"Up-North" Wisconsin

Part 1

2.
     Asian-Long Horned Beetle - Null Hypothesis: There will be no difference between the average numbers of Asian-Long Horned Beetles in Buck County compared to the average of the whole state of Pennsylvania. Alternative Hypothesis: There will be a difference between the average numbers of Asian-Long Horned Beetles in Buck County compared to the average of the whole state of Pennsylvania. Conclusion: Reject the null hypothesis. There was a difference between the average number of Asian-Long Horned Beetles in Buck County compared to the average of the whole state of Pennsylvania. There was a lower amount of these beetles found in Buck County compared to the whole state average. This part of the state does not have as much of a concern with this particular invasive species when comparing to the state average.

     Emerald Ash Borer Beetle – Null Hypothesis: There will be no difference between the average numbers of Emerald Ash Borer Beetles in Buck County compared to the average of the whole state of Pennsylvania. Alternative Hypothesis: There will be a difference between the average numbers of Emerald Ash Borer Beetle in Buck County compared to the average of the whole state of Pennsylvania. Conclusion: Reject the null hypothesis. There was a difference between the average number of Emerald Ash Borer Beetles in Buck County compared to the average of the whole state of Pennsylvania. There was a higher amount of these beetles found in Buck County compared to the whole state average. This part of the state has a concern with this invasive species when being compared to the state average.

     Golden Nematode – Null Hypothesis: There will be no difference between the average numbers of Golden Nematodes in Buck County compared to the average of the whole state of Pennsylvania. Alternative Hypothesis: There will be a difference between the average numbers of Golden Nematodes in Buck County compared to the average of the whole state of Pennsylvania. Conclusion: Reject the null hypothesis. There was a difference between the average numbers of Golden Nematodes in Buck County compared to the average for the whole state of Pennsylvania. There was a higher amount of Golden Nematodes found in Buck County compared to the whole state average. This part of the state has a concern with this invasive species when being compared to the state average.

3. 

      Null Hypothesis: There is not a difference of persons per party visiting a particular wilderness park from the 1960 study and sample taken in 1985. Alternative hypothesis: There is a difference of persons per party visiting a particular wilderness park from the 1960 study and sample taken in 1985. The corresponding probability value was 7.22 which gives an almost 100% chance that there is a difference between the studies.  

Part 2

Introduction:

     In the state of Wisconsin, the tourism board has inquired about the concept of “Up-North”. The board wants to see if there is a statistical difference between the northern and southern zones of Wisconsin. The state of Wisconsin has provided a large set of data with different variables for each county across the entire state. From the numerous variables, four will be examined to see if there is a difference between the two parts of the state. The four variables chosen include resident and non-resident deer gun licenses sold as well as resident and non-resident deer bow licenses sold.  For the purpose of this study, Highway 29 running across the state will be used as the dividing line for the northern and southern zone boundary. The map below shows the boundary what is deemed as "Up-north" for the purpose of this study (Figure 1).

Figure 1. This map shows where the boundary is representing what is the northern and southern portions of the state.

Methodology: 

     In order to start the analysis, the data needed to be manipulated to fit the objectives of the assignment. A shapefile for all the counties of the state of Wisconsin (provided in a previous lab) needed to be joined with the master data set provided by the state. Once the tables were joined, the next step was to add fields to the combined data set. Four new fields were created, one for each of the variables that were to be used for analysis.  Once the four fields were created, they needed to be filled with information that could be used for statistical testing.

     The objectives of this assignment called for Chi-Squared testing to be conducted on each of the four variables. Chi-Squared is a test that is used to compare the observed distribution to the expected distribution of a frequency. In order to complete this test absolute values have to be used. Rates, percentages or proportions are not acceptable to use in this testing.

     The variables needed to be broken up into different classes in order for Chi-Squared testing to be effective. The assignment called for the variables to be broken into four classes based on an equal interval.  After the new classes had been made, the data was then exported to a dBase table. This file type is compatible with IBM SPSS software, which is what will be used for Chi-Squared testing.

Results:

The results from this analysis were very interesting. One would expect there to be a major difference with the concept of "Up-North" and the southern part of the state. The first variable of non-resident bow deer licenses sold is shown below (Figure 2).

Figure 2 Shows the number of non-resident bow
deer licenses sold in 2005 for the state of Wisconsin.

Table 1. The result of running Chi-Squared
testing on the first variable. 

