Introduction:

The Northwoods have long been described as an ‘outdoor playground’ where boating and skiing are intensely promoted.  When asked to describe the Northwoods as a region, images of crystal clear lakes surrounded by ancient pines while a lone fisherman is hauling in their early morning catch spring to a person’s mind.  It is these images that give birth to the ‘playground’ while the idyllic lifestyle of camp is advertised to the fullest.  This stereotypical view gives the impression of a slower lifestyle where days are measured by the pots of coffee and the nights by the number of logs on the fire.  When pictured en route, the usual Northwoods advertisement will show a plaid laden individual dipping their paddle blade while the canoe slices silently through the still water and early morning fog.  When winter rolls around, canoes are hung in garages and skis take over as the outdoorsman’s transportation.  These romanticized visions of the Northwoods raised some suspicions regarding the truth behind the so-called outdoor playground of the North.  Using these stereotypes, this analysis aspires to delineate and quantify the boundaries between this silent sport paradise and the rest of the Upper Midwest. 
Unfortunately, this idealized version of the Northwoods cannot be obtained by investigating the distribution of canoe and/or ski shops.  If fact, the spatial patterns of these retail and rental sites are seemingly random when viewed without reference to Michigan’s, Minnesota’s, and Wisconsin’s water resources.   The distribution of canoe and ski shops is no different in the North than it is in the South when water access is granted.  Due to this unforeseen circumstance, the quantification of the Northwoods by way of canoe and/or ski shops has been disproven through regression analysis, geo-spatial cluster analysis, and correlation analysis.

Methods:

The first step in statistically analyzing and delineating a region as ambiguous as the Northwoods with only two dependant variables is to first collect data regarding the locations of all applicable data points.  To do so, www.yellowpages.com was utilized with a search radius of 100 miles to gather all the canoe and/or cross-country ski shops within this boundary of randomly selected cities (Figure 1). 

Chart 1.

Figure 1.

Figure 1. Surveyed City Buffer Zones

After all of the data points were collected, organized via Microsoft Excel™ and joined spatially to county files complete with population data (collected from http://factfinder.census.gov) and county lake information via ArcMap™, analysis could begin.  The first variables to be analyzed were the total number of canoe and/or cross country ski shops in a county.  This is done simply by summarizing the attribute table within ArcMap™ then displaying the results in a choropleth map (Figure 2 & 3).

Figure 2.

Figure 3.

Once the number of canoe and ski shops has been efficiently displayed, true analysis can commence.  For the first step, the total number of canoe/ski shops per county was divided by the counties’ population per one thousand persons.  This formula was chosen to eliminate some of the insignificant digits in the data returned for cartographic purposes.  This map shows the total number of customers per county one canoe/ski shop could potentially serve (Figure 3, Figure 4). 

Figure 4.

Figure 4. Ski Shops per 1,000 Persons

After determining that there is no difference in the number of potential customers served in the North versus the South, more analysis was needed as an attempt to find a link between the canoe and ski shops of the North and their link with the region referred to as ‘The Northwoods’.  To do so, statistical methods were employed. 
Using the coordinates for each canoe shop and the coordinates for each ski shop, in conjunction with the standardized maps of Michigan, Minnesota, Wisconsin, and a computer program known as Geoda, spatial autocorrelation and Moran’s I values for each state was able to be calculated.   Spatial autocorrelation is the correlation of a variable to itself through space.  This means that spatial autocorrelation quantifies Tobler’s First Law of Geography: “everything is related to everything else, but near things are more related than distant things.”  By investigating spatial autocorrelation, it is possible to test the strength of spatial autocorrelation throughout a map.  By applying this process to delineation of the Northwoods, spatial autocorrelation should be able to define a boundary between the Northwoods and regions lying outside of the Northwoods.

Moran’s I is the statistical standard for determining spatial autocorrelation.  When used to interpret the locations of canoe shops and ski shops within the three states of this study, the results determine the amount of clustering based on a single, common variable, which in this case is the canoe or ski shop.   The strength of autocorrelation is based on a range from -1 to 1.  As the resulting product of the Moran’s I calculation approaches 1, the stronger the spatial correlation.  This means that as more canoe or ski shops appear in each county, when viewed county by county, the more clustering is occurring therefore resulting in a higher Moran’s I value.

