For LAS measurements, both wet and dry, two sets of results were collected:
We have examined the two sets of data separately and then in combination, after first excluding the outliers. As a result of this process, three mean bootstrap curves with 95% confidence limits are provided for both LAS-W and LAS-D. The issue is then to decide which mean curve or curves is most appropriate as a reference for SRM 114p using the LAS technique. Note that high and low intervals are not symmetric about the mean. These limits can be asymmetric around the sample mean. This is caused by a slight skewness of the generated bootstrapped sampling distribution of the mean.
All individual data sets used in this analysis are reported elsewhere [Ferraris et al., 2002b]. Six outliers were found for LAS-W out of 25 participants, and two outliers were determined for LAS-D out of 13 participants. The bootstrap results are given in Table 1 for LAS-W and Table 2 for LAS-D. A graphical comparison of the three distributions is provided in Fig. 1 for LAS-W and Fig. 2 for LAS-D. As shown in these figures, the differences between the three PSDs are not very large. Because the combined distribution represents a larger statistical pool, it could be argued that the combined PSD should be used as a single consensus reference curve.
| TABLE 1−Bootstrap data for LAS-W (after excluding outliers). Size refers to equivalent spherical particle diameter. | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| PM Only | SM Only | PM + SM | |||||||
| Size [µm] | Mean | Low | High | Mean | Low | High | Mean | Low | High |
| 1 | 5.0 | 3.5 | 6.3 | 6.0 | 3.9 | 8.3 | 5.4 | 4.2 | 6.7 |
| 1.5 | 7.9 | 6.4 | 9.5 | 9.5 | 7.2 | 12.1 | 8.7 | 7.2 | 10.0 |
| 2 | 11.1 | 9.6 | 12.5 | 13.7 | 11.6 | 15.9 | 12.2 | 10.9 | 13.5 |
| 3 | 16.3 | 14.8 | 17.8 | 19.0 | 16.7 | 21.3 | 17.5 | 16.2 | 19.0 |
| 4 | 20.5 | 19.0 | 22.1 | 23.4 | 21.1 | 25.7 | 21.8 | 20.4 | 23.2 |
| 6 | 27.9 | 26.5 | 29.4 | 30.7 | 28.3 | 33.3 | 29.1 | 27.7 | 30.6 |
| 8 | 34.1 | 32.8 | 35.5 | 37.3 | 34.9 | 39.7 | 35.5 | 34.1 | 37.0 |
| 12 | 45.8 | 43.9 | 47.8 | 49.0 | 45.7 | 52.1 | 47.2 | 45.4 | 49.1 |
| 16 | 54.7 | 52.7 | 56.6 | 58.0 | 55.0 | 61.2 | 56.2 | 54.2 | 57.9 |
| 24 | 69.7 | 68.0 | 71.6 | 72.5 | 69.8 | 75.1 | 71.0 | 69.5 | 72.6 |
| 32 | 80.4 | 78.8 | 82.1 | 83.4 | 81.3 | 85.3 | 81.7 | 80.3 | 83.1 |
| 48 | 92.6 | 91.5 | 93.7 | 94.3 | 93.0 | 95.5 | 93.4 | 92.5 | 94.2 |
| 64 | 97.1 | 96.4 | 97.9 | 98.3 | 97.5 | 98.9 | 97.6 | 97.1 | 98.1 |
| 96 | 99.4 | 99.0 | 99.7 | 99.7 | 99.5 | 99.9 | 99.6 | 99.3 | 99.8 |
| 128 | 99.9 | 99.7 | 100.0 | 100.0 | 99.9 | 100.0 | 99.9 | 99.8 | 100.0 |
| TABLE 2−Bootstrap data for LAS-D for PM (after excluding outliers). Size refers to equivalent spherical particle diameter. | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| PM Only | SM Only | PM + SM | |||||||
|
| |||||||||
| Size [µm] | Mean | Low | High | Mean | Low | High | Mean | Low | High |
| 1 | 5.0 | 2.7 | 7.3 | 4.4 | 2.6 | 6.2 | 4.7 | 3.3 | 6.1 |
| 1.5 | 7.9 | 4.5 | 10.9 | 6.7 | 3.9 | 9.2 | 7.3 | 5.4 | 9.5 |
| 2 | 12.3 | 10.2 | 14.5 | 11.9 | 10.3 | 13.3 | 12.1 | 10.6 | 13.4 |
| 3 | 18.1 | 15.5 | 20.6 | 17.2 | 15.4 | 19.3 | 17.7 | 16.1 | 19.3 |
| 4 | 23.0 | 20.2 | 26.0 | 21.5 | 19.3 | 23.6 | 22.3 | 20.3 | 24.2 |
| 6 | 30.9 | 27.6 | 34.4 | 28.7 | 26.0 | 30.8 | 29.9 | 27.8 | 32.0 |
| 8 | 37.1 | 33.9 | 40.5 | 34.7 | 32.1 | 36.7 | 35.9 | 33.9 | 38.1 |
| 12 | 47.3 | 44.0 | 50.7 | 45.3 | 43.2 | 47.3 | 46.4 | 44.4 | 48.4 |
| 16 | 55.3 | 52.2 | 58.4 | 53.7 | 52.0 | 55.4 | 54.6 | 52.8 | 56.7 |
| 24 | 68.9 | 65.9 | 71.6 | 67.9 | 66.7 | 69.3 | 68.4 | 66.9 | 70.1 |
| 32 | 78.8 | 76.4 | 81.2 | 78.6 | 77.6 | 79.7 | 78.7 | 77.3 | 80.2 |
| 48 | 90.7 | 88.7 | 92.6 | 91.5 | 90.4 | 92.7 | 91.1 | 89.9 | 92.2 |
| 64 | 95.9 | 94.2 | 97.5 | 96.7 | 95.9 | 97.7 | 96.3 | 95.3 | 97.3 |
| 96 | 98.7 | 97.5 | 99.7 | 99.5 | 99.2 | 99.8 | 99.1 | 98.3 | 99.6 |
| 128 | 99.1 | 97.9 | 99.9 | 99.9 | 99.8 | 100.0 | 99.5 | 98.8 | 100.0 |
FIG. 1−Graphical comparison of the Bootstrap mean curves obtained in Table 1 (LAS-W). For clarity, the confidence intervals are not shown here, but can be found in Table 1.
FIG. 2−Graphical comparison of the Bootstrap mean curves obtained in Table 2 (LAS-D). For clarity, the confidence intervals are not shown here, but can be found in Table 2.