Evaluating Methods for Counting Aircraft Operations at Non-Towered Airports (2015)

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A P P E N D I X A Appendix A provides information for those readers of the report that desire more details on the work performed to support the findings in Chapter 3, Methods for Estimating Annual Airport Operations, on OPBA and extrapolation from a sample count. OPBA Method to Estimate Annual Airport Operations The objective of this research task was to determine if there was a consistent number(s) of OPBA that occur at small, tow- ered airports and if it varied by climate or population, and if having a flight school affected this number. Since there is no valid source for operations data at non-towered airports, data on small, towered airports were used as a proxy for non- towered airports. Chapter 2 includes a description of the STAD developed for this research project. Initial analysis revealed that an extremely large range of OPBAs exist for the STAD airports overall and by region, and practical use of any aver- ages would not produce confident results. With this in mind, the research team attempted to actually model total OPBA through regression analysis to determine if an equation could be produced that offered better results. To do this, the research team modeled total OPBA at non-towered airports from operations data at small, towered airports using infor- mation about the population, NOAA climate region, and flight schools. The sources for the data on the STAD airports used in this analysis were the FAA TAF and the FAA OPSNET databases from 2006 to 2010 (see Chapter 2 on dataset sources). To more accurately describe the operations at a non-towered airport, total general aviation operations at small, towered airports were used in the analysis rather than total operations. Table A-1 identifies the name of each variable, its descrip- tion, and its sources used in this analysis. This table may be referred to while reading the analysis that follows. Table A-2 summarizes the results for the analysis of the OPBA for the 205 STAD airports that were used in this study. These tables are repeated in this appendix for convenience of the reader. The 95% confidence intervals for the OPBAs and the OPBA ranges shown in Table A-2 highlight the wide range of OPBA within the STAD. Averaging the Data for Years 2006–2010 For each airport, data from each of the five years from 2006 to 2010 were collected and stored in the STAD. The research team analyzed the data to see if an average of the five years of data for each airport could be used instead of the data from each year. An average of the five years of air- port data allows for statistically accurate analysis of the 205 airports in the dataset, and simplifies the statistical analyses and outputs. To test the use of averages, the research team analyzed the operations data to see if there was a statistically significant difference between the GA OPBA aircraft data for each of the five years. A one-way analysis of variance (ANOVA) test was performed to determine if the Total GA OPBA (Total GA OPBA) have a statistically significant difference by year. The ANOVA test is used when three or more groups are stud- ied. The ANOVA analyzes the variances and determines if there is a significant difference between the true means of the groups. In this test, a p-value (or probability number) is determined, which is a numerical way of describing the significance of results. Using the data and a 95% confidence level (or an alpha of 0.05), the research team could not show a statistically significant difference between the true means for Total GA OPBA for the years 2006–2010. While there is no statistically significant difference, there is an observable difference in the averages of the data. The ANOVA deter- mines if there is a statistically significant difference in the true means for each group. The presence of a p-value greater than or equal to 0.05 indicates that the true means of each of the five years are believed to be the same, as there is not Supporting Statistical Information for Chapter 3 A-1

A-2 to determine the effect that each of the variables in Table A-1 has on AvgOPBA in the STAD. The analysis includes: A. Full model and reduced model using AvgOPBA. B. Transformation of AvgOPBA and average based aircraft (AvgBA). C. Full model and reduced model using transformed data. D. Full model and reduced model using operations (OPS). E. Overview of models and conclusions. A full model regression uses every variable, with no vari- ables removed from the model. A reduced model regression removes variables from the full model one at a time until the remaining variables are all statistically significant at the 0.05 level. The reduced model is used to filter out uninforma- tive variables and, thereby, simplify the model. The reduced model may explain nearly as much as the complete model, but with fewer pieces of information. enough evidence to show that the true means are different. In this case, the p-value was 0.624; therefore, the research team concludes that the Total GA OPBA is not different for each year and the use of the 5-year average was statistically acceptable. As a result, the Total GA OPBA ratios for the five years for each airport were averaged to obtain the Average GA OPBA (AvgOPBA) for each of the Small Non-Towered Airports. AvgOPBA was then used in the following regression analysis. Analysis Analysis of regression models was performed to determine if there is a consistent number(s) of OPBA that occur at small, towered airports (that could then be applied to non-towered airports). The regression analysis also considered if the OPBA varied by climate or population and if having a flight school affected this number. Regression analysis of the data was used Variable Description Source AvgOPBA Average general aviation operations per based aircraft for each airport 2006-2010. OPBA calculated from OPSNET and TAF data Enp Enplanements or revenue passenger boardings TAF OPS Average general aviation operations for each airport 2006-2010 OPSNET Data AvgPop The average population for the years 2006- 2010 for the city or town surrounding the airport U.S. Census. United States Census Bureau. Population Estimates 2000-2009 http://www.census.gov/popest/data/cities/totals/200 9/SUB-EST2009-4.html United States Census Bureau. 2010 Population Finder http://www.census.gov/popfinder/index.php Pop Scaled The average population scaled by 10,000 for the city or town surrounding the airport for the years 2006-2010 AvgPop/10,000 NFS The number of flight schools at the airport AOPA (Training and Safety) http://www.aopa.org/learntofly/school/index.cfm FS Y/N The presence of a flight school. (1=Yes and 0=No) AOPA (Training and Safety) http://www.aopa.org/learntofly/school/index.cfm CTHrs Yearly hours of control tower operations FAA Airport Facility Directory. (March 2013 data as no historical data was available) C 1 for Central; 0 for other regions Definition from NOAA and data from OPSNET EN 1 for East North Central; 0 for other regions Definition from NOAA and data from OPSNET NE 1 for Northeast; 0 for other regions Definition from NOAA and data from OPSNET NW 1 for Northwest; 0 for other regions Definition from NOAA and data from OPSNET S 1 for South; 0 for other regions Definition from NOAA and data from OPSNET SE 1 for Southeast; 0 for other regions Definition from NOAA and data from OPSNET SW 1 for Southwest; 0 for other regions Definition from NOAA and data from OPSNET CM 1 for Commercial airport; 0 for GA or RL National Plan of Integrated Airport Systems RL 1 for Reliever airport; 0 for CM or GA National Plan of Integrated Airport Systems Notes: West is not defined here, but it occurs when all other regions are set to 0. GA is not defined here, but it occurs when CM and RL are set to 0. North West Central is not included because there are no airports from this region that meet the selection criteria for airports to be included in the dataset. Prepared by: Purdue University Table A-1. Variables and descriptions of sources.

