Land Cover Stratified Accuracy Assessment For Digital Elevation Model derived from Airborne LIDAR Dade County, Florida

Transcription

1 Land Cover Stratified Accuracy Assessment For Digital Elevation Model derived from Airborne LIDAR Dade County, Florida FINAL REPORT Submitted October 2004 Prepared by: Daniel Gann Geographic Information Systems and Remote Sensing Center Florida International University SW 8 th St Miami, FL (305) gannd@fiu.edu OCTOBER 2004

2 TABLE OF CONTENTS Executive Summary...2 Methods...4 Results and Discussion...8 References...11 Appendices...12 Appendix A: Control Data...12 Appendix B: SAS Output Summary Statistics...13 FIGURES Figure 1 Control Points at FIU University Park Campus...5 Figure 2 Control Points at Coral Gables...6 Figure 3 Control Points at FIU Bisacayne Bay Campus...7 Figure 4 Kernel Density Estimator applied to differences of Interpolated DEM - Control Point measurements...8 TABLES Table 1 Classification scheme...3 Table 2 Sample count for all regions within Miami-Dade County...4 Table 3 Sample count by category...4 Table 4 Samples aggregated at Level 1 by sampling location...5 Table 5 Summary statistics of the differences (interpolated DEM - Control) by category...9 Table 6 Wilcoxon and Kolmogorov-Smirnov test results testing for three variables: land-cover class, location and data collection method

3 Executive Summary The Geographic Information Systems and Remote Sensing Center (GIS/RS Center) of Florida International University (FIU) conducted an accuracy assessment for a Digital Elevation Model (DEM) derived from LIght Detection And Ranging (LIDAR) data. This report describes the sampling design, control point acquisition, and accuracy assessment. The purpose of this assessment was to estimate the vertical error of interpolated LIDAR data for different land-cover strata. The elevation grid to be evaluated had been generated from data collected by the International Hurricane Research Center (IHRC) by applying a progressive morphological filter in order to remove nonground measurements (Zhang et al. 2003, Zhang et al. in press). Since performance of the algorithm is likely to be dependent on the vertical complexity of the land cover, an assessment of algorithm performance based on land cover needed to be conducted. For this purpose a hierarchical classification scheme was developed, which would allow for class aggregation and disaggregating during the evaluation process. The classification system has 4 different levels. Level 1 distinguishes between Asphalt, Grass and Closed Canopy. Closed Canopy is further subdivided into under-story and no under-story and the category Grass contains sub-categories tall and short. Each of these categories is further stratified by slope into flat and inclined as well as center areas and edges (Table 1). A first analysis was performed exclusively at Level 1. There seems to be a non-random distribution of error for interpolated elevations derived from a morphological filter algorithm applied to LIDAR data. The spatial distribution of the error is significantly different between land cover classes Closed Canopy, Grass, and Asphalt. A test for difference in sampling location and sampling method indicates no differences with one exception for class grass by location. Interpolation of the results across Miami-Dade County is not necessarily given due to the non-random nature of the sampling locations. Nevertheless the representation of class samples within urban settings as well as state parks 2

4 provides data on both ends of the spectrum of occurrence within Miami-Dade County. Level 1 Level 2 Level 3 Level 4 Code Center Understory 1 Flat 1 Edge Closed Canopy 100 Grass 200 Asphalt 300 No Understory 2 Tall 1 Short 2 Table 1 Classification scheme 0 Center Inclined 2 Edge Center Flat 1 Edge Center Inclined 2 Edge Center Flat 1 Edge Center Inclined 2 Edge Center Flat 1 Edge Center Inclined 2 Edge Center Flat 1 Edge 2, Building , 44 Center Inclined 2 Edge

5 Methods The control data set was collected using differential GPS for areas that allow for GPS satellite signal reception and a Theodolite or Total Station for areas covered by vegetation or obstructed by tall buildings. Control points were collected in three different areas within Miami-Dade County, at FIU University Park Campus (Figure 1) and Biscayne Bay Campus (Figure 2) and in Coral Gables (Figure 3) mainly in Matheson Hammock State Park. Base station locations for differential correction have been surveyed in all three locations. The same locations were used for surveys with the total station. For spatial distribution of base stations and sampling points with GPS rover and total station as well as by Level 1 Category see (Table 2, 4 and Figures 1,2,3). FIU University Park FIU Biscayne Bay Coral Gables Total Base Stations GPS Rover Total Station Total Table 2 Sample count for all regions within Miami-Dade County Code Count Level1 Count Table 3 Sample count by category 4

