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Procedures and Guidelines for Validating Contractor Test Data (2020)

Chapter: Annex C - Statistical Tables

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Page 89
Suggested Citation:"Annex C - Statistical Tables." National Academies of Sciences, Engineering, and Medicine. 2020. Procedures and Guidelines for Validating Contractor Test Data. Washington, DC: The National Academies Press. doi: 10.17226/25823.
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Page 89
Page 90
Suggested Citation:"Annex C - Statistical Tables." National Academies of Sciences, Engineering, and Medicine. 2020. Procedures and Guidelines for Validating Contractor Test Data. Washington, DC: The National Academies Press. doi: 10.17226/25823.
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Page 90
Page 91
Suggested Citation:"Annex C - Statistical Tables." National Academies of Sciences, Engineering, and Medicine. 2020. Procedures and Guidelines for Validating Contractor Test Data. Washington, DC: The National Academies Press. doi: 10.17226/25823.
×
Page 91
Page 92
Suggested Citation:"Annex C - Statistical Tables." National Academies of Sciences, Engineering, and Medicine. 2020. Procedures and Guidelines for Validating Contractor Test Data. Washington, DC: The National Academies Press. doi: 10.17226/25823.
×
Page 92
Page 93
Suggested Citation:"Annex C - Statistical Tables." National Academies of Sciences, Engineering, and Medicine. 2020. Procedures and Guidelines for Validating Contractor Test Data. Washington, DC: The National Academies Press. doi: 10.17226/25823.
×
Page 93
Page 94
Suggested Citation:"Annex C - Statistical Tables." National Academies of Sciences, Engineering, and Medicine. 2020. Procedures and Guidelines for Validating Contractor Test Data. Washington, DC: The National Academies Press. doi: 10.17226/25823.
×
Page 94
Page 95
Suggested Citation:"Annex C - Statistical Tables." National Academies of Sciences, Engineering, and Medicine. 2020. Procedures and Guidelines for Validating Contractor Test Data. Washington, DC: The National Academies Press. doi: 10.17226/25823.
×
Page 95
Page 96
Suggested Citation:"Annex C - Statistical Tables." National Academies of Sciences, Engineering, and Medicine. 2020. Procedures and Guidelines for Validating Contractor Test Data. Washington, DC: The National Academies Press. doi: 10.17226/25823.
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Page 96

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Proposed Practice for Validating Contractor Test Data 89 ANNEX C – STATISTICAL TABLES Table C.1. Critical Values, tcrit, for the t-test for multiple levels of significance (Two-Tail) * Two-tail `, degrees of freedom ` = 0.01 ` = 0.025 ` = 0.05 ` = 0.10 1 63.657 25.452 12.706 6.314 2 9.925 6.205 4.303 2.920 3 5.841 4.177 3.182 2.353 4 4.604 3.495 2.776 2.132 5 4.032 3.163 2.571 2.015 6 3.707 2.969 2.447 1.943 7 3.499 2.841 2.365 1.895 8 3.355 2.752 2.306 1.860 9 3.250 2.685 2.262 1.833 10 3.169 2.634 2.228 1.812 11 3.106 2.593 2.201 1.796 12 3.055 2.560 2.179 1.782 13 3.012 2.533 2.160 1.771 14 2.977 2.510 2.145 1.761 15 2.947 2.490 2.131 1.753 16 2.921 2.473 2.120 1.746 17 2.898 2.458 2.110 1.740 18 2.878 2.445 2.101 1.734 19 2.861 2.433 2.093 1.729 20 2.845 2.423 2.086 1.725 21 2.831 2.414 2.080 1.721 22 2.819 2.405 2.074 1.717 23 2.807 2.398 2.069 1.714 24 2.797 2.391 2.064 1.711 25 2.787 2.385 2.060 1.708 26 2.779 2.379 2.056 1.706 27 2.771 2.373 2.052 1.703 28 2.763 2.368 2.048 1.701 29 2.756 2.364 2.045 1.699 30 2.750 2.360 2.042 1.697 40 2.704 2.329 2.021 1.684 50 2.678 2.311 2.009 1.676 60 2.660 2.299 2.000 1.671 70 2.648 2.291 1.994 1.667 80 2.639 2.284 1.990 1.664 90 2.632 2.280 1.987 1.662 100 2.626 2.276 1.984 1.660 110 2.621 2.272 1.982 1.659 120 2.617 2.270 1.980 1.658  2.576 2.242 1.960 1.645 *Table generated using MS Excel (T.INV.2T) function.