A-3 Scaled), Yearly Hours of Control Tower Operations (CTHrs), Central (C), East North Central (EN), Northeast (NE), South (S), Southeast (SE), Southwest (SW), Commercial airport (CM), Reliever airport (RL) (see Table A-1 for descriptions of these variables). Table A-3 provides supplemental statis- tics for the analysis. The regression equation for the full model using AvgOPBA is as follows: = − + + + + − − − − + − AvgOPBA 347 1.21 AvgBA 24 NFS 77 FS Y/N 0.603 Pop Scaled 0.0534 CTHrs 180 C 185 EN 188 NE 168 NW 44 S 27 SE +129 SW + 85 CM + 201 RL The regression model is statistically significant at the 95% level (alpha = 0.05). The R-Squared (adjusted) equals 27.6%. Adjusted R-Squared [R-Sq(adj)] is the proportion of the total variation of outcomes explained by the model, taking into consideration the number of variables in the model. R-Sq(adj) measures how well the independent variables [in this case based aircraft, flight schools, population, climate, and airport category (commercial, reliever, or GA)] explain the variation of the dependent variable (in this case the AvgOPBA). Residual NOAA Climate region Number of airports AvgBA per region Avg Ops per region AvgPop OPBA mean OPBA OPBA range median 95% Confidence Interval for the median Low High Alaska 1 965.8 152,018 283,382 157.40 157.40 NA NA NA Central 33 141.01 49,187 162,441 429.54 360.13 (298.02, 426.85) 201.75 1,015.54 E. N. Central 13 188.52 67,823 260,933 473.92 462.29 (266.65, 550.52) 177.42 798.85 Hawaii 1 22.80 104,224 13,689 4,771.68 4771.6 NA NA NA Northeast 28 187.06 72,081 353,687 432.95 408.37 (351.95, 504.20) 225.91 828.52 Northwest 8 202.90 80,577 224,704 382.95 779.38 (264.80, 453.03) 219.87 779.38 South 41 154.19 65,312 352,947 597.89 338.00 (302.52, 522.53) 132.17 2,481.89 Southeast 38 212.66 95,457 171,804 561.74 439.42 (338.62, 572.66) 190.89 2,491.54 Southwest 15 394.01 16,802 391,318 487.23 396.66 (336.31, 646.39) 192.52 819.86 West 27 381.98 124,391 388,546 370.13 326.30 (282.28, 362.85) 139.69 875.89 W.N. Central 0 NA NA NA NA NA NA NA NA Overall 205 222.35 85,890 394,118 501.68 377.78 (350.30, 412.86) 132.17 4,471.68 Legend: Avg = Average BA = Based Aircraft Ops = Operations OPBA = Operations per Based Aircraft NA = Not Applicable Prepared by: Purdue University Table A-2. Summary of small towered airport data by region used in this study. Each regression was also checked to determine if it met the necessary assumptions for statistical validity. For regression and ANOVA to be valid, the following statistical standards, or assumptions, must be met: 1. The sample is representative of the population. 2. The independent variables are linearly independent (are not good predictors of each other), and are measured with no error. 3. There is a constant variance (the variance of y is the same for all values of x; and there is no pattern in the variance). 4. Linearity exists (mean response y has a straight line rela- tionship with x). 5. Normality exists (for any fixed value of x the response y varies according to a normal distribution). 6. Independence exists (y variable responses are indepen- dent of each other). A. Full model and reduced model using AvgOPBA. First, the full model regression was created using AvgOPBA as the variable to be estimated by the regression equation. The vari- ables used in the full model regression analysis are: Avg OPBA, AvgBA, Number of Flight Schools at the airport (NFS), Flight School Yes/No (FS Y/N), Based Aircraft (BA), Population (Pop

A-4 p value=0.000 Predictor Coef SECoef t p Constant 346.5 200.7 1.73 0.086 AvBA -1.2134 0.2559 -4.74 0.000 NFS 23.99 14.02 1.71 0.089 FSY/N 77.5 105.1 0.74 0.462 Pop Scaled 0.6027 0.1335 4.51 0.000 CTHrs 0.05338 0.03076 1.74 0.084 C -179.5 112.5 -1.59 0.112 EN -184.8 132.5 -1.39 0.165 NE -188.3 112.3 -1.68 0.095 NW -168.1 153.5 -1.09 0.275 S 43.7 103.4 0.42 0.673 SE -27.3 103.2 -0.26 0.791 SW 129.4 120.9 1.07 0.286 CM 85.5 100.5 0.85 0.396 RL 201.09 68.79 2.92 0.004 Prepared by: Purdue University Table A-3. Supplemental statistics showing significance of each variable in the full model using AvgOPBA. 200010000-1000 99.9 99 90 50 10 1 0.1 Residual Pe rc en t 2400180012006000 2000 1000 0 -1000 Fitted Value R es id ua l 2000160012008004000-400 80 60 40 20 0 Residual Fr eq ue nc y 200180160140120100806040201 2000 1000 0 -1000 Observation Order R es id ua l Normal Probability Plot Versus Fits Histogram Versus Order Residual Plots for AvgOPBA Prepared by: Purdue University Figure A-1. Residual plots for AvgOPBA for full model. plots are used by statisticians to assess if a regression model is a good fit to the data, and to examine the underlying statistical assumptions required for regression. The analysis of the residual plots (see Figure A-1) indicated that regression is invalid due to the violation of two required statistical assumptions described above that must be met in order to use regression. The two assumptions are constant variance (right half of the residual plots in Figure A-1) and non-normal residuals (left half of the residual plots in Fig- ure A-1). Ideally, the normal probability plot will have red dots tracing over the blue line; and the top right graph (Fitted Value vs. Residual) will appear to be scattered in a random pat-

A-5 dots tracing over the blue line; and the top right graph (Fitted Value vs. Residual) will appear to be scattered in random pat- tern, or sometimes thought of as birdshot. In this case, the red dots do not follow the line closely enough to be considered normally distributed (and the histogram below it reinforces this view). The variance is not believed to be constant as the red dots in the top right graph are scattered in a cone pattern, so that the variance moves from small to larger as the fitted value increases. B. Transformation of AvgOPBA and AvgBA. As described in Section A, the violation of two statistical assump- tions for regression to be used (the existence of non-constant variance and non-normally distributed residuals) resulted in invalid regression results using AvgOPBA for either the full or reduced model regression. To try to understand the non-constant variance, the variable with the most influence in the models was studied further. AvgBA is by far the largest contributor to the AvgOPBA model presented in Part A. The fitted line plot in Figure A-3 shows that there is a non-linear relationship between AvgOPBA and AvgBA. The data (red dots) appear to form a curve; therefore, the reasonable con- clusion is that there is a non-linear relationship. This non- linear relationship between AvgBA and AvgOPBA appears to explain the non-constant variance and the non-normal resid- uals seen in the full and reduced model regression described under Part A (Figure A-1 and A-2). In Figure A-3, the R-Sq(adj) of 14.3% means that 14.3% of the variation in AvgOPBA is explained by the variation of AvgBA. This R-Sq(adj) is typically considered to be too low for practical use in this type of application, in addition to being invalid due to not meeting the required assumptions. Comparison of this R-Sq(adj) of 14.3% to the R-Sq(adj) of approximately 27% for the models in Part A indicate that AvgBA is contributing about half of the explanation of variation. Based on algebraic principles, it is possible to transform data to create a linear relationship. The linear relationship is necessary in order to meet the assumptions for statisti- cal validity of the model, as described under the full and tern, or sometimes thought of as birdshot. In this case, the red dots do not follow the line closely enough to be considered normally distributed (and the histogram below it reinforces this view). The variance is not believed to be constant as the red dots in the top right graph are scattered in a cone pattern, so that the variance moves from small to larger as the fitted value for AvgOPBA increases. Next, the reduced model regression was analyzed using AvgOPBA. The variables used in the reduced model regres- sion analysis are: AvgOPBA, AvgBA, NFS, Pop scaled, S, SW, RL. (See Table A-1 for descriptions of these variables.) (Note: A reduced model regression removes variables from the full model one at a time until the remaining variables were all sta- tistically significant at 0.05.) Table A-4 provides supplemental statistics for the analysis. The regression equation for the Reduced Model using AvgOPBA is as follows: − + + + + + AvgOPBA = 572 .1.11 AvgBA 30.9 NFS 0.613 Pop scaled 146 S 214 SW 177 RL The regression is statistically significant at the 95% level (alpha = 0.05). The R-Sq(adj) equals 27.5%. R-Sq(adj) is the proportion of the total variation of outcomes explained by the model, taking into consideration the number of variables in the model. R-Sq(adj) measures how well the independent variables (in this case based aircraft, flight schools, population, climate, and airport category) explain the variation of the dependent variable (in this case, AvgOPBA). Residual Plots are used by statisticians to assess if a regression model is a good fit to the data, and to examine the underlying statistical assumptions required for regression. The analysis of the residual plots (see Figure A-2) indicated that regression is invalid due to the violation of two required statistical assumptions described earlier that must be met in order to use regression. The two assumptions are constant variance (right half of the residual plots in Figure A-2) and non-normal residuals (left half of the residual plots in Fig- ure A-2). Ideally, the normal probability plot will have red p value=0.000 Predictor Coef SECoef t p Constant 571.83 64.91 8.81 0.000 AvgBA -1.1128 0.2308 -4.82 0.000 NFS 30.92 13.10 2.36 0.019 Pop Scaled 0.6131 0.1327 4.62 0.000 S 146.33 66.39 2.20 0.029 SW 214.5 105.0 2.04 0.042 RL 176.56 62.44 2.83 0.005 Prepared by: Purdue University Table A-4. Supplemental statistics showing significance of each variable in the reduced model using AvgOPBA.