Geoda is an open source program that, among other things, is extremely proficient in the mapping of spatially autocorrelated data.  The following figures show the maps and Moran’s I figures for the three states in this study.  In each map, the local indicators of spatial autocorrelation (LISA) are shown.  LISA maps spatially relate the degree of spatial autocorrelation.  In other words, LISA maps illustrate the Moran’s I.

Interpreting the LISA maps is slightly different from reading a choropleth map.  In a LISA map there are five categories:  High-High, High-Low, Low-Low, Low-High, and Not Significant.  High-High (in red) designations are areas of high amounts of clustering surrounded by more areas of high clustering.  High-Low (in pink) is areas of high amounts of clustering surrounded by areas of low levels of clustering.  Low-Low (in blue) counties are counties with low amount of clustering surrounded by counties of low clustering.  Low-High (in light blue) are counties with low amounts of clustering surrounded by counties with high amounts of clustering.  Not significant (in white) counties are counties with significance values, as determined by a t-test with a significance level of 95%, of greater than .05.  This means that all counties that show significant amounts clustering or scattering will appear in either a shade of red, pink, blue, or light blue, while those which do not, will appear in white.

Results:

Figure 5 through Figure 11 show the LISA maps and the Moran’s I for each of the states in the study.

Figure 5. Michigan Canoe Shop Autocorrelation and Moran’s I Value

Figure 6. Michigan Ski Shop Autocorrelation and Moran’s I Value

After analyzing the canoe and/or ski shops of Michigan, the Northwoods is not clearly defined.  With a Moran’s I value of .1182 for both canoe and ski shops, the amount of spatial autocorrelation is minimal.  This suggests that where canoe and/or ski shops are located is a function of randomness.  By taking into consideration the unpredictability of human nature and the location of lakes, it is no surprise that canoe and/or ski shops in Michigan have a randomized scattering throughout the state although the Upper Peninsula seems to have an unusually low concentration of canoe and/or ski shops as compared with the mainland.

Figure 7. Minnesota Canoe Shop Autocorrelation and Moran’s I Value

Figure 8. Minnesota Ski Shop Autocorrelation and Moran’s I Value

Minnesota’s canoe shop Moran’s I returned the most favorable results in this attempt to define the Northwoods.  Counties bordering Lake Superior and north of the City of Duluth had the highest amounts of clustering and the remaining counties were counted as not significant when compared to these four counties.  After comparing the clustering of these counties with the percentage of each county that is covered by water, vague patterns emerged.

Figure 9.

Figure 9. Surface Area of County Covered by Water

Since Minnesota was the only state to return a significant Moran’s I for Canoe shop spatial autocorrelation, investigation into the counties with high levels of clustering surrounded by additional counties of high clustering was a necessity.  After comparing the lake cover map and the cluster analysis, the counties in the northern half of Minnesota, on average, have a higher percentage of their total area that is covered by water.  By researching even farther, a world-class canoeing destination, the Boundary Waters Canoe Area Wilderness, is also located in the North-Eastern most counties.  This natural area is sure to have a striking effect on the number of canoe shops and their location within this region of the state.

Figure 10. Wisconsin Canoe Shop Autocorrelation and Moran’s I Value

Figure 11. Wisconsin Ski Shop Autocorrelation and Moran’s I Value

The analysis of Wisconsin returned a Moran’s I of incredibly low values in both the canoe shop clustering and the ski shop clustering.  With a value of .0327 in both categories, there is almost no clustering of canoe and/or ski shops at all.  This is perhaps the most surprising return because northern Wisconsin has been the focal point of the stereotypical ‘Northwoods’.  91.66% of Wisconsin’s counties are deemed insignificant statistically, while the counties with highest percentage of lake cover are shown as Not Significant, and furthermore, only the counties with the lowest amount of clustering appear on the LISA map.

Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate 1 .253a .064 .052 1.870 a. Predictors: (Constant), Perc_Lake, TOTAL_POP, PERC_POV Coefficients Model Unstandardized Coefficients Standardized Coefficients t Sig. B Std. Error Beta 1 Canoe Shops .380 .377   1.008 .315 Total  Pop. 1.552E-6 .000 .155 2.478 .014 Poverty Rate .020 .036 .036 .569 .570 Lake Cover .155 .049 .197 3.145 .002 a. Dependent Variable: Canoe_Count

Table 1. Regression Analysis of Canoe Shops Versus Total Population, Poverty Percent and Lake Cover

Using the only variable to show any sign of delineating the Northwoods was the Canoe Shops, multiple regression was used to test three independent variables against the dependent variable (canoe shops) when testing a hypothesis.  For this analysis, the null hypothesis asserts that there is no difference in the number of canoe shops in the north versus the south in all three states.  The alternative hypothesis therefore maintains that there is a difference in the number of canoe shops in the north versus the south in all three states.  In multiple regression, the independent variables are those variables whose numbers change with no influence from an outside variable.  The dependent variable is the variable whose value is a function of an outside influence.  For example, table 1 expresses that the dependent variable of canoe shops, when viewed as a function of Lake Cover, has a significance level of .002.  This, statistically speaking, states that there is a 99.8% chance of a type I error not occurring.  Type one errors are errors in which a true null hypothesis is rejected.  However, this is not the most definitive independent variable of the three selected.  By looking at the column labeled ‘Beta’ we can see how each independent variable affects the dependent variable.  As the beta weights are shown, Lake Cover is the independent variable that most affects the dependent variable.  This means that as the Lake Cover of a county increases by any given amount, the dependent variable, Canoe Shops, will increase by .197 times the amount as well. Unfortunately, this regression model gives us an R2 value of only .064.  The R2 value is the Coefficient of Determination.  This coefficient explains how well, or how poorly, the independent variable(s) explain the dependant variable. This means that although the beta weights show a change, the R2 value is so low as to prove that there is no correlation between any of the three independent variables and the dependent.

The independent variable ‘population’ states that there is a 99.98% of a type I error not occurring.  With both of these independent variables returning significance values this positive, the only choice statistically is to fail to reject the null hypothesis therefore stating there is no difference in the number of canoe shops in the north versus the south in all three states. 

Conclusion:

The Northwoods may be seen as the outdoor playground filled with canoeing and cross-country skiing, but the statistical analysis proves otherwise.  There is simply not enough difference in the distribution of the canoe and/or ski shops in any of the three states in this study to formally defend that the Northwoods is a region that can be characterized by its above average amount of canoe and/or ski shops.  This is not to say that an above average amount of these activities doesn’t take place, but the actual retail or rental opportunities simply do not vary enough between the southern and northern regions of the states to be able to quantify the Northwoods as its own unique region within the larger area known as “the Midwest”.

References:

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McGrew, J. Chapman Jr. and Charles B. Monroe.  An Introduction to Statistical Problem
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Weichelt, Ryan. "Correlation." Lecture, Quantitative Techniques in Geography from University of Wisconsin-Eau Claire, Eau Claire, Wi, November 3, 2009.

Weichelt, Ryan. "Hypothesis Testing." Lecture, Quantitative Techniques in Geography from University of Wisconsin-Eau Claire, Eau Claire, Wi, September 29, 2009.

Weichelt, Ryan. "Regression Analysis." Lecture, Quantitative Techniques in Geography from University of Wisconsin-Eau Claire, Eau Claire, Wi, November 12, 2009.

Weichelt, Ryan. "Spatial Autocorrelation." Lecture, Quantitative Techniques in Geography from University of Wisconsin-Eau Claire, Eau Claire, Wi, November 10, 2009.

"Yellow Pages Local Directory - YELLOWPAGES.COM." Yellow Pages Local Directory - YELLOWPAGES.COM. http://www.yellowpages.com (accessed November 1, 2009).