90 Procedures and Guidelines for Validating Contractor Test Data Table C.2. Critical Values, Fcrit, for the F-test for a level of significance, α = 0.01 (Two-Tail)* Degrees of Freedom for numerator 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 D eg re es o f F re ed om f or d en om in at or 1 16211 20000 21615 22500 23056 23437 23715 23925 24091 24224 24334 24426 24505 24572 24630 2 198.5 199.0 199.2 199.2 199.3 199.3 199.4 199.4 199.4 199.4 199.4 199.4 199.4 199.4 199.4 3 55.55 49.80 47.47 46.19 45.39 44.84 44.43 44.13 43.88 43.69 43.52 43.39 43.27 43.17 43.08 4 31.33 26.28 24.26 23.15 22.46 21.97 21.62 21.35 21.14 20.97 20.82 20.70 20.60 20.51 20.44 5 22.78 18.31 16.53 15.56 14.94 14.51 14.20 13.96 13.77 13.62 13.49 13.38 13.29 13.21 13.15 6 18.63 14.54 12.92 12.03 11.46 11.07 10.79 10.57 10.39 10.25 10.13 10.03 9.95 9.88 9.81 7 16.24 12.40 10.88 10.05 9.52 9.16 8.89 8.68 8.51 8.38 8.27 8.18 8.10 8.03 7.97 8 14.69 11.04 9.60 8.81 8.30 7.95 7.69 7.50 7.34 7.21 7.10 7.01 6.94 6.87 6.81 9 13.61 10.11 8.72 7.96 7.47 7.13 6.88 6.69 6.54 6.42 6.31 6.23 6.15 6.09 6.03 10 12.83 9.43 8.08 7.34 6.87 6.54 6.30 6.12 5.97 5.85 5.75 5.66 5.59 5.53 5.47 11 12.23 8.91 7.60 6.88 6.42 6.10 5.86 5.68 5.54 5.42 5.32 5.24 5.16 5.10 5.05 12 11.75 8.51 7.23 6.52 6.07 5.76 5.52 5.35 5.20 5.09 4.99 4.91 4.84 4.77 4.72 13 11.37 8.19 6.93 6.23 5.79 5.48 5.25 5.08 4.94 4.82 4.72 4.64 4.57 4.51 4.46 14 11.06 7.92 6.68 6.00 5.56 5.26 5.03 4.86 4.72 4.60 4.51 4.43 4.36 4.30 4.25 15 10.80 7.70 6.48 5.80 5.37 5.07 4.85 4.67 4.54 4.42 4.33 4.25 4.18 4.12 4.07 16 10.58 7.51 6.30 5.64 5.21 4.91 4.69 4.52 4.38 4.27 4.18 4.10 4.03 3.97 3.92 17 10.38 7.35 6.16 5.50 5.07 4.78 4.56 4.39 4.25 4.14 4.05 3.97 3.90 3.84 3.79 18 10.22 7.21 6.03 5.37 4.96 4.66 4.44 4.28 4.14 4.03 3.94 3.86 3.79 3.73 3.68 19 10.07 7.09 5.92 5.27 4.85 4.56 4.34 4.18 4.04 3.93 3.84 3.76 3.70 3.64 3.59 20 9.94 6.99 5.82 5.17 4.76 4.47 4.26 4.09 3.96 3.85 3.76 3.68 3.61 3.55 3.50 21 9.83 6.89 5.73 5.09 4.68 4.39 4.18 4.01 3.88 3.77 3.68 3.60 3.54 3.48 3.43 22 9.73 6.81 5.65 5.02 4.61 4.32 4.11 3.94 3.81 3.70 3.61 3.54 3.47 3.41 3.36 23 9.63 6.73 5.58 4.95 4.54 4.26 4.05 3.88 3.75 3.64 3.55 3.47 3.41 3.35 3.30 24 9.55 6.66 5.52 4.89 4.49 4.20 3.99 3.83 3.69 3.59 3.50 3.42 3.35 3.30 3.25 25 9.48 6.60 5.46 4.84 4.43 4.15 3.94 3.78 3.64 3.54 3.45 3.37 3.30 3.25 3.20 26 9.41 