6 Frequency Percent Row Pct Col Pct Closed Canopy Grass Asphalt Total Coral Gables Biscayne Bay University Park Total Table 4 Samples aggregated at Level 1 by sampling location. Figure 1 Control points at FIU University Park Campus 5

7 Figure 2 Control points at Coral Gables For each GPS Rover and Total Station sample the interpolated elevation was extracted from the DEM using Imagine 8.7 Pixel to ASCII tool. Differences between Level 1 Categories were analyzed in three different ways. First the root mean square error (RMSE) was calculated to quantitatively estimate the error for all measurements as well as stratified by land cover. The RMSE is calculated according to equation 1. RMSE z = ( zn, i zm, i ) n 2 where RMSE z is the root mean square error, z m,i is the elevation of the ith control point, z n,i is the interpolated DEM elevation at the control point, and n is the number of control points. Accuracy is also reported in measurement units (Feet) at the 95% confidence level (Table 5). (1) 6

8 Figure 3 Control points at FIU Bisacayne Bay Campus Secondly a Kruskal-Wallis test on Wilcoxon scores for elevation differences was used to test for significance in shifts of the mean differences. A third test analyzed the deviation of the distribution of differences between classes. The Kolmogorov-Smirnov statistic measures the maximum deviation of an empirical distribution function (EDF) within the classes from a pooled EDF. Both tests were performed for three different variables. The first pair wise comparison tests for differences between Categories, and it is expected that there is a significant difference between classes. The second variable was location. It is expected that there are no significant differences in elevation difference distribution across sites. The sites that were chosen for this analysis are the ones that had more sampling points (Table 4). In the case of Closed Canopy the sites that were compared are Coral Gables and Biscayne Bay, for categories Grass and Asphalt the chosen sites are Coral Gables and University Park. Similarly for the third variable Method distinguishing between GPS Rover versus Total Station it was expected that there are no significant 7

9 differences in elevation difference distribution. The class Closed Canopy was excluded in this procedure, since by definition this class has been sampled by total station only. Results and Discussion From the distribution of elevation differences it is obvious that there is a shift of the mean towards the negative, which means that overall the progressive morphological filter algorithm interpolates lower elevations than ground control reveals, or underestimates the ground elevation (Figure 4, Table 5). Figure 4 Kernel Density Estimator applied to differences of Interpolated DEM - Control Point measurements, Units = Feet. 8

10 RMSE values differ little for all points and between individual classes, with Asphalt being the lowest with.319 Feet and Grass the largest with.394 Feet (Table 5). All Closed Canopy Grass Asphalt N Mean Std Conf 95% UL Conf 95% LL Conf 95% Range RMSE Table 5 Summary statistics of the differences (interpolated DEM - Control) by category, Units for RMSE, Conf 95%, Std and Mean in Feet. UL = Upper Limit, LL = Lower Limit The Kruskal-Wallis test on Wilcoxon scores indicates that based on the Chi-Square distribution we have to reject the null hypothesis that the difference between two class means is zero. This means that the difference between the class means is significant. The results for the tests of elevation differences for different stratification schemes are summarized in Table 6. VARIABLE WILCOXON EDF Kolmogorov-Smirnov DF CHI SQUARE p-value KS D p-value Elevation Difference Distribution by Category Closed Canopy - Grass < <.0001 Closed Canopy - Asphalt < <.0001 Grass - Asphalt < <.0001 Elevation Difference Distribution by Location and Class Closed Canopy: Coral Gables - Biscayne Bay Grass: Coral Gables - University Park < <.0001 Asphalt:Coral Gables - University Park Elevation Difference Distribution by Method Rover - Total Station Table 6 Wilcoxon and Kolmogorov-Smirnov test results testing for three variables: landcover class, location and data collection method. 9

