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12 CHAPTER 2 Results and Analysis of Ruggedness Experiments 2.1 Analysis Approach while Table 12 and Table 13 present results for tests in FHWA's laboratory using the IPC Global equipment. These Linear regression is an efficient method for analyzing the tables present p-values indicating the significance of the re- ruggedness data. For each combination of mixture, laboratory, gression coefficients for each of the factors included in the temperature, frequency, and confinement, the ruggedness ruggedness experiment. The p-value is the probability of re- test data can be fit to a linear model of the form: jecting the null hypothesis when it is in fact true. For this analysis, it is the probability that the regression coefficient for a Y = B0 + B1X1 + B2X2 + B3X3 + B4X4 + B5X5 particular ruggedness factor is zero when the analysis indicates + B6X6 + B7X7 + Error (1) that it is either greater or less than zero. Thus, low p-values where: indicate the regression coefficient is statistically significant and the ruggedness factor affects the results of the test. Y = measured value The key to analyzing the ruggedness test in this manner is X1, X2, X3, X4, X5, X6, X7 = seven factors included in the selecting critical p-values above which the regression coeffi- ruggedness testing cient is not significant, and it can be concluded that the B0, B1, B2, B3, B4, B5, B6, B7 = model coefficients ruggedness factor does not affect the test result over the range Error = model error tested. It is important to keep the objective of ruggedness test- ing in mind when selecting critical p-values. The objective of From this analysis, the statistical significance of the model ruggedness testing is to identify those controllable factors that coefficients can be determined. For statistically significant likely affect a test, and to establish levels for their control. This factors, the model coefficients can then be used to estimate is different from the usual objective of regression analysis, values for each of the factors that will keep their effect below which is to develop a model to predict an outcome. A predic- a specified level. tive model should only include variables that are highly re- lated to the predicted outcome, so a very low p-value of 0.05 or less is normally used to detect significant variables for pre- 2.2 Dynamic Modulus Test diction models. However, for analysis of ruggedness test data, The results of the dynamic modulus ruggedness testing are selecting a very low p-value may result in the erroneous con- presented in Appendix A. The dynamic modulus ruggedness clusion that one or more of the ruggedness factors does not experiment included the factors listed in Table 3. The re- affect the test result over the range tested and controlling sponses measured in the dynamic modulus ruggedness ex- that factor is not important. For this analysis higher critical periment are listed in Table 9. These include the measured p-values than used in regression modeling should be selected. dynamic modulus and phase angle, and the computed data A critical p-value of 0.10 was used. In Table 10 through quality indicators. Table 13, factors with p-values less than or equal to 0.10 are Regression equations of the form of Equation 1 were de- shown in bold. The analysis was not performed for the un- veloped for each parameter listed in Table 9. The results are confined 40C data for the dense graded mixture tested in summarized in Table 10 through Table 13 for the dynamic the IPC device because the quality of the data was poor. modulus and phase angle. Table 10 and Table 11 present re- The modulus measured in the equipment for this condition sults for tests in AAT's laboratory with the ITC equipment was below the calibrated limit of the machine.