6.54 5.41 4.79 4.38 4.10 3.89 3.73 3.60 3.49 3.40 3.33 3.26 3.20 3.15 27 9.34 6.49 5.36 4.74 4.34 4.06 3.85 3.69 3.56 3.45 3.36 3.28 3.22 3.16 3.11 28 9.28 6.44 5.32 4.70 4.30 4.02 3.81 3.65 3.52 3.41 3.32 3.25 3.18 3.12 3.07 29 9.23 6.40 5.28 4.66 4.26 3.98 3.77 3.61 3.48 3.38 3.29 3.21 3.15 3.09 3.04 30 9.18 6.35 5.24 4.62 4.23 3.95 3.74 3.58 3.45 3.34 3.25 3.18 3.11 3.06 3.01 40 8.83 6.07 4.98 4.37 3.99 3.71 3.51 3.35 3.22 3.12 3.03 2.95 2.89 2.83 2.78 50 8.63 5.90 4.83 4.23 3.85 3.58 3.38 3.22 3.09 2.99 2.90 2.82 2.76 2.70 2.65 60 8.49 5.79 4.73 4.14 3.76 3.49 3.29 3.13 3.01 2.90 2.82 2.74 2.68 2.62 2.57 70 8.40 5.72 4.66 4.08 3.70 3.43 3.23 3.08 2.95 2.85 2.76 2.68 2.62 2.56 2.51 80 8.33 5.67 4.61 4.03 3.65 3.39 3.19 3.03 2.91 2.80 2.72 2.64 2.58 2.52 2.47 90 8.28 5.62 4.57 3.99 3.62 3.35 3.15 3.00 2.87 2.77 2.68 2.61 2.54 2.49 2.44 100 8.24 5.59 4.54 3.96 3.59 3.33 3.13 2.97 2.85 2.74 2.66 2.58 2.52 2.46 2.41 110 8.21 5.56 4.52 3.94 3.57 3.30 3.11 2.95 2.83 2.72 2.64 2.56 2.50 2.44 2.39 120 8.18 5.54 4.50 3.92 3.55 3.28 3.09 2.93 2.81 2.71 2.62 2.54 2.48 2.42 2.37  7.88 5.30 4.28 3.72 3.35 3.09 2.90 2.75 2.62 2.52 2.43 2.36 2.30 2.24 2.19 *Table generated using MS Excel (F.INV) function.

Proposed Practice for Validating Contractor Test Data 91 Table C.3. Critical Values, Fcrit, for the F-test for a level of significance, α = 0.025 (Two-Tail)* Degrees of Freedom for numerator 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 D eg re es o f F re ed om f or d en om in at or 1 2593 3200 3458 3600 3689 3750 3794 3828 3854 3876 3893 3908 3920 3931 3941 2 78.5 79.0 79.2 79.2 79.3 79.3 79.4 79.4 79.4 79.4 79.4 79.4 79.4 79.4 79.4 3 29.07 26.35 25.22 24.60 24.20 23.93 23.73 23.57 23.45 23.36 23.28 23.21 23.15 23.10 23.06 4 18.62 15.89 14.77 14.15 13.75 13.48 13.28 13.13 13.01 12.91 12.83 12.76 12.70 12.65 12.61 5 14.52 11.93 10.86 10.28 9.90 9.64 9.45 9.31 9.19 9.10 9.02 8.95 8.90 8.85 8.81 6 12.40 9.93 8.91 8.35 8.00 7.75 7.56 7.42 7.31 7.22 7.14 7.08 7.02 6.98 6.94 7 11.12 8.74 7.77 7.22 6.88 6.64 6.46 6.32 6.21 6.12 6.05 5.99 5.93 5.89 5.85 8 10.28 7.96 7.02 6.49 6.15 5.92 5.74 5.61 5.50 5.41 5.34 5.28 5.23 5.18 5.14 9 9.68 7.42 6.49 5.98 5.65 5.41 5.24 5.11 5.00 4.92 4.85 4.79 4.73 4.69 4.65 10 9.23 7.01 6.10 5.60 5.27 5.04 4.88 4.74 4.64 4.56 4.48 4.42 4.37 4.33 4.29 11 8.89 6.70 5.81 5.31 4.99 4.76 4.60 