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available dataset, the comparison of the precision esti- size class for Type 1 samples, the #18 size class for mates was made between the mechanical roundo- Type 3 samples, and the #14 size class for Type 5 meter and the COM-A SPHT and b/l parameters. samples. As shown in Table 37, both the COM-A SPHT and b/l parameters provided lower variability than did Size Measurements the roundometer; the b/l parameter provided better repeatability and reproducibility precision than did the Tables 38, 39, and 40 summarize the percent SPHT parameter for measuring the roundness of the retained statistics for the three sample types. The Type 5 glass beads. computed and critical t-values for a 5% level of sig- nificance were used to compute the rejection proba- Summary of Precision in Roundness Measurement bilities provided in the last column of the tables. A The COM-A b/l parameter consistently provided rejection probability smaller than 0.05 would indi- the smallest repeatability and reproducibility standard cate that measured and target retained values are sig- deviations for roundness of the three types of glass nificantly different. bead samples examined in this study. Although the SPHT precisions surpassed the roundometer preci- Type 1 Samples sions for all three sample types, the SPHT precisions Table 38 compares the percent retained measure- were consistently lower than the b/l precisions. A def- ments on the #50 sieve from the various measuring inite conclusion about the variability of the COM-B methods. As the results indicate, the mechanical sieve results cannot be made at this point because only one and COM-A did not provide accurate measurements set of results on the roundness of each Type 3 and of the size distribution of Type 1 samples. The p val- Type 5 was provided. In addition, the number of data- ues of 0.001 and 0.007 show that the mechanical sieve sets reported for Type 1 glass beads was much smaller and COM-A were statistically different from the tar- than the number of results reported by the roundome- get percent retained value of 50%. The COM-B mea- ter and the COM-A device. surement, on the other hand, was not significantly dif- ferent from the target sieve size as indicated by the COMPARISON OF BIAS OF VARIOUS rejection probability of 0.111. MEASUREMENT METHODS Type 3 Samples The bias of an estimator, i.e., the statistical com- parison of the average measured properties with the Table 39 compares the percent retained measure- target values, is an indication of the accuracy of a test ments on the #18 sieve for the Type 3 samples by the method. In this research, the one-sample t-test was various measuring methods. The COM-B measure- used to test the significance of the difference between ments could not be compared statistically since the measured and target properties and indicate which only one set of size measurements of the Type 3 sam- of the methods evaluated provided the most accurate ples was available. The computed t-values exceed measurements of size and roundness. This analysis of the critical t-statistics for both the COM-A and the bias included a t-test on the size and roundness mea- mechanical sieve methods, indicating that both mea- surements of the most prevalent size class of each surements were statistically different from the target glass bead type. The prevalent size classes are the #50 value. However, the COM-A measurements were Table 38 Results of t-test for comparison of measured and target percent retained on #50 sieve of Type 1 samples Method of No. Average% % Rejection Measurement-- of Retained, Retained, Probability Sample Type Labs Measured Target Sx Computed t Critical t Decision (p) Mechanical 14 48.4 50.0 1.350 4.435 2.160 Reject 0.001 Sieve--Type 1 COM-A--Type 1 8 46.4 50.0 2.697 3.775 2.365 Reject 0.007 COM-B--Type 1 4 46.7 50.0 2.945 2.241 3.182 Accept 0.111 19