areas with more bars tend to be the loudest and rowdiest, as geographers we are here to spatial analyze what the data tells us. Not to say that there is not an association between the number of bars and disorderly conducts. In this assignment as an independent researcher I was given the data and tasked with exploring the number of disorderly conducts violations in all of Eau Claire from 2003 and 2009. The location of bars throughout Eau Claire are also noted. Furthermore I want to investigate whether or not there is a link been violence and the bar scene. The addresses of the disorderly conducts are also attached to the points to give a spatial reference.  The issue here is that older citizens and family oriented people would not want to raise a family or live where there is a high probability of a fight being started. My research is looking into this to see if there is a link between the location of bars and the number of disorderly conducts related to those areas. The sole purpose is simply to determine if areas with more bars, have more disorderly conducts reported. This assignment was completed using ESRI ArcMap. In the maps I will display mean center, weighted mean center, and standard deviation. Graduated symbols will be used to display the number of disorderly conducts in each area, including different colors for the year 2003 to 2009.

Methodology

            A few terms that are crucial to understanding what is happening in this assignment in the mean center, weighted mean center, standard deviation and z- score. A mean center is a point that is the center of all data point, basically using the longitude and latitude is a simple way to look at it. The weighted mean center is the geographic center of a set of points that is adjusted to account for the influence of each point. Standard deviation is the distance from the mean, for the purposes of this assignment I will be only going out one standard deviation which will include 68% of all the data points. Finally the z-score is a number that tells you how far the data point is away from the mean. A z-score of 0 would mean that the date point is the average, there can be negative and positive z-scores. In the context of this assignment, a z-score of 2.0 would mean that there are more disorderly conducts occurring in that area in comparison to the mean.

In order to get a good idea of what we were looking at I first put the bars in Eau Claire on the layer in ArcMap. Then I added in the Disorderly Conducts from the years 2003 and 2009. From there I calculated the mean center and the weighted mean center. Both of these operations were done in the Arc toolbox under the spatial statistics tab. The only difference was that for the weighted mean center I had to select count under the weighted category tab. The steps that were done above accounted for three of my maps that I produced. The maps contained the mean center and weighted mean center for 2003 and 2009, and one combining the data from both. Each of the first three maps featured graduated symbols to show where the most disorderly conducts occurred by location. I will speak more about them in the discussion section. I ran this tool four times, once for mean center 2003, weighted mean center 2009, mean center 2009 and weighted mean center 2009. With these four points on the same map it starts to give us an idea of the shift in disorderly conducts from 2003 to 2009. Also while on the subject, the mean center of the bars in Eau Claire was calculated for 2003 and 2009 in the same way that the mean centers for disorderly conduct were done.

Next standard distances were calculated in order to get an idea of where most of the disorderly conducts were happening in relation to the mean center in Eau Claire. Because we want to see what area has the most disorderly conducts I am only going out one standard deviation. The tool for calculating standard distance is also under the measuring geographic statistics tab near where we calculated the mean center. Just as the first three maps produced I made another three displaying the standard distances. Map 1 was for 2003, Map 2 for 2009 and the third and final map was 2003 and 2009 together so we could analyze the shift over the six year span. To produce the standard distance I again selected 2003 disorderly conducts for the input and the count for the weighted tab. After the Arc is done processing there will be a symmetric circle that displays all the data that is within one standard deviation from the mean. The data is correct, though it is important to note that the Geographic Coordinate System that you choose to use can affect the circle, simply because the world is not flat as ArcMap portrays on screen. Next I made my circle 50% transparent underneath the display tab, in order to not draw the map viewer from other aspects on the map. I then repeated the steps above for 2009. Each of these standard distances were placed on their own maps for 2003 and 2009, then they were placed on the same map along with the disorderly conducts for each year, the bar data and the mean center and weighted mean center.

The last portion of this assignment is to deal with the z-scores and standard deviations. The block group data is where the z-scores were calculated from. The block groups were displayed using a choropleth map which illustrates the amount of standard deviations above or below the mean the block groups are. To choose the colors I wanted I went under the symbology tab and chose colors that represented high and low standard deviations.

Results

            After run a series of data processing tools to better understand the data, I would say that the citizens of Eau Claire do have a basis to imply that the more bars there are, the more disorderly conducts will be associated with them. The mean centers and the weighted mean centers for 2003 and for 2009 did not shift what I consider significantly. I am failing to reject the idea that bars are related to disorderly conduct. The mean centers and the weighted mean centers for 2003 and for 2009 are located within a few blocks of a number of water street bars. When closely examining the weighted mean centers for 2003 and for 2009 the centers fall in the Chippewa River near the west side of the river by the water street bridge. I have one main idea as to why they fall there. I think that students who have been at house parties that are underage avoid the foot bridge because historically cops wait around the bridge getting people going back to the dorms. This in turn creates a pinch point on the water street bridge. Also another factor that could contribute is that there is housing on both sides of the Chippewa, not only near the bars.

Map 1: Disorderly Conduct in 2003

            Below is a Map of disorderly conduct in Eau Claire in 2003, symbolized by a graduated symbol legend. We can see the number of disorderly conducts displayed by the color brown. The Larger the circle the more disorderly conducts that occurred there. Also displayed is the mean center displayed by orange and the 2003 weighted mean center, displayed in red. We can see that the weighted mean center has shifted slightly southwest from just the mean center. The shift of the weighted mean center from the original mean center is telling us that it is pulled that way because there were more crimes occurring in that direction.