4.47 4.36 4.28 4.21 4.15 4.10 4.05 4.01 12 8.61 6.45 5.57 5.08 4.76 4.54 4.37 4.25 4.14 4.06 3.99 3.93 3.88 3.83 3.80 13 8.39 6.26 5.38 4.90 4.58 4.36 4.20 4.07 3.97 3.88 3.81 3.75 3.70 3.66 3.62 14 8.20 6.09 5.23 4.74 4.43 4.21 4.05 3.92 3.82 3.74 3.67 3.61 3.56 3.51 3.48 15 8.05 5.95 5.10 4.62 4.31 4.09 3.93 3.80 3.70 3.62 3.55 3.49 3.44 3.39 3.36 16 7.91 5.83 4.98 4.51 4.20 3.98 3.82 3.70 3.60 3.51 3.44 3.39 3.33 3.29 3.25 17 7.80 5.73 4.89 4.42 4.11 3.89 3.73 3.61 3.51 3.42 3.36 3.30 3.25 3.20 3.16 18 7.70 5.65 4.80 4.33 4.03 3.82 3.65 3.53 3.43 3.35 3.28 3.22 3.17 3.13 3.09 19 7.61 5.57 4.73 4.26 3.96 3.75 3.59 3.46 3.36 3.28 3.21 3.15 3.10 3.06 3.02 20 7.53 5.50 4.67 4.20 3.90 3.69 3.53 3.40 3.30 3.22 3.15 3.09 3.04 3.00 2.96 21 7.46 5.44 4.61 4.15 3.84 3.63 3.47 3.35 3.25 3.17 3.10 3.04 2.99 2.94 2.91 22 7.40 5.38 4.56 4.10 3.79 3.58 3.42 3.30 3.20 3.12 3.05 2.99 2.94 2.90 2.86 23 7.34 5.33 4.51 4.05 3.75 3.54 3.38 3.26 3.16 3.08 3.01 2.95 2.90 2.85 2.82 24 7.29 5.29 4.47 4.01 3.71 3.50 3.34 3.22 3.12 3.04 2.97 2.91 2.86 2.82 2.78 25 7.24 5.25 4.43 3.97 3.67 3.46 3.31 3.18 3.08 3.00 2.93 2.87 2.82 2.78 2.74 26 7.20 5.21 4.40 3.94 3.64 3.43 3.27 3.15 3.05 2.97 2.90 2.84 2.79 2.75 2.71 27 7.16 5.18 4.36 3.91 3.61 3.40 3.24 3.12 3.02 2.94 2.87 2.81 2.76 2.72 2.68 28 7.13 5.15 4.33 3.88 3.58 3.37 3.22 3.09 2.99 2.91 2.84 2.79 2.74 2.69 2.65 29 7.09 5.12 4.31 3.85 3.56 3.35 3.19 3.07 2.97 2.89 2.82 2.76 2.71 2.67 2.63 30 7.06 5.09 4.28 3.83 3.53 3.32 3.17 3.04 2.95 2.86 2.80 2.74 2.69 2.64 2.60 40 6.84 4.90 4.10 3.66 3.36 3.16 3.00 2.88 2.78 2.70 2.63 2.57 2.52 2.48 2.44 50 6.71 4.79 4.00 3.56 3.27 3.06 2.91 2.78 2.69 2.61 2.54 2.48 2.43 2.38 2.34 60 6.63 4.72 3.93 3.49 3.20 3.00 2.84 2.72 2.63 2.54 2.48 2.42 2.37 2.32 2.28 70 6.57 4.67 3.89 3.45 3.16 2.96 2.80 2.68 2.58 2.50 2.43 2.37 2.32 2.28 2.24 80 6.53 4.63 3.85 3.41 3.13 2.92 2.77 2.65 2.55 2.47 2.40 2.34 2.29 2.25 2.21 90 6.50 4.60 3.83 3.39 3.10 2.90 2.74 2.62 2.53 2.44 2.38 2.32 2.27 2.22 2.18 100 6.47 4.58 3.80 3.37 3.08 2.88 2.72 2.60 2.51 2.43 2.36 2.30 2.25 2.20 2.16 110 6.45 4.56 3.79 3.35 3.07 2.86 2.71 2.59 2.49 2.41 2.34 2.28 2.23 2.19 2.15 120 6.43 4.55 3.77 3.34 3.05 2.85 2.70 2.58 2.48 2.40 2.33 2.27 2.22 2.17 2.13  6.24 4.38 3.62 3.19 2.91 2.71 2.56 2.44 2.34 2.26 2.19 2.13 2.08 2.03 1.99 *Table generated using MS Excel (F.INV) function.

92 Procedures and Guidelines for Validating Contractor Test Data Table C.4. Critical Values, Fcrit, for the F-test for a level of significance, α = 0.05 (Two-Tail)* Degrees of Freedom for numerator 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 D eg re es o f F re ed om f or d en om in at or 1 648 799 864 900 922 937 948 957 963 969 973 977 980 983 985 2 38.5 39.0 39.2 39.2 39.3 39.3 39.4 39.4 39.4 39.4 39.4 39.4 39.4 39.4 39.4 3 17.44 16.04 15.44 15.10 14.88 14.73 14.62 14.54 14.47 14.42 14.37 14.34 14.30 14.28 14.25 4 12.22 10.65 9.98 9.60 9.36 9.20 9.07 8.98 8.90 8.84 8.79 8.75 8.71 8.68 8.66 5 10.01 8.43 7.76 7.39 7.15 6.98 6.85 6.76 6.68 6.62 6.57 6.52 6.49 6.46 6.43 6 8.81 7.26 6.60 6.23 5.99 5.82 5.70 5.60 5.52 5.46 5.41 5.37 5.33 5.30 5.27 7 8.07 6.54 5.89 5.52 5.29 5.12 4.99 4.90 4.82 4.76 4.71 4.67 4.63 4.60 4.57 8 7.57 6.06 5.42 5.05 4.82 4.65 4.53 4.43 4.36 4.30 4.24 4.20 4.16 4.13 4.10 9 7.21 5.71 5.08 4.72 4.48 4.32 4.20 4.10 4.03 3.96 3.91 3.87 3.83 3.80 3.77 10 6.94 5.46 4.83 4.47 4.24 4.07 3.95 3.85 3.78 3.72 3.66 3.62 3.58 3.55 3.52 11 6.72 5.26 4.63 4.28 4.04 3.88 3.76 3.66 3.59 3.53 3.47 3.43 3.39 3.36 3.33 12 6.55 5.10 4.47 4.12 3.89 3.73 3.61 3.51 3.44 3.37 3.32 3.28 3.24 3.21 3.18 13 6.41 4.97 4.35 4.00 3.77 3.60 3.48 3.39 3.31 3.25 3.20 3.15 3.12 3.08 3.05 14 6.30 4.86 4.24 3.89 3.66 3.50 3.38 3.29 3.21 3.15 3.09 3.05 3.01 2.98 2.95 15 6.20 4.77 4.15 3.80 3.58 3.41 3.29 3.20 3.12 3.06 3.01 2.96 2.92 2.89 2.86 16 6.12 4.69 4.08 3.73 3.50 3.34 3.22 3.12 3.05 2.99 2.93 2.89 2.85 2.82 2.79 17 6.04 4.62 4.01 3.66 3.44 3.28 3.16 3.06 2.98 2.92 2.87 2.82 2.79 2.75 2.72 18 5.98 4.56 3.95 3.61 3.38 3.22 3.10 3.01 2.93 2.87 2.81 2.77 2.73 2.70 2.67 19 5.92 4.51 3.90 3.56 3.33 3.17 3.05 2.96 2.88 2.82 2.76 2.72 2.68 2.65 2.62 20 5.87 4.46 3.86 3.51 3.29 3.13 3.01 2.91 2.84 2.77 2.72 2.68 2.64 2.60 2.57 21 5.83 4.42 3.82 3.48 3.25 3.09 2.97 2.87 2.80 2.73 2.68 2.64 2.60 2.56 2.53 22 5.79 4.38 3.78 3.44 3.22 3.05 2.93 2.84 2.76 2.70 2.65 2.60 2.56 2.53 2.50 23 5.75 4.35 3.75 3.41 3.18 3.02 2.90 2.81 2.73 2.67 2.62 2.57 2.53 2.50 2.47 24 5.72 4.32 3.72 3.38 3.15 2.99 2.87 2.78 2.70 2.64 2.59 2.54 2.50 2.47 2.44 25 5.69 4.29 3.69 3.35 3.13 2.97 2.85 2.75 2.68 2.61 2.56 2.51 2.48 2.44 2.41 26 5.66 4.27 3.67 3.33 3.10 2.94 2.82 2.73 2.65 2.59 2.54 