11 The shift of means for different class combinations is significant for all possible class combinations for α = (visible in Figure 4). The same holds true for the distribution shape (EDF). When testing for differences based on sampling location and also for sampling method we expect not to see any differences between the groups. In the case of Closed Canopy and Asphalt there is no difference between sites. For the class Grass on the other hand we cannot reject the null hypothesis. Looking at the difference between the two sampling methods Rover versus Total Station we find the expected outcome that there is no significant difference between the samples taken by rover or total station. The Kolmogorov-Smirnov test of distribution deviation shows the same result as the Kruskal-Wallis test for the shift of means (Table 6). In conclusion the spatial distribution of the error is significantly different between land cover classes Closed Canopy, Grass, and Asphalt. A test for difference in sampling location and sampling method indicates no differences with one exception for class grass by location. The reason for this difference needs to be investigated further. 10

12 References Zhang, K., S.C. Chen, D. Whitman, M.L. Shyu, J.H. Yan, and C.C. Zhang, A progressive morphological filter for removing nonground measurements from airborne LIDAR data, IEEE Transactions on Geoscience and Remote Sensing, 41, , Zhang K. and D. Whitman, Comparison of three algorithms for filtering airborne LIDAR data. Photogrammetric Engineering and Reomote Sensing, in press. 11

13 Appendices Appendix A: Base Stations (See BaseStations.shp) Control Data (See ControlPoints.shp) 12

14 Appendix B: SAS Output Summary Statistics 13

15 Interpolated DEM - Control The UNIVARIATE Procedure Variable: DIFF (Difference) Moments N 2028 Sum Weights 2028 Mean Sum Observations Std Deviation Variance Skewness Kurtosis Uncorrected SS Corrected SS Coeff Variation Std Error Mean Basic Statistical Measures Location Variability Mean Std Deviation Median Variance Mode Range Interquartile Range Tests for Location: Mu0=0 Test -Statistic p Value Student's t t Pr > t <.0001 Sign M Pr >= M <.0001 Signed Rank S Pr >= S <.0001 Quantiles (Definition 5) Quantile Estimate 100% Max % % % % Q % Median % Q % % % % Min

16 The UNIVARIATE Procedure Variable: DIFF (Difference) Extreme Observations -----Lowest Highest---- Value Obs Value Obs

17 Category=Closed Canopy The UNIVARIATE Procedure Variable: DIFF (Difference) Moments N 736 Sum Weights 736 Mean Sum Observations Std Deviation Variance Skewness Kurtosis Uncorrected SS Corrected SS Coeff Variation Std Error Mean Basic Statistical Measures Location Variability Mean Std Deviation Median Variance Mode Range Interquartile Range NOTE: The mode displayed is the smallest of 6 modes with a count of 3. Tests for Location: Mu0=0 Test -Statistic p Value Student's t t Pr > t Sign M -37 Pr >= M Signed Rank S Pr >= S Quantiles (Definition 5) Quantile Estimate 100% Max % % % % Q % Median % Q % % % % Min

18 Category=Closed Canopy The UNIVARIATE Procedure Variable: DIFF (Difference) Extreme Observations -----Lowest Highest---- Value Obs Value Obs

19 Category=Grass The UNIVARIATE Procedure Variable: DIFF (Difference) Moments N 819 Sum Weights 819 Mean Sum Observations Std Deviation Variance Skewness Kurtosis Uncorrected SS Corrected SS Coeff Variation Std Error Mean Basic Statistical Measures Location Variability Mean Std Deviation Median Variance Mode Range Interquartile Range NOTE: The mode displayed is the smallest of 8 modes with a count of 4. Tests for Location: Mu0=0 Test -Statistic p Value Student's t t Pr > t <.0001 Sign M -210 Pr >= M <.0001 Signed Rank S Pr >= S <.0001 Quantiles (Definition 5) Quantile Estimate 100% Max % % % % Q % Median % Q % % % % Min

20 Category=Grass The UNIVARIATE Procedure Variable: DIFF (Difference) Extreme Observations -----Lowest Highest---- Value Obs Value Obs