 

 

 

 

 

 

 

 

Map 2: Disorderly Conduct in 2009

            Using the same graduated symbols as map one but with a different color I mapped the disorderly conducts that were reported in 2009. The mean center is represented by a blue dot and the weighted mean center by a white dot. We can see the weighted mean center shifted to the southwest in comparison to the mean center. There is a cluster of disorderly conducts that occurred on the water street strip of bars.

Map 3: Disorderly Conducts from 2003 Compared to 2009

            Map three is a map that displays the data from both Maps 1 and 2. I did this in order to get a better idea of the changes that occurred in disorderly conduct from 2003 to 2009. This map displays the amount of disorderly conducts from both years, along with both mean centers and weighted mean centers. The map shows that from 2003 to 2009 both the mean center and the weighted mean centers shifted north. Though the show similarity in the way the weighted mean centers are pulled. What we can gather from this map is that in the six years between the data collections that more crime is being committed in the northern part of Eau Claire. This information also tells us that maybe the number of disorderly conducts is decreases in the downtown water street area, at least marginally.

Map 4: Disorderly Conducts in 2003 with the Standard Distance

            Map 4 below relates to the standard distance, which is telling us that 68% of all the disorderly conducts were committed within the circle which is one standard deviation away from the weighted mean center. When we were calculating the one standard distance we calculated it from the weighted mean center rather than the mean center. It is not shocking that all of the campus of UWEC falls within the circle. Under further investigation we find that there are many crimes committed within this circle, along with the disorderly conducts comes a large number of bars. This still does not prove that the consumption of alcohol causes violence, but there is coincidentally a large number of fights and bars near each other.

Map 5: Disorderly Conduct in 2009 with the Standard Distance

            Similar to Map 4, Map 5 is again showing us a standard distance that encompasses 68% of the disorderly conducts in Eau Claire. There is really not much of a change in the location of the circle in comparison to 2003. To no surprise the campus of UWEC and all the bars on Water Street are encompassed by the one standard deviation. The weighted mean center is the white dot just to the west of the center of the circle. A large amount of the disorderly conducts are near establishments that serve alcoholic beverages. But yet again there is no direct link that can be proven due to lack of data. Majority of off campus student housing is to the west and northwest of Water Street, if a smaller circle was drawn to really dial in on the crimes it would include basically just areas where students live.

Map 6: Standard Deviations/Distances from 2003 to 2009

            The map below is a combination of map 4 and map 5, this allows us to compare data side by side from 2003 to 2009. The weighted mean center shifted northwest from 2003 to 2009 and the similarly the standard distance also shifted north from 2003 to 2009. Thought the differences are noticeable we do see a lot of similarity. A reason for the shift to the north/ northewest may be more students moving into those neighborhood, or maybe at a larger scale just more violence north of this area that is drawing it there.

Map 7: Locations of Bars in Eau Claire and Standard Deviations of Disorderly Conduct

            The map below shows the locations of bars throughout Eau Claire. The red circle is the mean center of the bars in Eau Claire. The legend shows what is above and below the standard deviations, there is both negative and positive block groups, meaning that some areas have more crime and some have less. The dark blue block areas represent high disorderly conducts, it is clear to see that they are near the student housing, minus one block to the southwest to the city. I don’t know much about the area to the southwest of the city but if I had to guess I would say that it is an area that has a low income, due to the fact that there is not a high concentration of bars in the block. This map also shows us that there is quiet a variance in the standard deviations of disorderly conduct around Eau Claire. There was many block groups that had 0 disorderly conducts recorded, in contrast one block group had 42. The city of Eau Claire had an average of 5.3593 Disorderly Conduct Crimes per Block Group. In correspondence, there is a standard deviation of 7.81490. With these numbers as our baseline we were also tasked with calculating z-scores for a few blocks.

 

(Xi): Disorderly Conducts

Block Group 41- Near Oakwood Mall

Xi:10

Mean: 5.3593

Standard Deviation: 7.8149

Z-Score-(10-5.3593)/7.8149

Z-Score-0.5938

Block Group 46: Old Downtown

 Xi: 40
Mean: 5.3593

Standard Deviation: 7.8149

Z-Score: (40-5.3593)/7.8149

Z-Score: 4.4326

Block Group 57: Southwest Eau Claire

Xi: 1
Mean: 5.3593
Standard Deviation: 7.8149

Z-Score : (1-5.3593)/7.8149

Z-Score : -0.5578

Conclusion

            In Conclusion I would say that overall a large amount of the disorderly conducts in Eau Claire occurred near Water Street. Both the 2003 and the 2009 data sets were very similar, with just slight differences. I think that the citizens of Eau Claire have some basis as to their accusations. Though with the data we had there was no real definitive correlation that could be made. I found that the water street area absolutely does have a pull on the data, while it is not the only area where incidents were high, it is easy to see on every map that it contributed a large amount. Two blocks in this area were over two standard deviations above the mean, hence more disorderly conducts occurred there. The implications of this could possibly be to have classes regarding fighting around student housing and the bars. While there still isn’t a link between drinking and disorderly conducts it wouldn’t hurt to have a class on safe drinking and when to know that you’ve had enough. I think that the use of things such as the safe ride could solve this, less people walking around would mean less confrontation. Some areas that could be lacking is we may not have all of the data, not every fight is documented, and the cops aren’t always called. Also the concentration of police in the downtown area is much higher than that of a more upper class neighborhood. So possibly there are more fights in other areas there is just less cops around to catch them. Much more extensive data and research would have to be conducted. Lastly, I believe personally that alcohol is a contributing factor. If there was a definitive way to find that out I think a small percentage of the disorderly conduct in the Water Street and student housing area would be between sober parties.