1 Date: 5/25/2012 To: Chuck Wyatt, DCR, Virginia From: Christos Siderelis Chuck Wyatt with the DCR in Virginia inquired about the classification of state parks having resort type characteristics and, if possible, to identify those park systems. I have attempted to accommodate his request with the AIX database and the following program. Other than associating the results with the revenue and the operating expenditure per visit, which I assume was the point of Chuck s query from the 2012 Outlook Letter, what more can we do with the classification scheme? Let me know.
2 Step 1. I start with inventory of facilities for 50 states for all ij s, where i = 1 n facilities and j = 1 50 states (AIX, 2011, Table 2). I did not include the number of lodges so as not to bias the results. Rather, the number of rooms is the capacity measure of a lodge much like golf course holes are for the golf courses; otherwise, I fear we are double counting. Step 2. I weight the facility inventory amounts with the 2011 operating expenditure (c) to account for the different sizes of the park systems so that the facility variable (y) is now,, and. Step 3. I visually inspect the spearman correlation table and classify the different facilities into three categories trails, amenities, and primitive and note the statistical significances between the pairs with 50 0.05 level (Table 1). Table 1. Spearman Correlation Results (p 0.05) Legend A B A Ski slopes 1.00 B Trails 0.32 1.00 C D E F G H I J K C Cabins & cottages 1.00 D Campsites 0.53 1.00 E Golf course (holes) 0.49 1.00 F Group facility 0.42 0.33 1.00 G Lodge rooms 0.74 0.52 0.61 0.36 1.00 H Marina 0.42 0.48 0.34 0.36 1.00 I Restaurant 0.50 0.27 0.62 0.60 0.45 1.00 J Stables 0.40 0.35 0.43 0.52 0.38 0.44 1.00 K Swimming pool 0.62 0.34 0.57 0.47 0.65 0.28 0.47 0.48 1.00 L L Primitive campsites 1.00 The null hypothesis is H 0 : The facilities are independent. Rejection of the null (p 0.05) implies the facilities are not independent with the correlations in Table 1. Even with the non significance of the group facilities (F) and the developed campsites (D) among several pairs, I elect to group the facility items into three categories (Table 2).
3 Table 2. Categories and Facility Items Trails Amenities Primitive Trails Campsites (developed) Campsites (primitive) Ski slopes Cabins & cottages Group facilities Lodge rooms Golf course holes Marinas Restaurants Swimming pools Stables Step 4. I rank order the weighted values in step 2 from the highest (50) to the lowest (1). Where, is the number of s for i = 1 n facilities. An aside. Why rank order and not standardize the facility measures? The standardization process requires the values of the different facility measures be normally distributed, which is clearly not the case. With the exception of cabins and cottages, the skewness results are above 1.00, which implies non normally distributions (see Table 3). In addition, given the limited data, multivariate statistical methods (e.g., factor analysis) are difficult to defend regarding the statistical assumptions and conditions necessary for this application. I take the low tech approach.
4 Table 3. Descriptive Statistics Facility Mean Standard Deviation Skewness Cabins & cottages 604.8 531.0 0.74 Campsites 12,624.6 10,195.0 1.45 Golf course (holes) 151.2 247.5 2.45 Group facility 32.2 52.0 3.52 Lodge rooms 501.1 858.3 2.09 Marina 22.9 26.5 2.30 Primitive campsites 4,651.1 7,282.7 2.65 Restaurant 17.3 20.5 1.08 Ski slopes 13.5 54.1 4.90 Stables 7.5 11.1 1.84 Swimming pool 21.1 30.6 1.95 Trails 3,066.2 4,484.0 2.67 Step 5. I add the rankings for the k = 1 3 categories to arrive at an overall score (z) for a park system, for the j = 1 m park systems. Step 6. I replace the z scores with z*, 100 for the k = 1 3 categories. This places the scores on a 100 point scale in each category for ease of comparison. I sort the scores from highest to lowest, so that s for k = 1 3 categories and j = 1 50 park systems, and refer to the categories as the potential sources of revenue in Table 4. Although the purposes of the parks amenities are for public use and maybe offered at prices below the marginal costs, they exhibit revenue producing potential to park operators. The park systems having the greatest amenities and hence, resort potential are New York, Oklahoma, Kentucky, Indiana, and so on (Table 4, column 3).