21 Category=Asphalt The UNIVARIATE Procedure Variable: DIFF (Difference) Moments N 473 Sum Weights 473 Mean Sum Observations Std Deviation Variance Skewness Kurtosis Uncorrected SS Corrected SS Coeff Variation Std Error Mean Basic Statistical Measures Location Variability Mean Std Deviation Median Variance Mode Range Interquartile Range NOTE: The mode displayed is the smallest of 3 modes with a count of 4. Tests for Location: Mu0=0 Test -Statistic p Value Student's t t Pr > t <.0001 Sign M Pr >= M <.0001 Signed Rank S Pr >= S <.0001 Quantiles (Definition 5) Quantile Estimate 100% Max % % % % Q % Median % Q % % % % Min

22 Category=Asphalt The UNIVARIATE Procedure Variable: DIFF (Difference) Extreme Observations -----Lowest Highest---- Value Obs Value Obs

23 Closed Canopy - Grass Differences WILCOXON EDF The NPAR1WAY Procedure Wilcoxon Scores (Rank Sums) for Variable DIFF Classified by Variable LEVEL1 Sum of Expected Std Dev Mean LEVEL1 N Scores Under H0 Under H0 Score ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ Closed Canopy Grass Average scores were used for ties. Wilcoxon Two-Sample Test Statistic Normal Approximation Z One-Sided Pr > Z <.0001 Two-Sided Pr > Z <.0001 t Approximation One-Sided Pr > Z <.0001 Two-Sided Pr > Z <.0001 Z includes a continuity correction of 0.5. Kruskal-Wallis Test Chi-Square DF 1 Pr > Chi-Square <

24 Closed Canopy - Grass Differences WILCOXON EDF The NPAR1WAY Procedure Kolmogorov-Smirnov Test for Variable DIFF Classified by Variable LEVEL1 EDF at Deviation from Mean LEVEL1 N Maximum at Maximum ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ Closed Canopy Grass Total Maximum Deviation Occurred at Observation 1362 Value of DIFF at Maximum = Kolmogorov-Smirnov Two-Sample Test (Asymptotic) KS D KSa Pr > KSa <.0001 Cramer-von Mises Test for Variable DIFF Classified by Variable LEVEL1 Summed Deviation LEVEL1 N from Mean ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ Closed Canopy Grass Cramer-von Mises Statistics (Asymptotic) CM CMa Kuiper Test for Variable DIFF Classified by Variable LEVEL1 Deviation LEVEL1 N from Mean ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ Closed Canopy Grass Kuiper Two-Sample Test (Asymptotic) K Ka Pr > Ka <

25 Closed Canopy - Asphalt Differences WILCOXON EDF The NPAR1WAY Procedure Wilcoxon Scores (Rank Sums) for Variable DIFF Classified by Variable LEVEL1 Sum of Expected Std Dev Mean LEVEL1 N Scores Under H0 Under H0 Score ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ Closed Canopy Asphalt Average scores were used for ties. Wilcoxon Two-Sample Test Statistic Normal Approximation Z One-Sided Pr < Z <.0001 Two-Sided Pr > Z <.0001 t Approximation One-Sided Pr < Z <.0001 Two-Sided Pr > Z <.0001 Z includes a continuity correction of 0.5. Kruskal-Wallis Test Chi-Square DF 1 Pr > Chi-Square <

26 Closed Canopy - Asphalt Differences WILCOXON EDF The NPAR1WAY Procedure Kolmogorov-Smirnov Test for Variable DIFF Classified by Variable LEVEL1 EDF at Deviation from Mean LEVEL1 N Maximum at Maximum ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ Closed Canopy Asphalt Total Maximum Deviation Occurred at Observation 1150 Value of DIFF at Maximum = Kolmogorov-Smirnov Two-Sample Test (Asymptotic) KS D KSa Pr > KSa <.0001 Cramer-von Mises Test for Variable DIFF Classified by Variable LEVEL1 Summed Deviation LEVEL1 N from Mean ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ Closed Canopy Asphalt Cramer-von Mises Statistics (Asymptotic) CM CMa Kuiper Test for Variable DIFF Classified by Variable LEVEL1 Deviation LEVEL1 N from Mean ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ Closed Canopy Asphalt Kuiper Two-Sample Test (Asymptotic) K Ka Pr > Ka <