When initially looking at the map, it appears that there is an obvious difference between the two parts of the state. In the northwestern portion of the map there is an obvious cluster of higher amounts of licenses sold. This would make sense because the locations with the highest amounts of licenses sold are also closest to bordering states. The table shown above shows the results of the Chi-Squared testing (Table 1). The test is used based upon a 95% confidence rating. The result of the test show that we fail to reject the null hypothesis. There is not a statistical difference between the northern are southern parts of the states for non-resident bow deer licenses sold. Although, initial predictions based off the map seem to show there is a difference, it was statistically proven that there is no difference.

Table 2. The result of running Chi-Squared
testing on the second variable.

Figure 3 Shows the number of non-resident gun
deer licenses sold in 2005 for the state of Wisconsin.

The next variable the was used was the non-resident gun deer licenses sold. The map to the right shows the distribution of where licenses were sold (Figure 3). When comparing this to figure 2, they are very similar. Many of the areas that were high in bow licenses sold are also high in gun licenses sold. The numbers of licenses sold are higher farther inward from the borders. This map also appears to give the impression that there would be a great difference between the northern and southern parts of the state. The table shown above shows us a different perspective (Table 2). The result of the Chi-Squared test are based on a 95% confidence level. We fail to reject the null hypothesis. There is no difference between the expected results the observed results of licenses sold. 

Table 3. The result of running Chi-Squared
testing on the third variable.

Figure 3 Shows the number of resident gun
deer licenses sold in 2005 for the state of Wisconsin.

The third variable was the resident gun deer licenses sold. The map to the left shows the distribution of resident gun deer licenses sold (Figure 4). This pattern is much different than that of figure 3. The amount of licenses sold seems to correlate to areas of higher population. The counties with the highest amount of licenses sold also have a higher population. The map does not have an apparent split like the first two maps. The table above is the result of the Chi-Squared test (Table 3). The results show that we fail to reject the null hypothesis.  It shows that there is no statistical difference between the expected amounts of licenses to be sold and the observed amount of licenses sold.

Table 4. The result of running Chi-Squared
testing on the fourth variable.

Figure 4 Shows the number of resident bow
deer licenses sold in 2005 for the state of Wisconsin.

The fourth and final variable used was resident bow deer licenses sold. The map to the right shows the distribution of resident deer bow licenses sold (Figure 5). This map is very similar to that of figure 4. Many areas of higher amounts of sales also correlate to the counties with higher populations. There does not seem to be an apparent split of the state. The table above shows the results of the Chi-Squared test   (Table 4). The test was based on a 95% confidence interval. With this variable, we fail to reject the null hypothesis. There is no statistical difference between the expected amounts of licenses to be sold and the observed amount of licenses sold.

Conclusion:

The results of this lab were surprising. Initially, I had thought there would be a difference between the northern part of the state compared to the southern portion. Although the maps do appear to show a difference, there was no statistical difference between the two. It was apparent that the most popular spot for non-residents to hunt deer in the state were in the counties that bordered other states. The map does not show if that reason is because of geographical distance or if there is more opportunity for deer hunting in the border counties. 



Sources:

State of Wisconsin

Kansas and Oklahoma Tornado Shelters

Introduction:

This particular investigation is related to the frequency and sizes of tornadoes in Kansas and Oklahoma. Data has been provided for the location and size of each tornado for the years from 1995-2012. The data is broken up into two different block groups. The first being year 1995-2006 and the second being 2007-2012. The second block group also has the number of tornadoes for each county along with the location and size. There is a debate of whether or not to build tornado shelters in particular locations. Some of the public believe that there is a pattern as to where tornadoes are occurring with a higher frequency, while another group believes just the opposite. The other opinion is that not all places see tornadoes and therefore, it is an unnecessary waste of money to build these shelters. The state believes it is better to build the shelters in order to be on the safe side in case disaster strikes.

Methodology:

There were multiple tools that needed to be used in order to accurately assess whether or not shelters should be built. When modeling the data, it was broken up into the two different block groups. The first statistic to be mapped was the mean center. Each tornado location has an X coordinate and Y coordinate attached to it. In order to find the mean distance, all of these different points needed to be added up. The average from all the X points and Y points make up the two final points that represent the mean center. This shows where the exact middle is from all of the data points provided.

Figure 1 show the locations of Tornadoes in Kansas and Oklahoma for the years of 1995-2006. The locations are shown on the map by the size of the tornado's width in feet. The mean center and weighted mean center are also shown

The next tool used, which is very similar to mean center, is weighted mean center. Instead of only taking the average of the points, the weighted mean center also takes into consideration different frequencies of the grouped data. In other words, the points are weighted by frequencies which will most likely cause a different result than the mean center. 

Figure 2 show the locations of Tornadoes in Kansas and Oklahoma for the years of 2007-2012. The locations are shown on the map by the size of the tornado's width in feet. The mean center and weighted mean center are also shown

These two maps above (Figures 1 and 2) show the locations of tornadoes for the different years as well as the different mean centers and weighted mean centers. When looking at Figure 1, you notice that there is a shift of the weighted mean center to the south. This shows there were more tornadoes to the south of the mean center, rather than to the north of it. Figure 2 had a similar phenomena happen as what was shown in Figure 1. The one difference is the shift was in more of a southeastern direction, rather than straight south. 

Figure 3 show the locations of Tornadoes in Kansas and Oklahoma for the years of 1995-2012. The locations are shown on the map by the size of the tornado's width in feet. The mean center and weighted mean center are also shown

The map above (Figure 3) is the compilation of both Figure 1 and 2. When comparing the two results, the mean center has shifted north from the first block year to the second, but the weighted mean center has continued to move to the south. 

The second set of tools that were used involved standard distance. The standard distance is the spatial equivalent to the standard deviation. The standard distance shows where a particular percentage of tornadoes will occur around a particular point. For this example, 1 standard distance was used. The weighted mean center was the point used as the center maker for the standard distance. Since the weighted mean center was used, the map created was actually the weighted standard distance. You cannot create a weighted standard distance if there is not a weighted mean.

Figure 4 shows the tornado locations from
1995-2006 as well as where the weighted
standard distance is located. 

Figure 5 shows the tornado locations from
1995-2006 as well as where the weighted
standard distance is located. 

 The map to the left (Figure 4) shows the result of creating a weighted standard distance around the mean center. The map to the right (Figure 5) also shows the weighted standard distance. 

When comparing Figures 4 and 5, it is interesting to see the results. The map below (Figure 6) shows both maps combined together. Although Figure 3 had previously shown a shift to the south and east from the mean center to the weighted mean centers, The shift of weighted standard distance is to the northeast. Although this is the opposite of Figure 3, it is reasonable result. It is only comparing the results of the weighted mean center from the first block group to the second. Since it is only using these two points, the shift is understandable. 

Figure 6 is a compilation map of the weighted standard distance maps with the tornado locations overlaid to show where all the tornadoes have occurred from 1995-2012.

The last set of tools used was to find the standard deviation of the number of tornadoes that occurred. The data provided only had occurrences from the year 2007-2012, so the results will not reflect the two block groups that have been used for the duration of this project. The standard deviation shows allows you to see what areas are above or below the average number of tornado occurrences. The map below (Figure 7) shows how the standard deviation varies across the two different states. 

Figure 7 shows the standard deviation for the amount of tornadoes that occured from 2007-2012. The mean of this data set was four tornadoes. The map shows a large portion of tornadoes that occurred above the average were in central Kansas. 

Results:

While looking at the results of all the different, the assignment also called for finding Z scores for three different counties. The counties were Russel, Co, KS, Caddo, Co. OK and Alfalfa, Co. OK. The Z score results for the counties were the following:

Russell: 4.80

Caddo: 2.09

Alfalfa: .23

After looking at the Z score for those three counties, the assignment also wanted to know how many tornadoes will occur 70% and 20% of the time for the next five years. The results are as follows:

There is a 70% chance that one tornado will occur over the next five years in the study area. There is a 20% chance that seven tornadoes will occur over the next five years in the study area. 

Conclusion:

When looking at all of the maps and the numbers associated with them, the findings were interesting. When looking at the probability of tornadoes occuring, according to the Z scores, the number seems very low. This would mean that it would not be a necessity to build shelters. On the other hand, when analyzing the different maps, it seems as if some areas are more prone to tornadoes and it may be a good investment to build storm shelters. 

Overall, it is hard to estimate where shelters should be built due to the large size of the study area. In order to get a more accurate representation of where shelters should be located, multiple maps may need to be made in specific locations within Kansas or Oklahoma.