In both round robins, the results for SRM 114p were analyzed separately from the other cements with the objective of producing a reference curve that instrument operators could use to "calibrate" their systems or to validate their methodology. In other words, the reference distribution of SRM 114p could potentially be used to check that the PSD obtained by a particular instrument falls within a defined margin of error, or it could be used to offset measured values by a size-range-dependent factor to bring them within the acceptable margin of error. The more significant errors associated with the measured PSD curves coming from different laboratories and users are most likely due to systematic differences that result because devices differ in systematic ways on nuisance factors. To determine the reference distribution for SRM 114p, two approaches were considered:
Both approaches have advantages and disadvantages. In the first approach (all-inclusive), the calibration curve would be less precise (greater margin of error) as a result of cumulative variations in the precision of different methods. On the other hand, the first approach is simple and convenient, because every customer would use the same calibration curve. In the second approach (technique-specific), the calibration should be more precise, because variations resulting from differences in measurement principle or precision would be eliminated. As a disadvantage, several calibration curves would need to be established independently, one curve for each method, and this would require a statistically relevant pool of round robin participants for each technique. The best possible approach, of course, would be to establish a calibration curve based on an independent determination of the "true" PSD, using a method that can be validated theoretically and/or experimentally; such a method does not currently exist for cement.
In the second round robin (used as the basis for development of a reference curve), 39 participants (93% of all participants) used the LAS technique. Of these, 26 (62% of all participants) dispersed their powders in a liquid (LAS-W) and 13 (31%) used a dry powder method (LAS-D). On the other hand, there was only one participant that reported using SEM and two who reported using EZS. Therefore, using the technique-specific approach (Approach 2), a statistically relevant calibration curve could only be determined for LAS-W and LAS-D. Obviously, all 42 sets could be used if the all-inclusive method (Approach 1) was followed, but the resulting curve would be heavily weighted by the relatively large number of LAS results. Therefore, it was determined that an all-inclusive calibration curve was not appropriate for this database and the development of a reference PSD curve was limited to the LAS technique.
To determine the curve that best represents the consensus PSD for LAS, outliers must first be identified and excluded from calculation of the reference curve. The method that was adopted here is based on calculation of the mean and the two-sided 95% confidence limits using the bootstrap method. The bootstrap method replaces difficult (or even impossible analytical) solutions to statistical problems with raw computing power (details on the bootstrap method are provided in Appendix C of ref. [Ferraris et al., 2002a]). The bootstrap method does not explicitly provide the criteria needed to determine outliers. Therefore, we selected the following criteria for elimination of outliers: if more than 27% of points (i.e., four data points) in a single round robin data set (i.e., a curve provided by one round robin participant) exceed by more than 5% the confidence limits determined by analysis of all data sets in the grouping (i.e., curves provided by all participants), then this individual data set is identified as an outlier. The tolerance value of 5% is based on the absolute difference between the measured value and the closest confidence limit value. Once the outliers are determined, the mean and 95% confidence limits are recalculated excluding the outliers. The resulting mean curve is then defined as the consensus reference curve representing SRM 114p. No judgment was made on how the data were generated in the LAS, i.e., what parameters were used such as refractive indices, dispersion methodology, etc. Discussion of these parameters will be given below.