27 Grass - Asphalt Differences WILCOXON EDF The NPAR1WAY Procedure Wilcoxon Scores (Rank Sums) for Variable DIFF Classified by Variable LEVEL1 Sum of Expected Std Dev Mean LEVEL1 N Scores Under H0 Under H0 Score ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ Grass Asphalt Average scores were used for ties. Wilcoxon Two-Sample Test Statistic Normal Approximation Z One-Sided Pr < Z <.0001 Two-Sided Pr > Z <.0001 t Approximation One-Sided Pr < Z <.0001 Two-Sided Pr > Z <.0001 Z includes a continuity correction of 0.5. Kruskal-Wallis Test Chi-Square DF 1 Pr > Chi-Square <

28 Grass - Asphalt Differences WILCOXON EDF The NPAR1WAY Procedure Kolmogorov-Smirnov Test for Variable DIFF Classified by Variable LEVEL1 EDF at Deviation from Mean LEVEL1 N Maximum at Maximum ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ Grass Asphalt Total Maximum Deviation Occurred at Observation 292 Value of DIFF at Maximum = Kolmogorov-Smirnov Two-Sample Test (Asymptotic) KS D KSa Pr > KSa <.0001 Cramer-von Mises Test for Variable DIFF Classified by Variable LEVEL1 Summed Deviation LEVEL1 N from Mean ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ Grass Asphalt Cramer-von Mises Statistics (Asymptotic) CM CMa Kuiper Test for Variable DIFF Classified by Variable LEVEL1 Deviation LEVEL1 N from Mean ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ Grass Asphalt Kuiper Two-Sample Test (Asymptotic) K Ka Pr > Ka <

29 Closed Canopy: Coral Gables - Biscayne Bay WILCOXON EDF The NPAR1WAY Procedure Wilcoxon Scores (Rank Sums) for Variable DIFF Classified by Variable LOCATION Mean Score Sum of Expected Std Dev LOCATION N Scores Under H0 Under H0 ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ Coral Gables Biscayne Bay Campus Average scores were used for ties. Wilcoxon Two-Sample Test Statistic Normal Approximation Z One-Sided Pr < Z Two-Sided Pr > Z t Approximation One-Sided Pr < Z Two-Sided Pr > Z Z includes a continuity correction of 0.5. Kruskal-Wallis Test Chi-Square DF 1 Pr > Chi-Square

30 Closed Canopy: Coral Gables - Biscayne Bay WILCOXON EDF The NPAR1WAY Procedure Kolmogorov-Smirnov Test for Variable DIFF Classified by Variable LOCATION EDF at Deviation from Mean LOCATION N Maximum at Maximum ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ Coral Gables Biscayne Bay Campus Total Maximum Deviation Occurred at Observation 149 Value of DIFF at Maximum = Kolmogorov-Smirnov Two-Sample Test (Asymptotic) KS D KSa Pr > KSa Cramer-von Mises Test for Variable DIFF Classified by Variable LOCATION Summed Deviation LOCATION N from Mean ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ Coral Gables Biscayne Bay Campus Cramer-von Mises Statistics (Asymptotic) CM CMa Kuiper Test for Variable DIFF Classified by Variable LOCATION Deviation LOCATION N from Mean ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ Coral Gables Biscayne Bay Campus Kuiper Two-Sample Test (Asymptotic) K Ka Pr > Ka <

31 Grass: Coral Gables - University Park WILCOXON EDF The NPAR1WAY Procedure Wilcoxon Scores (Rank Sums) for Variable DIFF Classified by Variable LOCATION Sum of Expected Std Dev Mean LOCATION N Scores Under H0 Under H0 Score ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ Coral Gables University Park Average scores were used for ties. Wilcoxon Two-Sample Test Statistic Normal Approximation Z One-Sided Pr > Z <.0001 Two-Sided Pr > Z <.0001 t Approximation One-Sided Pr > Z <.0001 Two-Sided Pr > Z <.0001 Z includes a continuity correction of 0.5. Kruskal-Wallis Test Chi-Square DF 1 Pr > Chi-Square <