2.49 2.45 2.42 2.39 27 5.63 4.24 3.65 3.31 3.08 2.92 2.80 2.71 2.63 2.57 2.51 2.47 2.43 2.39 2.36 28 5.61 4.22 3.63 3.29 3.06 2.90 2.78 2.69 2.61 2.55 2.49 2.45 2.41 2.37 2.34 29 5.59 4.20 3.61 3.27 3.04 2.88 2.76 2.67 2.59 2.53 2.48 2.43 2.39 2.36 2.32 30 5.57 4.18 3.59 3.25 3.03 2.87 2.75 2.65 2.57 2.51 2.46 2.41 2.37 2.34 2.31 40 5.42 4.05 3.46 3.13 2.90 2.74 2.62 2.53 2.45 2.39 2.33 2.29 2.25 2.21 2.18 50 5.34 3.97 3.39 3.05 2.83 2.67 2.55 2.46 2.38 2.32 2.26 2.22 2.18 2.14 2.11 60 5.29 3.93 3.34 3.01 2.79 2.63 2.51 2.41 2.33 2.27 2.22 2.17 2.13 2.09 2.06 70 5.25 3.89 3.31 2.97 2.75 2.59 2.47 2.38 2.30 2.24 2.18 2.14 2.10 2.06 2.03 80 5.22 3.86 3.28 2.95 2.73 2.57 2.45 2.35 2.28 2.21 2.16 2.11 2.07 2.03 2.00 90 5.20 3.84 3.26 2.93 2.71 2.55 2.43 2.34 2.26 2.19 2.14 2.09 2.05 2.02 1.98 100 5.18 3.83 3.25 2.92 2.70 2.54 2.42 2.32 2.24 2.18 2.12 2.08 2.04 2.00 1.97 110 5.16 3.82 3.24 2.90 2.68 2.53 2.40 2.31 2.23 2.17 2.11 2.07 2.02 1.99 1.96 120 5.15 3.80 3.23 2.89 2.67 2.52 2.39 2.30 2.22 2.16 2.10 2.05 2.01 1.98 1.94  5.03 3.69 3.12 2.79 2.57 2.41 2.29 2.19 2.11 2.05 1.99 1.95 1.90 1.87 1.83 *Table generated using MS Excel (F.INV) function.

Proposed Practice for Validating Contractor Test Data 93 Table C.5. Critical Values, Fcrit, for the F-test for a level of significance, α = 0.1 (Two-Tail)* Degrees of Freedom for numerator 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 D eg re es o f F re ed om f or d en om in at or 1 161 200 216 225 230 234 237 239 241 242 243 244 245 245 246 2 18.5 19.0 19.2 19.2 19.3 19.3 19.4 19.4 19.4 19.4 19.4 19.4 19.4 19.4 19.4 3 10.13 9.55 9.28 9.12 9.01 8.94 8.89 8.85 8.81 8.79 8.76 8.74 8.73 8.71 8.70 4 7.71 6.94 6.59 6.39 6.26 6.16 6.09 6.04 6.00 5.96 5.94 5.91 5.89 5.87 5.86 5 6.61 5.79 5.41 5.19 5.05 4.95 4.88 4.82 4.77 4.74 4.70 4.68 4.66 4.64 4.62 6 5.99 5.14 4.76 4.53 4.39 4.28 4.21 4.15 4.10 4.06 4.03 4.00 3.98 3.96 3.94 7 5.59 4.74 4.35 4.12 3.97 3.87 3.79 3.73 3.68 3.64 3.60 3.57 3.55 3.53 3.51 8 5.32 4.46 4.07 3.84 3.69 3.58 3.50 3.44 3.39 3.35 3.31 3.28 3.26 3.24 3.22 9 5.12 4.26 3.86 3.63 3.48 3.37 3.29 3.23 3.18 3.14 3.10 3.07 3.05 3.03 3.01 10 4.96 4.10 3.71 3.48 3.33 3.22 3.14 3.07 3.02 2.98 2.94 2.91 2.89 2.86 2.85 11 4.84 3.98 3.59 3.36 3.20 3.09 3.01 2.95 2.90 2.85 2.82 2.79 2.76 2.74 2.72 12 4.75 3.89 