A-6 200010000-1000 99.9 99 90 50 10 1 0.1 Residual Pe rc en t 2400180012006000 2000 1000 0 -1000 Fitted Value R es id ua l 2000160012008004000-400 80 60 40 20 0 Residual Fr eq ue nc y 200180160140120100806040201 2000 1000 0 -1000 Observation Order R es id ua l Normal Probability Plot Versus Fits Histogram Versus Order Residual Plots for AvgOPBA Prepared by: Purdue University Figure A-2. Residual plots for AvgOPBA for reduced model. 10008006004002000 3000 2000 1000 0 -1000 Avg BA Av g O PB A S 395.965 R-Sq 14.7% R-Sq(adj) 14.3% Regression 95% CI 95% PI Fitted Line Plot AvgOPBA = 775.7 - 0.9967 AvgBA Prepared by: Purdue University Figure A-3. Fitted line plot for AvgOPBA vs. AvgBA.

A-7 The full model regression equation using log10AvgOPBA and log10AvgBA is as follows: log10AvgOPBA 3.95 0.681 log10AvgBA 0.000215 Pop Scaled 0.0246 NFS 0.0206 FS Y/N 0.000036 CTHrs 0.153 C 0.0921 EN 0.0716 NE 0.0421 NW 0.0704 S + 0.0079 SE 0.118 SW 0.0652 CM 0.0176 RL = − + + + + − − − − − + − − The regression is statistically significant at the 95% level (alpha equals 0.05). The R-Sq(adj) equals 51%. (Note: The adjusted R-Squared is the proportion of the total variation of outcomes explained by the model taking into consideration the number of variables in the model.) The analysis of the transformed data in this full model regres- sion analysis is valid based on the residual plots in Figure A-6 along with its ability to meet the other regression assumptions. Figure A-6 is much closer to the ideal residual plot than any of those in Section A. Next, the reduced model using log10AvgOPBA and log10AvgBA was analyzed. The variables used in the reduced model regression analysis are log10AvgOPBA, log10AvgBA, Pop Scaled, NFS, C, SE and SW. (See Table A-1 for descrip- tions of these variables. Note: A reduced model regression removes variables from the full model one at a time until the remaining variables all were statistically significant at alpha equals 0.05.) Table A-6 provides supplemental statistics for the analysis. reduced model regression discussion. To transform data, a mathematical operation is performed on each data point. The regression analyses are performed using the trans- formed data. Several possible transformations were ana- lyzed for this research, and the transformation that best met the required statistical assumptions was selected for further study. The AvgBA was transformed to log10AvgBA (for the log base 10 of AvgBA). The AvgOPBA was transformed to log10AvgOPBA (for the log base 10 of AvgOPBA). The fit- ted line plot in Figure A-4 shows a regression of the trans- formed data. The fitted line plot in Figure A-4 for log10AvgBA and log10AvgOPBA reveals a linear relationship with an R-sq(adj) of 35.8% and statistical significance at alpha equals 0.05. This is an improvement over the non-transformed model with a R-Sq(adj) of 14.3%. Analysis of the transformed data using regression and the ANOVA table indicates that it is valid (as may be interpreted from the residual plots in Figure A-5) for use in regression. Therefore, the next step is to use the transformed data to build models using the other variables. Figure A-5 is much closer to the ideal residual plot than any in Part A. C. Full model and reduced model using transformed data. Based on the findings in Part B, the full model regression using log10AvgOPBA and log10BA was performed. The vari- ables used in the full model regression analysis are as follows: log10AvgOPBA, log10AvgBA, Pop Scaled, NFS, FS Y/N, CTHrs, C, EN, NE, NW, S, SE, SW, CM, RL. (See Table A-1 for descrip- tions of these variables. Note: A full model regression uses every variable, with no variables removed from the model.) Table A-5 provides supplemental statistics for the analysis. 3.02.52.01.51.0 3.6 3.4 3.2 3.0 2.8 2.6 2.4 2.2 2.0 log10BA lo g1 0 O PB A S 0.187850 R-Sq 36.1% R-Sq(adj) 35.8% Regression 95% CI 95% PI Fitted Line Plot log10OPBA = 3.619 - 0.4256 log10BA Prepared by: Purdue University Figure A-4. Fitted line plot for Log10AvgOPBA vs. Log10AvgBA.

A-8 0.500.250.00-0.25-0.50 99.9 99 90 50 10 1 0.1 Residual Pe rc en t 3.23.02.82.62.4 0.50 0.25 0.00 -0.25 -0.50 Fitted Value R es id ua l 0.450.300.150.00-0.15-0.30-0.45 24 18 12 6 0 Residual Fr eq ue nc y 200180160140120100806040201 0.50 0.25 0.00 -0.25 -0.50 Observation Order R es id ua l Normal Probability Plot Versus Fits Histogram Versus Order Residual Plots for log10OPBA Prepared by: Purdue University Figure A-5. Residual plots of the transformed data. p value=0.000 Predictor Coef SE Coef t p Constant 3.9460 0.1579 24.99 0.000 log10 BA -0.68147 0.05966 -11.42 0.000 Pop Scaled 0.00021468 0.00006039 3.55 0.000 NFS 0.024623 0.006093 4.04 0.000 FS Y/N 0.02058 0.04745 0.43 0.665 CTHrs 0.00003573 0.00001369 2.61 0.010 C -0.15321 0.05006 -3.06 0.003 EN -0.09209 0.05860 -1.57 0.118 NE -0.07158 0.0490 -1.46 0.146 NW -0.04212 0.0685 -0.61 0.540 S -0.07036 0.04611 -1.53 0.129 SE 0.00788 0.04492 0.18 0.861 SW 0.11793 0.05444 2.17 0.032 CM -0.06518 0.04750 1.37 0.172 RL -0.01763 0.03369 -0.52 0.601 Prepared by: Purdue University Table A-5. Supplemental statistics showing significance of each variable in the full model using log10AvgOPBA and log10BA. The regression equation for the Reduced Model using log10AvgOPBA and log10AvgBA is as follows: = − + + − + + log10AvgOPBA 3.94 0.621 log10AvgBA 0.000232 Pop scaled 0.0279 NFS 0.0797 C 0.0631 SE 0.169 SW The regression is statistically significant at the 95% level (alpha equals 0.05). The R-Sq(adj) equals 50.4%. (Note: The adjusted R-Squared is the proportion of the total variation of outcomes explained by the model taking into consideration the number of variables in the model.) The analysis of the transformed data using a reduced model regression are valid based on the residual plots in