32 Grass: Coral Gables - University Park WILCOXON EDF The NPAR1WAY Procedure Kolmogorov-Smirnov Test for Variable DIFF Classified by Variable LOCATION EDF at Deviation from Mean LOCATION N Maximum at Maximum ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ Coral Gables University Park Total Maximum Deviation Occurred at Observation 335 Value of DIFF at Maximum = Kolmogorov-Smirnov Two-Sample Test (Asymptotic) KS D KSa Pr > KSa <.0001 Cramer-von Mises Test for Variable DIFF Classified by Variable LOCATION Summed Deviation LOCATION N from Mean ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ Coral Gables University Park Cramer-von Mises Statistics (Asymptotic) CM CMa Kuiper Test for Variable DIFF Classified by Variable LOCATION Deviation LOCATION N from Mean ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ Coral Gables University Park Kuiper Two-Sample Test (Asymptotic) K Ka Pr > Ka <

33 Asphalt: Coral Gables - University Park WILCOXON EDF The NPAR1WAY Procedure Wilcoxon Scores (Rank Sums) for Variable DIFF Classified by Variable LOCATION Sum of Expected Std Dev Mean LOCATION N Scores Under H0 Under H0 Score ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ Coral Gables University Park Average scores were used for ties. Wilcoxon Two-Sample Test Statistic Normal Approximation Z One-Sided Pr > Z <.0001 Two-Sided Pr > Z <.0001 t Approximation One-Sided Pr > Z <.0001 Two-Sided Pr > Z <.0001 Z includes a continuity correction of 0.5. Kruskal-Wallis Test Chi-Square DF 1 Pr > Chi-Square <

34 Asphalt: Coral Gables - University Park WILCOXON EDF The NPAR1WAY Procedure Kolmogorov-Smirnov Test for Variable DIFF Classified by Variable LOCATION EDF at Deviation from Mean LOCATION N Maximum at Maximum ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ Coral Gables University Park Total Maximum Deviation Occurred at Observation 335 Value of DIFF at Maximum = Kolmogorov-Smirnov Two-Sample Test (Asymptotic) KS D KSa Pr > KSa <.0001 Cramer-von Mises Test for Variable DIFF Classified by Variable LOCATION Summed Deviation LOCATION N from Mean ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ Coral Gables University Park Cramer-von Mises Statistics (Asymptotic) CM CMa Kuiper Test for Variable DIFF Classified by Variable LOCATION Deviation LOCATION N from Mean ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ Coral Gables University Park Kuiper Two-Sample Test (Asymptotic) K Ka Pr > Ka <

35 Rover - Total Station WILCOXON EDF The NPAR1WAY Procedure Wilcoxon Scores (Rank Sums) for Variable DIFF Classified by Variable MET Sum of Expected Std Dev Mean MET N Scores Under H0 Under H0 Score ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ Rover Total Station Average scores were used for ties. Wilcoxon Two-Sample Test Statistic Normal Approximation Z One-Sided Pr < Z Two-Sided Pr > Z t Approximation One-Sided Pr < Z Two-Sided Pr > Z Z includes a continuity correction of 0.5. Kruskal-Wallis Test Chi-Square DF 1 Pr > Chi-Square

36 Rover - Total Station WILCOXON EDF The NPAR1WAY Procedure Kolmogorov-Smirnov Test for Variable DIFF Classified by Variable MET EDF at Deviation from Mean MET N Maximum at Maximum ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ Rover Total Station Total Maximum Deviation Occurred at Observation 682 Value of DIFF at Maximum = Kolmogorov-Smirnov Two-Sample Test (Asymptotic) KS D KSa Pr > KSa Cramer-von Mises Test for Variable DIFF Classified by Variable MET Summed Deviation MET N from Mean ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ Rover Total Station Cramer-von Mises Statistics (Asymptotic) CM CMa Kuiper Test for Variable DIFF Classified by Variable MET Deviation MET N from Mean ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ Rover Total Station Kuiper Two-Sample Test (Asymptotic) K Ka Pr > Ka