As was done in the first round-robin analysis, results for SRM 114p were analyzed separately from the other cements with the objective of producing a reference material that instrument operators could use to "calibrate" their systems or at least to validate their methodology. In other words, the reference distribution of SRM 114p could be used to check that the PSD results obtained by a particular instrument fall within a defined margin of error, or it could be used to offset the measured values by a size-range-dependent factor in order to bring them within the acceptable margin of error. To achieve this goal, two approaches were considered:
1. Establish a single calibration curve that represents an average distribution for all methods inclusive (i.e., all-inclusive approach)
2. Establish a single calibration curve for each method, e.g., LAS-W or EZS (i.e., method-specific approach)
Both approaches have advantages and disadvantages. In the first approach (all-inclusive), the calibration curve would be less precise (greater margin of error) due to propagation of uncertainties as a result of variations in the precision of different methods. On the other hand, the first approach is simpler and more convenient because all customers would use the same calibration curve. In the second approach (method-specific), the calibration should be more precise, because variations resulting from differences in measurement principle or precision between different techniques would be eliminated. As a disadvantage, several calibration curves would have to be established independently: one curve for each method.
There were 39 participants (93 % of all participants) using the laser diffraction method. Of these, 26 (62 % of all participants) dispersed the specimen in a liquid (LAS-W) and 13 used a dry powder method (LAS-D). On the other hand, we had only one participant using SEM and two using EZS. Therefore, following the method-specific approach (Approach 2), we can determine only the calibration curve for LAS-W and LAS-D. Obviously, all 42 sets could be used if the all-inclusive method (Approach 1) is followed, but the resulting curve would be heavily weighted by diffraction results.
To determine the curve that best represents the results, outliers should not be considered in the calculation of the mean curve. Therefore, a key issue is elimination of outliers from the calculation of the reference distribution. The method that was adopted here is based on the calculation of the mean and the two-sided 95 % confidence limits using the bootstrap method (details on the bootstrap method are given in Appendix C of ref. [2]). The bootstrap method does not inherently provide the criteria needed to determine the outlier. Therefore, we selected the following criteria for elimination of outliers: if more than 27 % of the points in a data set (four data points) are greater than 5 % absolute value outside the confidence limits based on analysis of all data sets, then this data set is considered an outlier. The absolute value 5 % is defined as the absolute difference between the measured value and the confidence limits. Once the outliers are determined, the mean and 95 % confidence limits are recalculated excluding the outliers. This mean curve would be defined as the reference curve representing SRM 114p.
Therefore, in the following sections, various mean curves will be calculated depending on the two scenarios: