Application of LADAR in the Analysis of Aggregate Characteristics (2012)

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42 Complete distributions provide more information when comparing the morphological characteristics of different aggre- gates. However, statistical parameters, such as mean and stan- dard deviation, can be used to represent the entire distribution and distinguish different aggregates more concisely and con- veniently. Data transformation (square root of original values) has been performed for data analysis since it better fits the normal distribution. In Appendix H, the histogram and normal quantile plots have been developed using the statistical software JMP for the seven types of coarse aggregate in Set 1. A statistical analysis has been conducted to compare the variability of differ- ent measurement methods and determine whether the differ- ences among the measurement methods for sphericity, flatness ratio, elongation ratio, angularity, and texture are significant. The statistical analysis includes both ANOVA and t-test using JMP. 5.1 Analysis of Variance ANOVA can be used to compare several groups of obser- vations, which are independent and possibly have a different mean for each group. A test of importance is whether all the means are equal statistically. The basic assumptions of the ANOVA test are as follows: 1. Sample data are collected using a simple random sampling method, 2. Sample groups are independent from each other, 3. There are equal variances across groups, and 4. Each group follows a normal distribution. 5.1.1 ANOVA for Coarse Aggregates in Set 1 The ANOVA test performed in this section is used to compare sphericity and FE ratio of all seven coarse aggregates in Set 1 and to determine whether the differences among the measurement methods are significant for shape characteristics. Angularity and texture characteristics cannot be directly compared to each other using ANOVA in JMP because the angularity term and texture term are defined differently. The ANOVA test can only detect whether there are significant differences between results using different methods (i.e., FTI, AIMS II, UIAIA, and manual measurement). Once there is a difference between means of these groups, Tukey’s HSD test is conducted via JMP to deter- mine which mean is significantly different from the others. Table 5-1 presents the method groups for ANOVA. There are three methods used to characterize sphericity and four methods to characterize FE ratios for all the coarse aggregates in Set 1. ANOVA test for sphericity: H0: µ1 = µ2 = µ3 Ha: at least one mean differs where µ1, µ2, µ3 are the means of sphericity using the FTI system, the AIMS II system, and the manual measurements, respectively. Set a = 0.05; reject H0 if p-value < a = 0.05. Multiple comparison tests should be conducted using Tukey’s HSD test. ANOVA test for FE ratio: H0: µ1 = µ2 = µ3 = µ4 Ha: at least one mean differs where µ1, µ2, µ3, µ4 are the means of FE ratio using the FTI, AIMS II, and UIAIA systems, and manual measurements, respectively. Set a = 0.05, reject H0 if p-value < 0.05 (a = 0.05), and then multiple comparison tests should be conducted. Herein Tukey’s HSD test is performed. Table 5-2 and Table 5-3 show the ANOVA summaries for sphericity and FE ratio of the seven types of aggregate in Set 1. ANOVA plots of sphericity and FE ratio for copper ore aggre- gates via JMP are then shown for illustration in Figures 5-1 through 5-8. 5.1.2 ANOVA for Coarse Aggregates in Set 2 The ANOVA test is also performed in JMP to detect whether there is significant difference among the means of three FTI C h a p t e r 5 Statistical Analysis

43 Sphericity FE Ratio Method Group Method Group FTI 1 FTI 1 AIMS II 2 AIMS II 2 Manual measurement 3 UIAIA 3 Manual measurement 4 Table 5-1. Analysis method groups for ANOVA. Sphericity 3/4” 1/2” 3/8” #4 BFS The FTI mean is smaller than the other two means. No significant difference among three means. No significant difference among three means. No significant difference among three means. CO No significant difference among three means. No significant difference among three means. The FTI mean is greater than the other two means. No significant difference among three means. DLT No significant difference among three means. No significant difference among three means. The FTI mean is greater than the other two means. The FTI mean is the smallest, and the AIMS II mean is the greatest. GGC No significant difference among three means. The AIMS II mean is significantly greater than the other two means. The manual measurement mean is significantly smaller than the other two means. No significant difference among three means. GGR The FTI result is smaller than the other two means. The FTI mean is the greatest, and the AIMS II mean is the smallest. The manual measurement mean is significantly smaller than the other two means. No significant difference among three means. IO No significant difference among three means. No significant difference among three means. No significant difference among three means. No significant difference among three means. LST The FTI mean is very close to the manual measurement mean. The FTI mean is very close to the manual measurement mean. No significant difference among three means. No significant difference among three means. Table 5-2. ANOVA summary of sphericity for Set 1.

