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### Reference distribution using SRM 114p

The round-robin 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 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.
2. Establish a single calibration curve for each method, e.g., LAS-W or EZS.

Both approaches have advantages and disadvantages. In the first case (Approach 1), the calibration curve would be less precise (greater margin of error) due to variations in the precision of different methods being averaged. On the other hand, the first approach is simpler and more convenient because everyone would use the same calibration curve. In the second case (Approach 2), the distribution could be more precise, because variations resulting from differences in measurement principle or precision would be eliminated. As a disadvantage, several calibration curves would have to be established: one for each method.

From the data in Appendix B, there were 15 participants using the LASER diffraction method with the specimen dispersed in a liquid (LAS-W), while no more than two participants used any other method. Thus, following Approach 2 leads to the determination only of the calibration curve for LAS-W. Obviously, all 21 sets could be used if Approach 1 is followed.

Another key issue is to eliminate outliers from the calculation of the reference distribution curve. A criteria for determining outliers was needed. By examining the data in Appendix B for SRM 114p, it is clear that some sets of data are so different from the others that they can be considered as outliers (Figure 1). It is obvious that sets R and L should not be considered. To determine the outliers from the rest of the data, a more sophisticated method called bootstrapping was used. A description of this method and its use is presented in Appendix C. Full discussion of how to select the outliers and determine the mean distribution will be discussed in Sections 3.1.1 and 3.1.2.

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