A-9 of annual operations, and therefore, it may not provide use- ful estimates in a practical application. If only approximately 50% of the variation of the AvgOPBA is explained by the vari- ables in the equation (i.e., flight schools, population, climate, and airport category), then large variations from actual to estimated operations are likely to occur. Therefore, use of this model is not recommended. Nevertheless, examples using the reduced equation are explored below. REDUCED MODEL EXAMPLES Use of the reduced equation is explored in the following five examples. Please notice that the OPBAs estimated using the Figure A-7, along with its ability to meet the other regression assumptions. The reduced model has a very slight reduction in R-Sq(adj) than the full model (50.4% compared to 51%). However, the reduced model is preferable to the full model because it uses only six variables, while the full model uses 14 variables. Practi- cally speaking, to use this reduced model equation to estimate the OPBA, the only data a person needs are the number of based aircraft, the population (divided by 10,000) for the city or town surrounding the airport, the number of flight schools at the airport, and the NOAA region for the airport. However, this equation only accounts for approximately 50% of the behavior 0.250.00-0.25-0.50 99.9 99 90 50 10 1 0.1 Residual Pe rc en t 3.53.02.5 0.50 0.25 0.00 -0.25 -0.50 Fitted Value R es id ua l 0.450.300.150.00-0.15-0.30-0.45 30 20 10 0 Residual Fr eq ue nc y 200180160140120100806040201 0.50 0.25 0.00 -0.25 -0.50 Observation Order R es id ua l Normal Probability Plot Versus Fits Histogram Versus Order Residual Plots for log10OPBA Prepared by: Purdue University 0.50 Figure A-6. Residual plots for Log10AvgOPBA for full model. Table A-6. Supplemental statistics showing significance of each variable in the reduced model using log10AvgOPBA and log10BA. p value=0.000 Predictor Coef SECoef t p Constant 3.94252 0.09797 40.24 0.000 log10BA -0.62070 0.04791 -12.96 0.000 Pop Scaled 0.00023176 0.00005914 3.92 0.000 NFS 0.027871 0.005834 4.78 0.000 C -0.07966 0.03351 -2.38 0.018 SE 0.06305 0.03126 2.02 0.045 SW 0.16905 0.04649 3.64 0.000 Prepared by: Purdue University

A-10 log10AvgOPBA = 3.94 - 0.621 log10(10) + 0.000232 (20) + 0.0279 (1) - 0.0797 (0) + 0.0631 (0) + 0.169 (0). Solving this equation, the AvgOPBA for this airport would be 2247. Since the airport has 10 based aircraft, the estimated annual operations using this equation would be 22,470. Example 4. Consider a fictional airport in the South NOAA region with 10 based aircraft in a city of 50,000 people that has no flight schools. In this case BA = 10, Pop Scaled = 5, NFS = 0, C = 0, SE = 0, and SW = 0. log10AvgOPBA = 3.94 - 0.621 log10(10) + 0.000232 (5) + 0.0279 (0) - 0.0797 (0) + 0.0631 (0) + 0.169 (0). Solving this equation, the AvgOPBA for this airport would be 2090. Since the airport has 10 based aircraft, the estimated annual operations using this equation would be 20,900. Example 5. Consider a fictional airport in the Northeast NOAA region with 300 based aircraft in a city of 200,000 people that has one flight school. In this case BA = 300, Pop Scaled = 20, NFS = 1, C = 0, SE = 0, and SW = 0. log10AvgOPBA = 3.94 - 0.621 log10(300) + 0.000232 (20) + 0.0279 (1) - 0.0797 (0) + 0.0631 (0) + 0.169 (0). Solving this equation, the AvgOPBA for this airport would be 272. Since the airport has 300 based aircraft, the estimated annual operations using this equation would be 81,600. equations are not consistent with each other. In addition, the equa- tion explains only 50% of the variation seen in the data, and it was developed using small towered airport operations data that may or may not represent non-towered airport operations counts. Example 1. Consider a fictional airport in the southwest NOAA region with 100 based aircraft in a city of 100,000 people that has two flight schools. In this case BA = 100, Pop Scaled = 10, NFS = 2, C = 0, SE = 0, and SW = 1. log10AvgOPBA = 3.94 - 0.621 log10(100) + 0.000232 (10) + 0.0279 (2) - 0.0797 (0) + 0.0631 (0) + 0.169 (1). Solving this equation, the AvgOPBA for this airport would be 841. Since the airport has 100 based aircraft, the estimated annual operations using this equation would be 84,100. Example 2. Consider a fictional airport in the Central NOAA region with 10 based aircraft in a city of 20,000 people that has one flight school. In this case BA = 10, Pop Scaled = 2, NFS = 1, C = 1, SE = 0, and SW = 0. log10AvgOPBA = 3.94 - 0.621 log10(10) + 0.000232 (2) + 0.0279 (1) - 0.0797 (1) + 0.0631 (0) + 0.169 (0). Solving this equation, the AvgOPBA for this airport would be 1852. Since the airport has 10 based aircraft, the estimated annual operations using this equation would be 18,520. Example 3. Consider a fictional airport in the Northeast NOAA region with 10 based aircraft in a city of 200,000 people that has one flight school. In this case BA = 10, Pop Scaled = 20, NFS = 1, C = 0, SE = 0, and SW = 0. 0.500.250.00-0.25-0.50 99.9 99 90 50 10 1 0.1 Residual Pe rc en t 3.53.02.5 0.50 0.25 0.00 -0.25 -0.50 Fitted Value R es id ua l Normal Probability Plot Versus Fits 0.450.300.150.00-0.15-0.30-0.45 30 20 10 0 Residual Fr eq ue nc y Histogram 200180160140120100806040201 0.50 0.25 0.00 -0.25 -0.50 Observation Order R es id ua l Versus Order Residual Plots for log10OPBA Prepared by: Purdue University Figure A-7. Residual plots for Log10AvgOPBA for reduced model.

A-11 able (in this case the OPS). As stated before, residual plots are used by statisticians to assess if a regression model is a good fit to its data, and to examine the underlying statistical assumptions required for regression. The analysis of the residual plots (see Figure A-8) indicated that regression is invalid due to the violation of two required statistical assumptions described above that must be met in order to use regression. The two assumptions are constant variance (right half of the residual plots in Figure A-8) and non-normal residuals (left half of the residual plots in Fig- ure A-8). Ideally, the normal probability plot will have red dots tracing over the blue line; and the top right graph (Fitted Value vs. Residual) will appear to be scattered in random pattern, or sometimes thought of as birdshot. In this case, the red dots do not follow the line closely enough to be considered normally distributed (and the histogram below it reinforces this view). Even if there is disagreement with how close is close enough for normality of residuals, the variance of the residuals does not appear to be constant. The variance of the residuals is not believed to be constant as the red dots in the top right graph are scattered in a wide cone pattern, so that the variance moves from small to larger as the fitted value increases. Next, the reduced model using OPS was performed. The variables used in the reduced model regression analysis are OPS, AvgBA, NFS, SW, Pop Scaled and SE. (See Table A-1 for descriptions of these variables. Note: A reduced model regression removes variables from the full model one at a time until the remaining variables all were statistically signifi- cant at alpha equals 0.05.) Table A-8 provides supplemental statistics for the analysis. The regression equation for the Reduced Model using OPS is as follows: = + + OPS 16535 +199 AvgBA + 5174 NFS 44.1 OPS Scaled +14880 SE 52389 SW D. Full model and reduced model using OPS. Because using AvgOPBA did not prove to be a relatively accurate way to estimate operations, the research team chose to explore a different approach. While the research problem was to deter- mine if there was a consistent number of OPBA that could be used to estimate an airport’s annual OPS, the ultimate goal is to estimate the annual OPS, not the OPBA. Therefore, analysis of a regression model for estimating OPS rather than OPBA was performed. Previous research (GRA, Inc. 2001) has shown that statisti- cal models of operations may be more descriptive than mod- els of operations per based aircraft. In this analysis, full and reduced regression models using OPS were analyzed using the same variables as described in Table A-1. The variables used in the full model regression analysis are OPS, AvgBA, NFS, FS Y/N, Pop scaled, CTHrs, C, EN, NE, NW, S, SE, SW, CM, and RL. (See Table A-1 for descriptions of these variables.) Table A-7 provides supplemental statistics for the analysis. The full model regression equation using OPS is as follows: = + − − − − − OPS 8321 +185 AvgBA + 5185 NFS 1315 FS Y/N + 43.3 Pop Scaled + 3.39 CTHrs 19462 C 11778 EN 9125 NE + 3418 NW 9397 S + 5062 SE + 45472 SW 2670 CM + 3353 RL The regression is statistically significant at the 95% level (alpha equals 0.05). The R-Sq(adj) equals 64.6%. While this is the best adjusted R-Sq yet, the equation still only explains approximately 64% of the variation in operations. R-Sq(adj) is the proportion of the total variation of outcomes explained by the model taking into consideration the number of vari- ables in the model. R-Sq(adj) measures how well the inde- pendent variables (in this case flight schools, based aircraft, control tower hours of operation, population, climate, and airport category) explain the variation of the dependent vari- p value=0.000 Predictor Coef SECoef t p Constant 8321 19858 0.42 0.676 AvgBA 185.46 25.32 7.32 0.000 NFS 5185 1387 3.74 0.000 FSY/N 1315 10395 0.13 0.899 Pop Scaled 43.29 13.21 3.28 0.001 CTHrs 3.391 3.043 1.11 0.267 C -19462 11135 -1.75 0.082 EN -11778 13108 -0.90 0.370 NE -9125 11106 -0.82 0.412 NW 3418 15189 0.23 0.822 S -9397 10235 -0.92 0.360 SE 5062 10207 0.50 0.621 SW 45472 11966 3.80 0.000 CM -2670 9939 -0.27 0.788 RL 3353 6805 0.49 0.623 Prepared by: Purdue University Table A-7. Supplemental statistics showing significance of each variable in the full model using OPS (operations).

A-12 statistical assumptions described above that must be met in order to use regression. The two assumptions are constant variance (right half of the residual plots in Figure A-9) and non-normal residuals (left half of the residual plots in Fig- ure A-9). Ideally, the normal probability plot will have red dots tracing over the blue line and the top right graph (Fitted Value vs. Residual) will appear to be scattered in random pattern, or sometimes thought of as birdshot. In this case, the red dots do not follow the line closely enough to be considered normally distributed (and the histogram below it reinforces this view). The variance is not believed to be constant as the red dots in the top right graph are scattered in a cone pattern, so that the vari- ance moves from small to larger as the fitted value increases. The regression is statistically significant at the 95% level (alpha equals 0.05). The R-Sq(adj) equals 65.3%. Since R-Sq(adj) is the proportion of the total variation of outcomes explained by the model, taking into consideration the num- ber of variables in the model, it measures how well the inde- pendent variables (in this case based aircraft, flight schools, population, and climate) explain the variation of the depen- dent variable (in this case the OPS). Once more, residual plots are used by statisticians to assess if a regression model is a good fit to its data, and to examine the underlying statistical assumptions required for regression. The analysis of the residual plots (see Figure A-9) indicated that regression is invalid due to the violation of two required 1000000-100000 99.9 99 90 50 10 1 0.1 Residual Pe rc en t 3000002000001000000 100000 50000 0 -50000 -100000 Fitted Value R es id ua l 12000080000400000-40000-80000 60 45 30 15 0 Residual Fr eq ue nc y 200180160140120100806040201 100000 50000 0 -50000 -100000 Observation Order R es id ua l Normal Probability Plot Versus Fits Histogram Versus Order Residual Plots for OPS Prepared by: Purdue University Figure A-8. Residual plots for operations (OPS) full model. p value=0.000 Predictor Coef SECoef t p Constant 16535 4508 3.67 0.000 AvgBA 198.98 21.41 9.30 0.000 NFS 5174 1299 3.98 0.000 Pop Scaled 44.13 12.74 3.46 0.001 SE 14880 6604 2.25 0.025 SW 52389 10286 5.09 0.000 Prepared by: Purdue University Table A-8. Supplemental statistics showing significance of each variable in the reduced model using OPS (operations).