5 Table 4. Potential Revenues Sources and Rankings of Park Systems Trails Amenities Primitive Wisconsin 100.0 New York 100.0 Nebraska 100.0 New Hampshire 96.8 Oklahoma 97.6 Kansas 98.0 New York 95.7 Kentucky 96.0 Wisconsin 95.9 California 90.4 Indiana 95.2 Washington 93.9 Pennsylvania 89.4 Tennessee 94.4 Alaska 91.8 Massachusetts 88.3 Ohio 90.3 Oklahoma 89.8 Alaska 86.2 West Virginia 86.3 New Mexico 87.8 Washington 75.5 Georgia 83.4 Wyoming 85.7 West Virginia 66.0 South Dakota 81.2 California 83.7 Michigan 64.9 Texas 80.2 Illinois 81.6 Connecticut 56.4 Arkansas 79.1 Colorado 79.6 North Dakota 52.1 Alabama 76.1 Texas 77.6 South Dakota 50.0 Florida 75.6 Nevada 75.5 Florida 44.7 Pennsylvania 74.5 Michigan 73.5 Idaho 43.6 Illinois 73.5 Montana 71.4 Minnesota 42.6 Missouri 73.2 Iowa 69.4 Ohio 40.4 California 72.7 Delaware 67.3 Tennessee 38.3 South Carolina 62.7 Maine 65.3 North Carolina 37.2 Mississippi 62.5 Utah 63.3 Virginia 36.2 Kansas 59.5 Kentucky 61.2 Colorado 35.1 Iowa 59.0 North Dakota 59.2 Georgia 34.0 Nebraska 59.0 New York 57.1 Maine 33.0 Minnesota 55.0 West Virginia 55.1 South Carolina 30.9 Virginia 54.4 Alabama 53.1 Nevada 29.8 Washington 53.6 Indiana 51.0 Oklahoma 28.7 Michigan 52.0 South Dakota 49.0 Nebraska 27.7 Delaware 46.4 Minnesota 46.9 Arkansas 26.6 Oregon 44.5 North Carolina 44.9 Vermont 25.5 New Jersey 43.2 Louisiana 42.9 Utah 24.5 Louisiana 42.9 Mississippi 40.8 Missouri 23.4 Massachusetts 41.0 Oregon 38.8 Illinois 22.3 Wyoming 38.9 New Hampshire 36.7 Kentucky 21.3 North Carolina 38.3 Tennessee 34.7 Alabama 19.1 Vermont 36.5 Arizona 32.7 Delaware 18.1 Colorado 33.5 Idaho 30.6 Hawaii 17.0 Utah 32.7 Pennsylvania 28.6 New Jersey 16.0 Idaho 31.6 Connecticut 26.5
6 New Mexico 13.8 Maryland 26.0 New Jersey 24.5 Arizona 12.8 North Dakota 24.9 Arkansas 22.4 Oregon 11.7 New Mexico 23.3 Massachusetts 20.4 Louisiana 10.6 Wisconsin 23.3 Vermont 18.4 Rhode Island 9.6 Rhode Island 23.1 South Carolina 16.3 Mississippi 8.5 Hawaii 20.1 Florida 14.3 Wyoming 7.4 New Hampshire 16.1 Virginia 12.2 Kansas 5.3 Arizona 14.7 Georgia 10.2 Maryland 4.3 Montana 6.4 Ohio 8.2 Iowa 3.2 Nevada 5.4 Missouri 6.1 Texas 2.1 Alaska 3.8 Rhode Island 4.1 Indiana 0.0 Connecticut 1.9 Hawaii 2.0 Montana 0.0 Maine 0.0 Maryland 0.0 Although not statistically significant (P> z 0.05), the associations between the revenue per visit for 2011 and the category ranking suggest that park systems with more amenities relative to their sizes have a higher probability (0.16) of increasing revenue than park systems with fewer amenities (Table 5, row 2). In fact, we are 95% confident that the probability of increased revenue per visit will be between 0.01 and 0.34 as the amount of amenities increases. Table 5. Potential Revenue Source as Predictors of Revenue Per Visit Sources Probability P> z 95% Confidence Interval Trails 0.046 0.635 0.235 0.143 Amenities 0.161 0.080 0.019 0.340 Primitive Campsites 0.084 0.395 0.278 0.109 The revenue source has no significant effect on expenditure per visit for 2011 (Table 6). However, the positive and negative signs on the probability values do indicate the positive or negative influences of the revenue sources on the expenditure per visit. Table 6. Potential Revenue Sources as Predictors of Expenditures Per Visit Sources Probability P> z 95% Confidence interval Trails 0.064 0.513 0.255 0.127 Amenities 0.064 0.458 0.106 0.235 Primitive campsites 0.125 0.228 0.328 0.078