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.

Figure 22—The original 10-foot spacing was increased to 20 feet to
evaluate sampling density.

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 |
|