44 result groups for coarse aggregates in Set 2 [i.e., FTI results before Micro-Deval testing (hereinafter referred to as “MD-0 min.”), FTI results after 15 min. of Micro-Deval testing (hereinafter referred to as “MD-15 min.”), and FTI results after 45 min. of Micro-Deval testing (hereinafter referred to as “MD-45 min.”)]. The hypothesis of the ANOVA test for FTI angularity is as follows: H0: µ1 = µ2 = µ3 Ha: at least one mean differs where µ1, µ2, µ3 are the means of the FTI angularity for MD-0 min., MD-15 min., and MD-45 min., respectively. Set a = 0.05; reject H0 if p-value < a = 0.05. Multiple comparison tests should be conducted using Tukey’s HSD test. The hypothesis of the ANOVA test for FTI texture is as follows: H0: µ1 = µ2 = µ3 Ha: at least one mean differs where µ1, µ2, µ3 are the means of the FTI texture for MD-0 min., MD-15 min., and MD-45 min., respectively. Set a = 0.05; reject H0 if p-value < a = 0.05. Multiple comparison tests should be conducted using Tukey’s HSD test. The ANOVA test results are plotted in Figure 5-9 through Figure 5-16. All the ANOVA tests show that there is insufficient sample evidence to indicate that the duration of the Micro- Deval test has an effect on the true mean of FTI angularity (or texture) of the five Broadway (or Maymead, Salem, and Stras- burg) aggregates. Possible reasons leading to such a conclusion are as follows: (1) the fact that some groups have a variance that is greater than twice the variances of the other groups may violate the third ANOVA assumption of equal variance among groups, and (2) a small sample population of five may violate the forth ANOVA assumption of normal distribution. There- fore, a large sample population of aggregates going through Micro-Deval tests at different times is necessary to study the abrasion effect on aggregates due to the different durations of FE Ratio 3/4” 1/2” 3/8” #4 BFS The FTI mean is greater than the AIMS II and manual measurement means. No significant difference among the four means. No significant difference among the four means. The FTI mean is very close to both the AIMS II and manual measurement means. CO The FTI is slightly greater than the AIMS II and UIAIA means. No significant difference among the four means. No significant difference among the four means. The UIAIA mean is significantly smaller than the other three means. DLT No significant difference among the four means. The UIAIA mean is significantly smaller than the other three means. The FTI and UIAIA means are very close, and both are much smaller than the AIMS II and manual measurement means. The UIAIA mean is significantly smaller than the other three means. GGC No significant difference among the four means. The AIMS II mean is significantly smaller than the other three means. The manual measurement mean is significantly greater than the other three means. The FTI mean is very close to the manual measurement mean, GGR The FTI mean is the greatest mean, and the AIMS II mean is the smallest. The AIMS II mean is significantly smaller than the other three means. The manual measurement and UIAIA means are much greater than the FTI and AIMS II means. No significant difference among the four means. IO No significant difference among the four means. No significant difference among the four means. No significant difference among the four means. No significant difference among the four means. LST The FTI mean is very close to the manual measurement mean. The FTI mean is very close to the manual measurement mean and the UIAIA mean. No significant difference among the four means. The FTI, AIMS II, and manual measurement means are very close to each other. Table 5-3. ANOVA summary of FE ratio for Set 1.