A-13 dramatically better than the OPBA model (65.3% versus 27.5%), but neither meet all the required statistical assump- tions for valid regression. As previously stated, similar results from other studies found that equations estimating OPS are more accurate than the equations estimating OPBA in esti- mation of activity at the non-towered airports. The model developed using log10AvgOPBA meets the statistical assumptions and has an R-Sq(adj) of 50.4%, but calculations may be more difficult than non-transformed data. Additionally, this equation only explains approximately 50% of the variation of operations at 205 small, towered air- ports included in the STAD. Furthermore, the data used in this model development was from small, towered airports, so it assumes that small towered airports are an accurate rep- resentation of non-towered airports. Therefore, it may not satisfy the need for accurately estimating OPBA or OPS at non-towered airports. Extrapolation Method to Estimate Annual Airport Operations The counting of operations is time-consuming. Sampling methods use statistical methods to reduce the amount of time needed for counting samples and still provide accu- rate estimates. Estimating annual operations using sampling While this model may be more attractive for use in the field, it still is not recommended by the research team because it fails to meet the required statistical assumptions and it only explains approximately 65% of the variation in the data. E. Overview of Models and Conclusions. Overall, the research team concludes that based on the study objectives and data, there were no practical and consistent OPBAs found or modeled at small, towered airports nationally or by climate region, even when considering the number of flight schools based at the airport. Therefore the research team cannot rec- ommend an OPBA for estimating annual operations at non- towered airports using the variables identified in Table A-1. From all the models analyzed, only the full and reduced model using transformed data (i.e., log10AvgOPBA and log10BA) met the necessary assumptions for statistical validity. However, the two regression equations developed for them only accounted for about 50% of the behavior of annual operations—that is, they did not explain a high proportion of the variability in the airport operations data tested, and therefore are unable to pre- dict airport operations with high certainty. Table A-9 shows a comparison of three regression equa- tions developed in this section. From the data, it can be shown that OPS are more accurately modeled than OPBA by comparing R-Sq(adj) for the models. The OPS model is 1000000-100000 99.9 99 90 50 10 1 0.1 Residual Pe rc en t 3000002000001000000 100000 50000 0 -50000 -100000 Fitted Value R es id ua l 1200009000060000300000-30000-60000-90000 40 30 20 10 0 Residual Fr eq ue nc y 200180160140120100806040201 100000 50000 0 -50000 -100000 Observation Order R es id ua l Normal Probability Plot Versus Fits Histogram Versus Order Residual Plots for Average Total GA OPS Prepared by: Purdue University Figure A-9. Residual plots for operations (OPS) reduced model.

A-14 methods is typically done either by statistical extrapolation of sample operations counts or by extrapolation using monthly/ seasonal adjustment factors developed from towered airport operations data. The process and results of testing these two methods using data from small, towered airports are described in Chapter 3 of this report. Additional details on the analysis are included below. Statistical Extrapolation The statistical extrapolation analysis presented in Chapter 3 was based on four sample sizes and timeframes. The sizes and timeframes are detailed here: One week in each season: The FAA-APO-85-7 requires a minimum of two weeks per season to produce an estimate of the variation for each season. Therefore, the research team assumed the one week used in this exercise was representa- tive of the whole season. While this method is not described in FAA-APO-85-7, it is a logical process to follow. For this exercise, actual daily operation data were collected for one randomly selected week in each season for each of 16 airports selected from the STAD. The random selection process was conducted separately for each airport. Accordingly, each air- port may have different weeks included in the analysis. The one week sample from each season was multiplied by 13 to obtain a seasonal estimate of operations. [Note: Four seasons of 13 weeks each were assumed for each year (i.e., 13 weeks multiplied by four seasons equals 52 weeks).] The estima- tions from all four seasons were summed to estimate total annual aircraft operations. Two weeks in each season: For this timeframe, actual daily operations data for two randomly selected weeks in each season for each of 16 airports selected from the STAD were used in the FAA Report No. FAA-APO-85-7 statistical esti- mation method. It was not required for the two randomly selected weeks to be consecutive. Again, the random selection process was conducted separately for each airport. The out- put consisted of total estimated annual operations for each airport. One month in spring, summer, or fall: For this timeframe, actual daily operations data for one month of four consecu- tive weeks during spring, summer, or fall was collected for each of 16 airports selected from the STAD. Again, the ran- dom selection process was conducted separately for each airport. The operations data were used in FAA-APO 85-7 statistical estimation method and the output contained an estimate of operations for the respective season for each air- port. To estimate annual operations, a seasonal distribution of operations is required by FAA-APO 85-7. A seasonal dis- tribution is needed because aircraft operations are known to vary by season depending upon the airport’s location. While the seasonal distribution is needed, it is not available if only one month in one season is sampled. Therefore, the monthly operations data were extrapolated into annual estimates using two methods of estimating the seasonal distribution. The first method assumed that each season contained an equal distribution of the year’s total operations; so each sea- son would account for 25% of the total annual operations. The second method for extrapolating the seasonal data into annual operations estimates used the distribution of opera- tions from the “two weeks in each season” section. One month in the winter: For this timeframe, actual oper- ations data for one month of four consecutive weeks dur- ing winter were collected for each of the 16 airports selected Equation R-square (adj) Regression p-Value OPS = 16535 + 199 AvgBA + 5174 NFS + 44.1 Pop Scaled + 14880 SE + 52389 SW Easiest to use of all methods analyzed. Does not meet all required statistical assumptions. Not recommended. 0.653 0.000 AvgOPBA = 572 - 1.11 AvgBA + 30.9 NFS + 0.613 Pop Scaled + 146 S + 214 SW + 177 RL Does not meet all required statistical assumptions. Not recommended. 0.275 0.000 log10AvgOPBA = 3.94 - 0.621 log10AvgBA + 0.000232 Pop Scaled + 0.0279 NFS - 0.0797 C + 0.0631 SE + 0.169 SW Meets all required statistical assumptions. Calculations may be complex. 0.504 0.000 Note: R-sq (adj) measures the proportionate reduction of total variation in Y associated with the use of the set of X variables.) Prepared by: Purdue University Table A-9. Comparison of OPS, OPBA, and Log10OPBA models (significant at p  0.05).

A-15 from the STAD. Again, the random selection process was conducted separately for each airport. The operations data were used in FAA-APO 85-7 statistical estimation method and the output contained an estimate of operations for the winter season. To estimate annual operations, a seasonal dis- tribution of operations is again required by FAA-APO 85-7. A seasonal distribution is needed because aircraft operations are known to vary by season depending upon the airport’s location. However, like before, as seasonal variation it is not available because only one month in one season is sampled. Therefore, the winter season estimate of operations was extrapolated into annual estimates using two methods of esti- mating the seasonal distribution. The first method assumed that each season contained an equal distribution of the year’s total operations so each season would account for 25% of the total annual operations. The second method for extrapolat- ing the seasonal data into annual operations estimates used the distribution of operations from the “two weeks in each season” section. Chapter 3 provides the results of this analysis. An example of using the FAA-APO-85-7 to estimate annual operations is provided in Appendix B. Extrapolation Using Monthly/Seasonal Adjustment Factors from Towered Airports This research exercise consisted of three elements: 1) calcu- late the percentage of operations that occur in each month for small, towered airports (i.e., STAD), and use these percent- ages to create monthly factors and seasonal factors for each region; 2) use those monthly and seasonal factors to extrapo- late annual operations for two randomly selected airports in each NOAA Climatic Region; and 3) present and compare the accuracy levels of this extrapolation process using different sampling sizes and times of year. Additional details of these elements are provided below. 1. Determine monthly and seasonal factors using all airports in the STAD. The first step in the analysis con- sisted of calculating monthly and seasonal factors for aircraft operations by region. To do this, the total operations for each month of 2010 were recorded from OPSNET for each airport in the STAD, and then monthly and seasonal factors for each region were calculated. To calculate each regional monthly factor, the total operations for each month were divided by the total yearly operations for all the airports in the region. (Note: Although there are nine NOAA Climatic Regions, the 205 airports in the STAD include airports that are in only eight NOAA regions. In addition to Alaska and Hawaii with only one airport each in the dataset, West North Central is not included because the dataset contains no airports for that region.) For seasonal factors, each season was assumed to be three months long. To calculate each region’s seasonal factor, the total operations for the three months in each season were added and then were divided by the total yearly operations. Table A-10 includes the monthly and seasonal factors for each region cal- culated from all airports in the STAD. Table A-11 includes the number of airports in each region used in the STAD. This analysis assumes all airports in a region have the same monthly and seasonal factors, that there are four seasons, Table A-10. Monthly and seasonal factors per region using STAD airports. Month Northeast Northwest South Southeast Southwest West Central East North Central January 0.07 0.06 0.07 0.08 0.08 0.07 0.05 0.05 February 0.05 0.07 0.07 0.08 0.08 0.07 0.06 0.06 March 0.08 0.09 0.09 0.09 0.09 0.09 0.09 0.09 April 0.09 0.09 0.09 0.10 0.08 0.08 0.09 0.08 May 0.10 0.10 0.09 0.09 0.08 0.09 0.09 0.09 June 0.10 0.10 0.09 0.08 0.09 0.09 0.09 0.10 July 0.10 0.10 0.09 0.08 0.08 0.09 0.10 0.12 August 0.10 0.10 0.09 0.08 0.08 0.09 0.10 0.10 September 0.08 0.09 0.09 0.08 0.09 0.09 0.09 0.09 October 0.08 0.08 0.09 0.09 0.09 0.08 0.10 0.09 November 0.08 0.05 0.08 0.08 0.08 0.08 0.08 0.07 December 0.06 0.05 0.07 0.07 0.08 0.07 0.06 0.05 Season Winter 0.20 0.22 0.23 0.24 0.25 0.23 0.20 0.20 Spring 0.28 0.29 0.27 0.27 0.25 0.26 0.27 0.27 Summer 0.28 0.30 0.26 0.23 0.25 0.27 0.29 0.31 Fall 0.23 0.19 0.24 0.25 0.24 0.23 0.24 0.22 Prepared by: Purdue University