3.49 3.26 3.11 3.00 2.91 2.85 2.80 2.75 2.72 2.69 2.66 2.64 2.62 13 4.67 3.81 3.41 3.18 3.03 2.92 2.83 2.77 2.71 2.67 2.63 2.60 2.58 2.55 2.53 14 4.60 3.74 3.34 3.11 2.96 2.85 2.76 2.70 2.65 2.60 2.57 2.53 2.51 2.48 2.46 15 4.54 3.68 3.29 3.06 2.90 2.79 2.71 2.64 2.59 2.54 2.51 2.48 2.45 2.42 2.40 16 4.49 3.63 3.24 3.01 2.85 2.74 2.66 2.59 2.54 2.49 2.46 2.42 2.40 2.37 2.35 17 4.45 3.59 3.20 2.96 2.81 2.70 2.61 2.55 2.49 2.45 2.41 2.38 2.35 2.33 2.31 18 4.41 3.55 3.16 2.93 2.77 2.66 2.58 2.51 2.46 2.41 2.37 2.34 2.31 2.29 2.27 19 4.38 3.52 3.13 2.90 2.74 2.63 2.54 2.48 2.42 2.38 2.34 2.31 2.28 2.26 2.23 20 4.35 3.49 3.10 2.87 2.71 2.60 2.51 2.45 2.39 2.35 2.31 2.28 2.25 2.22 2.20 21 4.32 3.47 3.07 2.84 2.68 2.57 2.49 2.42 2.37 2.32 2.28 2.25 2.22 2.20 2.18 22 4.30 3.44 3.05 2.82 2.66 2.55 2.46 2.40 2.34 2.30 2.26 2.23 2.20 2.17 2.15 23 4.28 3.42 3.03 2.80 2.64 2.53 2.44 2.37 2.32 2.27 2.24 2.20 2.18 2.15 2.13 24 4.26 3.40 3.01 2.78 2.62 2.51 2.42 2.36 2.30 2.25 2.22 2.18 2.15 2.13 2.11 25 4.24 3.39 2.99 2.76 2.60 2.49 2.40 2.34 2.28 2.24 2.20 2.16 2.14 2.11 2.09 26 4.23 3.37 2.98 2.74 2.59 2.47 2.39 2.32 2.27 2.22 2.18 2.15 2.12 2.09 2.07 27 4.21 3.35 2.96 2.73 2.57 2.46 2.37 2.31 2.25 2.20 2.17 2.13 2.10 2.08 2.06 28 4.20 3.34 2.95 2.71 2.56 2.45 2.36 2.29 2.24 2.19 2.15 2.12 2.09 2.06 2.04 29 4.18 3.33 2.93 2.70 2.55 2.43 2.35 2.28 2.22 2.18 2.14 2.10 2.08 2.05 2.03 30 4.17 3.32 2.92 2.69 2.53 2.42 2.33 2.27 2.21 2.16 2.13 2.09 2.06 2.04 2.01 40 4.08 3.23 2.84 2.61 2.45 2.34 2.25 2.18 2.12 2.08 2.04 2.00 1.97 1.95 1.92 50 4.03 3.18 2.79 2.56 2.40 2.29 2.20 2.13 2.07 2.03 1.99 1.95 1.92 1.89 1.87 60 4.00 3.15 2.76 2.53 2.37 2.25 2.17 2.10 2.04 1.99 1.95 1.92 1.89 1.86 1.84 70 3.98 3.13 2.74 2.50 2.35 2.23 2.14 2.07 2.02 1.97 1.93 1.89 1.86 1.84 1.81 80 3.96 3.11 2.72 2.49 2.33 2.21 2.13 2.06 2.00 1.95 1.91 1.88 1.84 1.82 1.79 90 3.95 3.10 2.71 2.47 2.32 2.20 2.11 2.04 1.99 1.94 1.90 1.86 1.83 1.80 1.78 100 3.94 3.09 2.70 2.46 2.31 2.19 2.10 2.03 1.97 1.93 1.89 1.85 1.82 1.79 1.77 110 3.93 3.08 2.69 2.45 2.30 2.18 2.09 2.02 1.97 1.92 1.88 1.84 1.81 1.78 1.76 120 3.92 3.07 2.68 2.45 2.29 2.18 2.09 2.02 1.96 1.91 1.87 1.83 1.80 1.78 1.75  3.84 3.00 2.61 2.37 2.21 2.10 2.01 1.94 1.88 1.83 1.79 1.75 1.72 1.69 1.67 *Table generated using MS Excel (F.INV) function.