45 Micro-Deval tests. Future research should be conducted on this topic using the FTI system. 5.2 Unpaired t -Test Analysis The t-test analysis assesses whether the means of two groups are statistically different from each other. The t-test can be used to check the validity of the FTI results in comparison to manual measurement results. Flatness ratios of all the ¾-in. aggregates in Set 1 are compared. Since the variance of the FTI results and manual measurements might be different, the unpaired t-test with unequal variances is performed via JMP. The unpaired t-test assesses whether the two groups of flatness ratio results are statistically different in the evaluation of the same aggre- gates. The unpaired t-test is performed as follows: H0: µ1 = µ2, there is no difference in the mean values between the FTI results and the manual measurements Ha: µ1 ≠ µ2, there is a difference in the mean values between the FTI results and the manual measurements where µ1 and µ2 are, respectively, the mean values of the flatness ratio using the FTI system and manual measurements for each type of aggregate. Set a = 0.02; reject H0 if p-value < a = 0.02. Table 5-4 shows the unpaired t-test results of the aggre- gates in Set 1. According to the t-test results, no significant differences are observed among six out of seven ¾-in. aggre- gates, showing consistent results of flatness ratio via FTI and manual measurements with a caliper, except for copper ore ¾-in. aggregates. The t-test result of copper ore ¾-in. aggre- gates indicates that the manually measured flatness ratio is slightly smaller than the results using FTI because the t-ratio is negative. Figure 5-17 through Figure 5-23 plot the t-test results of flatness ratio for all the ¾-in. aggregates via FTI and manual measurements. However, for conciseness, the t-test results for the other aggregates are not listed in this report. Figure 5-1. One-way ANOVA of sphericity for copper ore ¾-in. aggregates. Note: Since p-value = 0.0558 > 0.05, fail to reject H0. Therefore, there is no significant difference between the AIMS II, FTI, and manual measurement means. Figure 5-2. One-way ANOVA of FE ratio for copper ore ¾-in. aggregates. Note: Since p-value = 0.0117 < 0.05, reject H0. Therefore, there is sufficient sample evidence to support that there are significant differences among the four means. Tukey’s HSD test suggests that the manual mean (level B) is slightly smaller than the AIMS II and UIAIA means, whereas the FTI mean (level A) is slightly greater than the AIMS II and UIAIA means.

46 Figure 5-3. One-way ANOVA of sphericity for copper ore ½-in. aggregates. Note: Since p-value = 0.3520 > 0.05, fail to reject H0. Therefore, there is no significant difference among the three means. Figure 5-4. One-way ANOVA of FE ratio for copper ore ½-in. aggregates. Note: Since p-value = 0.4934 > 0.05, fail to reject H0. Therefore, there is insufficient sample evidence to support that there are significant differences among the four means.

47 Figure 5-6. One-way ANOVA of FE ratio for copper ore 3⁄8-in. aggregates. Note: Since p-value = 0.0848 > 0.05, fail to reject H0. Therefore, there is insufficient sample evidence to support that there are significant differences among the four means. Figure 5-5. One-way ANOVA of sphericity for copper ore 3⁄8-in. aggregates. Note: Since p-value = 0.0065 < 0.05, reject H0. Therefore, there is sufficient sample evidence to support that there are significant differences among the three methods. Tukey’s HSD test suggests that the FTI mean is greater than the AIMS II and manual measurement means.

48 Figure 5-8. One-way ANOVA of FE ratio for copper ore #4 aggregates. Note: Since p-value <0.0001 < 00.05, reject H0. Therefore, there is sufficient sample evidence to support that there are significant differences among the four means. Tukey’s HSD test suggests that the UIAIA mean is significantly smaller than the other three means. Figure 5-7. One-way ANOVA of sphericity for copper ore #4 aggregates. Note: Since p-value = 0.6664 > 0.05, fail to reject H0. Therefore, there is no significant difference among the AIMS II, FTI, and manual means.

49 Figure 5-9. One-way ANOVA of angularity for Broadway aggregates. Note: Since p-value = 0.7140 > 0.05, fail to reject H0. Therefore, there is insufficient sample evidence to suggest that there is significant difference of FTI angularity among the three groups (i.e., we cannot detect that the duration of the Micro-Deval test has an effect on the true mean of FTI angularity of the five Broadway aggregates). Figure 5-10. One-way ANOVA of texture for Broadway aggregates. Note: Since p-value = 0.6800 > 0.05, fail to reject H0. Therefore, there is insufficient sample evidence to suggest that there is significant difference of FTI texture among the three groups (i.e., we cannot detect that the duration of the Micro-Deval test has an effect on the true mean of FTI texture of the five Broadway aggregates).

50 Figure 5-11. One-way ANOVA of angularity for Maymead aggregates. Note: Since p-value = 0.6364 > 0.05, fail to reject H0. Therefore, there is insufficient sample evidence to suggest that there is significant difference of FTI angularity among the three groups (i.e., we cannot detect that the duration of the Micro-Deval test has an effect on the true mean of FTI angularity of the five Maymead aggregates). Figure 5-12. One-way ANOVA of texture for Maymead aggregates. Note: Since p-value = 0.4377 > 0.05, fail to reject H0. Therefore, there is insufficient sample evidence to suggest that there is significant difference of FTI texture among the three groups (i.e., we cannot detect that the duration of the Micro-Deval test has an effect on the true mean of FTI texture of the five Maymead aggregates).