A-16 and each season has 13 weeks. To maintain seasonal repre- sentation and to get all 12 months into four seasons for that calendar year, the seasons were identified as winter (January– March), spring (April–June), summer (July–September), and fall (October–December). In this way, the 2010 annual opera- tions could be compared to the estimates of annual opera- tions developed using seasonal factors. It is important to note, however, that in practice, climatic conditions may vary widely between regions and even within each region. 2. Extrapolate annual operations using the monthly and seasonal factors from the STAD airports. The next step for this research was to extrapolate annual operations using the monthly and seasonal factors (shown in Table A-10). A group of small, towered airports was selected for this pro- cedure because both actual operations and extrapolated oper- ations are compared to determine the accuracy of the process. Two STAD airports from each of eight NOAA climatic regions were randomly selected for use in the test, using a random numbers table. This resulted in 16 small towered test airports. (Note: These are the same airports included in the statis- tical extrapolation analysis presented earlier.) The airport codes for these 16 airports are listed in Table A-12. As in the other analyses, Alaska and Hawaii were excluded from this analysis because there is only one airport in each of these regions in the dataset. The West North Central region is also excluded from this task because there are no airports from this region that meet the criteria to be included in the STAD dataset. Four sampling scenarios were used to extrapolate annual operations estimates: A. One week in each season B. Two weeks in each season C. One month (either spring, summer or fall) D. One month in winter Each sampling scenario is explained in the following para- graphs. A summary of the analysis is shown in Table A-12. Again, the same 16 airports and the same time periods used in the statistical extrapolation described in Chapter 3 were used to estimate total yearly operations in this section. (See Table A-12 for the airport codes.) A. One week in each season: For each of the 16 test airports, one week of OPSNET data for each season were collected. The weekly data were multiplied by 4.3 weeks per month to obtain an estimate of monthly operations for that specific month. Using the monthly and seasonal factors developed for that region, an estimate of annual operations was calcu- lated. (See Table A-12 for annual estimates and Table A-10 for monthly and seasonal factors.) Table A-11. Number of airports in the dataset in each state and the number of airports used in the sample. State Region # of Airports in State (STAD) MI East North Central 4 MN East North Central 4 WI East North Central 5 IA East North Central 0 MO Central 5 IL Central 9 IN Central 5 OH Central 5 KY Central 2 WV Central 4 TN Central 3 ME Northeast 0 NH Northeast 2 VT Northeast 0 MA Northeast 6 RI Northeast 0 CT Northeast 5 NY Northeast 4 PA Northeast 4 NJ Northeast 3 DE Northeast 1 MD Northeast 3 OR Northwest 4 WA Northwest 4 ID Northwest 0 KS South 5 OK South 6 TX South 18 AR South 3 LA South 5 MS South 4 FL Southeast 24 AL Southeast 1 GA Southeast 6 SC Southeast 3 NC Southeast 3 VA Southeast 1 UT Southwest 2 CO Southwest 3 AZ Southwest 8 NM Southwest 2 CA West 26 NV West 1 WY West North Central 0 MT West North Central 0 ND West North Central 0 SD West North Central 0 NE West North Central 0 AK Alaska 1 HI Hawaii 1 Total 205 Prepared by: Purdue University

Table A-12. Estimates of annual operations using monthly/seasonal extrapolation and four sampling scenarios. Airport Region 1 Week each Season 2 Weeks each Season 1 Month Spring, Summer, or Fall Season Selected 1 Month Winter Month in Winter Selected Actual Operations (OPSNET) 1 Week each Season 2 Weeks each Season 1 Month Spring, Summer, or Fall 1 Month Winter CPS Central 113,764 126,605 97,938 Fall 126,909 Feb. 111,620 2% 13% -12% 14% DPA Central 101,692 82,865 72,858 Spring 72,360 Mar. 89,989 13% -8% -19% -20% ANE East North Central 80,256 78,920 79,473 Spring 78,928 Feb. and Mar. 79,603 1% -1% 0% -1% MIC East North Central 30,029 40,558 35,739 Summer 45,481 Feb. and Mar. 44,229 -32% -8% -19% 3% ASH Northeast 68,659 82,627 57,111 Fall 61,563 Jan. 74,111 -7% 11% -23% -17% RME Northeast 49,531 47,908 35,943 Summer 73,128 Feb. 47,790 4% 0% -25% 53% PDT West 12,106 12,440 14,016 Fall 13,034 Feb. and Mar. 12,994 -7% -4% 8% 0% TIW West 48,266 48,837 42,199 Spring 54,603 Jan. and Feb. 53,960 -11% -9% -22% 1% FTW South 83,370 81,069 72,014 Fall 91,839 Feb. 78,499 6% 3% -8% 17% GLS South 28,646 33,290 30,301 Summer 27,556 Feb. and Mar. 31,652 -9% 5% -4% -13% HEF Southeast 81,030 100,971 92,411 Summer 80,306 Feb. and Mar. 92,394 -12% 9% 0% -13% OPF Southeast 94,524 96,819 82,483 Spring 101,658 Jan. and Feb. 98,708 -4% -2% -16% 3% BJC Southwest 115,364 113,461 114,742 Fall 106,536 Jan. and Feb. 120,363 -4% -6% -5% -11% HOB Southwest 14,941 14,233 16,914 Spring 14,974 Feb. and Mar. 16,637 -10% -14% 2% -10% CMA West 151,100 148,393 165,637 Spring 174,536 Feb. and Mar. 146,863 3% 1% 13% 19% TOA West 118,025 79,103 85,326 Summer 115,623 Mar. 106,438 11% -26% -20% 9% Note: Positive % differences indicate that the actual annual operations are larger than the estimated annual operations. Negative % differences indicate that the actual annual operations are smaller than the estimated annual operations. Prepared by: Purdue University