Abbreviations and acronyms used without definitions in TRB publications: A4A Airlines for America AAAE American Association of Airport Executives AASHO American Association of State Highway Officials AASHTO American Association of State Highway and Transportation Officials ACI–NA Airports Council International–North America ACRP Airport Cooperative Research Program ADA Americans with Disabilities Act APTA American Public Transportation Association ASCE American Society of Civil Engineers ASME American Society of Mechanical Engineers ASTM American Society for Testing and Materials ATA American Trucking Associations CTAA Community Transportation Association of America CTBSSP Commercial Truck and Bus Safety Synthesis Program DHS Department of Homeland Security DOE Department of Energy EPA Environmental Protection Agency FAA Federal Aviation Administration FAST Fixing America’s Surface Transportation Act (2015) FHWA Federal Highway Administration FMCSA Federal Motor Carrier Safety Administration FRA Federal Railroad Administration FTA Federal Transit Administration HMCRP Hazardous Materials Cooperative Research Program IEEE Institute of Electrical and Electronics Engineers ISTEA Intermodal Surface Transportation Efficiency Act of 1991 ITE Institute of Transportation Engineers MAP-21 Moving Ahead for Progress in the 21st Century Act (2012) NASA National Aeronautics and Space Administration NASAO National Association of State Aviation Officials NCFRP National Cooperative Freight Research Program NCHRP National Cooperative Highway Research Program NHTSA National Highway Traffic Safety Administration NTSB National Transportation Safety Board PHMSA Pipeline and Hazardous Materials Safety Administration RITA Research and Innovative Technology Administration SAE Society of Automotive Engineers SAFETEA-LU Safe, Accountable, Flexible, Efficient Transportation Equity Act: A Legacy for Users (2005) TCRP Transit Cooperative Research Program TDC Transit Development Corporation TEA-21 Transportation Equity Act for the 21st Century (1998) TRB Transportation Research Board TSA Transportation Security Administration U.S. DOT United States Department of Transportation

TRA N SPO RTATIO N RESEA RCH BO A RD 500 Fifth Street, N W W ashington, D C 20001 A D D RESS SERV ICE REQ U ESTED ISBN 978-0-309-48144-1 9 7 8 0 3 0 9 4 8 1 4 4 1 9 0 0 0 0 N O N -PR O FIT O R G . U .S. PO STA G E PA ID C O LU M B IA , M D PER M IT N O . 88 Procedures and G uidelines for Validating Contractor Test D ata N CH RP Research Report 946 TRB

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In the development of a quality assurance program, a state highway agency (SHA) incorporates policies and procedures for assessing how well the materials and construction used by a contractor on a construction project satisfy the agency's specifications.

The TRB National Cooperative Highway Research Program's NCHRP Research Report 946: Procedures and Guidelines for Validating Contractor Test Data reviews and evaluates the procedures and practices used in the acceptance of construction materials. The report also proposes a related practice for incorporation into AASHTO Standard Specifications for Transportation Materials and Methods of Sampling and Testing.

Supplemental files to the report include Appendices A through E, available as a single PDF file, a State Highway Agency Survey (Appendix A), Survey Responses (Appendix B), Numerical Simulations (Appendix C), State Highway Agency Date Analysis (Appendix D), and Statistical Tables (Appendix E).

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