51 Figure 5-13. One-way ANOVA of angularity for Salem aggregates. Note: Since p-value = 0.8830 > 0.05, fail to reject H0. Therefore, there is insufficient sample evidence to suggest that there is significant difference of FTI angularity among the three groups (i.e., we cannot detect that the duration of the Micro-Deval test has an effect on the true mean of FTI angularity of the five Salem aggregates). Figure 5-14. One-way ANOVA of texture for Salem aggregates. Note: Since p-value = 0.4753 > 0.05, fail to reject H0. Therefore, there is insufficient sample evidence to suggest that there is significant difference of FTI texture among the three groups (i.e., we cannot detect that the duration of the Micro-Deval test has an effect on the true mean of FTI texture of the five Salem aggregates).

52 α = 0.02 3/4” Aggregates t-ratio p-value Statistical Result Description BFS 5.1939 1.0000 Fail to reject H0 No significant difference between the FTI and manual flatness ratios. CO -2.3407 0.0115 Reject H0 Manual flatness ratio is smaller than the FTI flatness ratio. DLT -1.8715 0.0330 Fail to reject H0 No significant difference between the FTI and manual flatness ratios. GGC -1.9938 0.0255 Fail to reject H0 No significant difference between the FTI and manual flatness ratios. GGR 0.3893 0.6507 Fail to reject H0 No significant difference between the FTI and manual flatness ratios. IO -1.9983 0.0252 Fail to reject H0 No significant difference between the FTI and manual flatness ratios. LST 0.2025 0.5798 Fail to reject H0 No significant difference between the FTI and manual flatness ratios. Table 5-4. Unpaired t-test results of aggregates in Set 1. Figure 5-15. One-way ANOVA of angularity for Strasburg aggregates. Note: Since p-value = 0.9925 > 0.05, fail to reject H0. Therefore, there is insufficient sample evidence to suggest that there is significant difference of FTI angularity among the three groups (i.e., we cannot detect that the duration of the Micro-Deval test has an effect on the true mean of FTI angularity of the five Strasburg aggregates). Figure 5-16. One-way ANOVA of texture for Strasburg aggregates. Note: Since p-value = 0.3074 > 0.05, fail to reject H0. Therefore, there is insufficient sample evidence to suggest that there is significant difference of FTI texture among the three groups (i.e., we cannot detect that the duration of the Micro-Deval test has an effect on the true mean of FTI texture of the five Strasburg aggregates).

53 Figure 5-17. t-test of flatness ratio for blast furnace slag ¾-in. aggregates. Note: Here p-value = 1.0000 > α = 0.02, fail to reject H0. There is no difference between the FTI flatness ratio and the manually measured flatness ratio for blast furnace slag 3/4-in. aggregates. Figure 5-18. t-test of flatness ratio for copper ore ¾-in. aggregates. Note: Here p-value = 0.0115 < α = 0.02, reject H0. There is a difference between the FTI flatness ratio and the manually measured flatness ratio for copper ore 3/4-in. aggregates. As the t-ratio (-2.3407) is negative, the manually measured flatness ratio is smaller compared to the FTI flatness ratio. Figure 5-19. t-test of flatness ratio for dolomite ¾-in. aggregates. Note: Here p-value = 0.0330 > α = 0.02, fail to reject H0. There is no difference between the FTI flatness ratio and the manually measured flatness ratio for dolomite 3/4-in. aggregates. Figure 5-20. t-test of flatness ratio for crushed glacial gravel ¾-in. aggregates. Note: Here p-value = 0.0255 > α = 0.02, fail to reject H0. There is no difference between the FTI flatness ratio and the manually measured flatness ratio for crushed glacial gravel 3/4-in. aggregates.

54 Figure 5-21. t-test of flatness ratio for rounded glacial gravel ¾-in. aggregates. Note: Here p-value = 0.6507 > α = 0.02, fail to reject H0. There is no difference between the FTI flatness ratio and the manually measured flatness ratio for rounded glacial gravel 3/4-in. aggregates. Figure 5-22. t-test of flatness ratio for iron ore ¾-in. aggregates. Note: Here p-value = 0.0252 > α = 0.02, fail to reject H0. There is no difference between the FTI flatness ratio and the manually measured flatness ratio for iron ore 3/4-in. aggregates. Figure 5-23. t-test of flatness ratio for limestone ¾-in. aggregates. Note: Here p-value = 0.5798 > α = 0.02, fail to reject H0. There is no difference between the FTI flatness ratio and manually measured flatness ratio for limestone 3/4-in. aggregates.