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Estimating Methods, Variability, and Sampling for Drop-Test Data

Appendix—Details on Cups, Error Variance, and Grid Spacing Continued

Grid Spacing

Gpc data collected from a previous drop test, which used a grid with cups in a 10- by 10-foot spacing, were used for the following comparisons. The 10- by 10-foot spacing provided a data set that could be divided into subsets for cross validation. Two subsets were created with the points in a 20- by 10-foot spacing, and three subsets were created with the points in a 30- by 10- foot spacing. Figures 22 and 23 show examples of these subsets. Tables 10 to 14 display the cross validation tabular results. Figures 24 and 25 display the QQ-plots comparing distributions.

Image of a subset example comparing the original 10- by 10-foot spacing with the new increased 20- by 10-foot spacing.
Figure 22—The original 10-foot spacing was increased to 20 feet to
evaluate sampling density.

Image of a subset example comparing the original 10- by 10-foot spacing with the new increased 30- by 10-foot spacing.
Figure 23—The original 10-foot spacing was increased to 30 feet to
evaluate sampling density.

Table 10—First comparison of observed gpc (gallons per hundred square feet) values from a 10- by 10-foot spacing with predicted values from a 20- by 10-foot spacing. MAE is mean absolute error and MSE is mean squared error.
  TRUE Triangulation (gpc)
Mean 1.534 1.509
Standard deviation 0.905 0.819
Minimum 0.037 0.068
1st quartile 0.950 0.962
Median 1.380 1.419
3rd quartile 2.008 2.052
Maximum 5.081 5.428
Correlation   0.905
n 319 319
Summary statistics for error distribution
  Triangulation (gpc)
Mean 0.02483
Standard deviation 0.386
Minimum -1.856
1st quartile -0.144
Median -0.021
3rd quartile 0.150
Maximum 2.206
MAE 0.246
MSE 0.149
n 319

Table 11—Second comparison of observed gpc (gallons per 100 square feet) values from a 10- by 10-foot spacing with predicted values from a 20- by 10-foot spacing. MAE is mean absolute error and MSE is mean squared error.
  TRUE Triangulation (gpc)
Mean 1.524 1.550
Standard deviation 0.922 0.805
Minimum 0.040 0.093
1st quartile 0.909 0.994
Median 1.412 1.411
3rd quartile 2.012 2.071
Maximum 8.183 4.060
Correlation   0.893
n 308 308
Summary statistics for error distribution
  Triangulation (gpc)
Mean -0.02628
Standard deviation 0.416
Minimum -1.044
1st quartile -0.201
Median -0.035
3rd quartile 0.096
Maximum 4.122
MAE 0.241
MSE 0.173
n 308

Table 12—First comparison of observed gpc (gallons per 100 square feet) values from a 10- by 10-foot spacing with predicted values from a 30- by 10-foot spacing. MAE is mean absolute error and MSE is mean squared error.
  TRUE Triangulation (gpc)
Mean 1.553 1.534
Standard deviation 0.962 0.736
Minimum 0.051 0.053
1st quartile 0.947 1.044
Median 1.400 1.481
3rd quartile 1.978 2.069
Maximum 8.183 3.676
Correlation   0.803
n 396 490
Summary statistics for error distribution
  Triangulation (gpc)
Mean 0.01857
Standard deviation 0.574
Minimum -1.337
1st quartile -0.217
Median -0.020
3rd quartile 0.147
Maximum 5.265
MAE 0.334
MSE 0.329
n 396