A-18 B. Two weeks in each season: For each of the 16 test airports, two weeks of OPSNET data for each season were col- lected. The weekly data were averaged and multiplied by 4.3 weeks per month to obtain an estimate of monthly operations for that specific month. Using the monthly and seasonal factors developed for that region, an estimate of annual operations was calculated. (See Table A-12 for annual estimates and Table A-10 for monthly and seasonal factors.) C. One month in spring, summer, or fall: For each of the 16 test airports, one month (four consecutive weeks) of OPSNET data for one season were collected. The monthly data were divided by the monthly factor for that month to estimate the annual operations. (See Table A-12 for annual estimates and Table A-10 for monthly and seasonal factors.) D. One month in winter: For each of the 16 test airports, one month (four consecutive weeks) of OPSNET data for the winter season were collected. The monthly data were divided by the monthly factor for that month to estimate the annual operations. (See Table A-12 for annual esti- mates and Table A-10 for monthly and seasonal factors.) 3. Compare actual operations to the estimates. The final task included a comparison of the actual operations of the 16 test airports to the estimated operations. The percent difference between each test airport’s estimated annual oper- ations and the actual OPSNET annual operations were calcu- lated and are shown in Table A-12. A summary of the percent differences between OPSNET data and the extrapolated esti- mates is shown in Table A-13. The estimates of percent dif- ferences are summarized by listing the average, the average of the absolute values, highest, the lowest, and the range for each of the four sampling scenarios. Discussion and Additional Analyses. As may be seen in Table A-13, estimates made using the sampling scenario of two weeks per season provided an estimate closest to actual operations for the test airports, on average. Estimates made using the sampling scenario of one month winter were the second closest to actual operations, on average. The ranges for estimated operations for the sampling scenarios of 2 weeks per season and 1 month (spring, summer or fall) were the closest to actual operations in terms of range of the percent differences. When reviewing the data in Tables A-12 and A-13, it is not immediately apparent if there are statistical differences in the results due to the sampling method (e.g., one week per season, two weeks per season, etc.). Box plots are another way to represent the data from Table A-13. Box plots split the data into quartiles with the box consisting of the second and third quartile and a horizontal line drawn between the two quartiles. This line is the median of the data set. Vertical lines extending above and/or below the box to show the small- est and largest quartiles, and outliers are shown as asterisks. The first boxplot (Figure A-10) summarizes the data based on sampling scenario. By observation, the sampling method of one month in the winter appears to have a wider standard deviation than the other methods. This finding is consistent with the range data shown in Table A-13. The next test was to determine which of the sampling methods were statistically different from the others. The one- way ANOVA for percent differences in annual operations was conducted for sampling scenario and the results reported in Table A-14. The one-way ANOVA analysis indicates which sampling methods are different from other sampling meth- ods, in terms of statistically significant percent differences. The p-value for sampling scenario (one week in each season; two weeks in each season; one month spring, summer or fall; and one month winter) is 0.009 and is smaller than the criti- cal alpha of 0.05. This evidence leads the research team to conclude that there is at least one sampling method that is different from the others. The Tukey test is performed after an ANOVA and is used to determine which sampling scenarios have significant differences from each other. Based on the Tukey Analysis shown in Table A-15, the percent differences from the actual % Difference from OPSNET Annual Operations 1 Week each Season 2 Weeks each Season 1 Month Spring, Summer, or Fall 1 Month Winter Average of real values 4% 2% 9% 2% Average of absolute values 9% 8% 12% 13% Highest 13% 13% 13% 53% Lowest -32% -26% -25% -20% Range 45% 39% 38% 73% Prepared by: Purdue University Table A-13. Summary of the percent difference between estimates and OPSNET annual operations.

A-19 1 M on th Wi nte r 1 M on th Sp rin g, Su mm er, or Fa ll 2 W ee ks ea ch Se as on 1 W ee k ea ch Se as on 0.50 0.25 0.00 -0.25 -0.50 Pe rc en t D iff er en ce Boxplot of Percent Differences Using 4 Sampling Scenarios Prepared by: Purdue University Figure A-10. Box plot of sampling methods: 1 week each season; 2 weeks each season; 1 month spring, summer, or fall; and 1 month winter. Table A-14. One-way ANOVA for sampling scenario. Source Degrees of Freedom Sum of Squares Mean Square F statistic P value Sampling Scenario 3 0.2075 0.0692 4.03 0.009 Error 124 2.1260 0.0171 Total 127 2.3336 Note: S = 0.1309 R-Sq = 8.89% R-Sq(adj) = 6.69% Prepared by: Purdue University Table A-15. Data summary and Tukey Analysis. Sampling Scenario N Mean of the % Differences Standard Deviation Tukey Grouping 1 Week each Season 32 -0.0393 0.1127 A B 2 Weeks each Season 32 -0.0134 0.0895 A B 1 Month Spring, Summer, or Fall 32 -0.0884 0.1234 B 1 Month Winter 32 0.0220 0.1806 A Notes: Pooled StDev = 0.1309. Means that do not share a letter are significantly different. Tukey Comparison 95% Confidence Level of the difference between Sampling Scenario using 1 Month Spring, Summer, or Fall subtracted and Sampling Scenario using 1 Month Winter: Lower Center Upper 0.0253 0.1105 0.1957 Individual confidence level = 98.96%. Prepared by: Purdue University operations data for the sampling method using one month in the winter are different from the sampling method using one month in the spring, summer, or fall. The 95% confi- dence interval for this difference between the two methods is 2.53% to 19.57%, with a mean of 11.05%. While the averages (means of the percent differences) have different values in Table A-15, the relatively large standard deviation makes the detection of a statistical difference difficult. In addition to the significant difference just described, the Tukey Analysis results show that there is not enough evidence to conclude that a significant difference in results occur when compar- ing 1 week each season, 2 weeks each season, and 1 month

A-20 winter (shown as Tukey Grouping A in Table A-15). More- over, the Tukey Analysis results show that there is not enough evidence to conclude that a significant difference in results occur when comparing 1 week each season, 2 weeks each season, and 1 month spring, summer, or fall (shown as Tukey Grouping B in Table A-15). The residual plots in Figure A-11 indicate that the assump- tions for ANOVA are met and the analysis may be used with confidence. Based on observation of the residual plots, the ANOVA analysis appears valid. Residual plots are used to make conclusions about the ANOVA assumptions regarding nor- mality of the residuals and constant variance of the residuals. Figure A-11. Residual plots for sampling scenario (one-way ANOVA). 0.500.250.00-0.25-0.50 99.9 99 90 50 10 1 0.1 Residual Pe rc en t 0.00-0.05-0.10 0.4 0.2 0.0 -0.2 -0.4 Fitted Value R es id ua l 0.450.300.150.00-0.15-0.30 24 18 12 6 0 Residual Fr eq ue nc y Normal Probability Plot Versus Fits Histogram Residual Plots for Sampling Scenario Prepared by: Purdue University