Guidance for the Design and Application of Shoulder and Centerline Rumble Strips (2009)

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161 A P P E N D I X F This appendix presents the generalized linear model (GLM) results to investigate the effect of treatment with shoulder rumble strips on the four crash types of interest: • TOT crashes • FI crashes • SVROR crashes • SVROR FI crashes Two groups of tables are presented in this appendix: • Tables F-1 through F-4: GLM results based on all site types (i.e., all nontreatment and treatment sites in the study) • Tables F-5 through F-8: GLM results based on all before-after sites and nontreatment cross-sectional sites (i.e., same sites as in Tables G-1 through G-4 but without treatment cross- sectional sites). These results should be most comparable to the SPF results since both approaches use the same types of sites. The statistics shown for each crash type, roadway type, and state (individually or combined) are: • Intercept: estimate and standard error • ADT (on natural log scale): estimate, standard error, and p-value (i.e., significance level) • Outside RHR: estimate, standard error, and p-value • Rumble strip effect: estimate, standard error, and p-value. Rumble strip statistics are bolded whenever the effect is statistically significant at the 0.10 level • Overdispersion parameter: estimate and standard error GLM Analysis Results for Safety Effectiveness of Shoulder Rumble Strips Each regression model is represented by the following equation: where a (i.e., intercept), b, c, and d are the coefficients whose estimates are shown in Tables F-1 through F-8. The coeffi- cient d only applies to treatment sites since IRS is a 0,1 variable where 0 indicates absence and 1 presence of shoulder rumble strips. For states that treat both sides of a divided highway as separate sites (i.e., Missouri and Pennsylvania), the RHR vari- ables in the models represent the values for a single side of the divided highway. When both sides of a divided highway are treated as a single site (i.e., Minnesota sites), the RHR variables in the model represent average values for both directions of travel. Similarly, the RHR variable in the model for rural two-lane roads represents the average RHR for both sides of the roadway. Tables F-1 through F-8 are the companion tables to Tables 29 through 36. Number of sites and number of site-years for each model are provided in those tables. To obtain the percent change due to rumble strip treatment shown in Tables 29 through 36, use the rumble strip coefficient, d, shown in Tables F-1 through F-8 and calculate: Lower and upper 95-percent confidence intervals for the percent change are calculated in a similar fashion based on lower and upper 95-percent confidence intervals of the esti- mates in Tables F-1 through F-8 (confidence limits calculated but not shown in these tables). Percent change d= ( )−[ ]100 1exp Expected crashes mi yr a blnADT cRHR dIOut= + + +exp RS( )

Intercept lnADT Outside RHR Rumble stripsa Overdispersion Roadway type State Estimate SE Estimate SE p-value Estimate SE p-value Estimate SE p-value Estimate SE Urban freeways PA –9.53 1.04 1.00 0.10 <.0001 0.15 0.10 0.111 –0.04 0.06 0.496 0.22 0.03 Combined –9.22 1.46 1.04 0.15 <.0001 0.01 0.07 0.890 0.23 0.03 MO –6.55 2.11 0.79 0.21 0.000 0.08 0.07 0.227 0.19 0.03 Rural freeways PA –4.27 1.85 0.50 0.19 0.008 0.08 0.11 0.480 0.21 0.05 Combined –5.90 1.10 0.64 0.12 <.0001 0.26 0.06 <.0001 0.18 0.08 0.021 0.24 0.03 MN –8.03 1.07 0.88 0.12 <.0001 0.15 0.06 0.010 0.15 0.08 0.053 0.11 0.02 MO –6.53 2.96 0.81 0.31 0.009 0.25 0.11 0.027 0.42 0.08 Rural multilane divided highways (nonfreeways) PA –0.97 4.23 0.20 0.46 0.653 –0.21 0.24 0.374 0.23 0.12 Combined –6.27 0.87 0.66 0.10 <.0001 0.26 0.04 <.0001 –0.15 0.11 0.178 0.54 0.04 MN –5.72 1.11 0.56 0.14 <.0001 0.31 0.05 <.0001 –0.04 0.07 0.594 0.27 0.04 MO –4.71 2.01 0.64 0.23 0.006 –0.18 0.88 0.836 0.99 0.11 Rural two-lane roads PA –4.55 0.80 0.57 0.10 <.0001 –0.28 0.19 0.145 0.36 0.06 a Statistics are bolded when p ≤ 0.10. Intercept lnADT Outside RHR Rumble strips a Overdispersion Roadway type State Estimate SE Estimate SE p-value Estimate SE p-value Estimate SE p-value Estimate SE Urban freeways PA –11.19 1.27 1.08 0.12 <.0001 0.20 0.12 0.086 –0.10 0.08 0.222 0.28 0.05 Combined –10.55 1.26 1.08 0.13 <.0001 –0.08 0.07 0.284 0.10 0.03 MO –9.95 1.67 1.02 0.17 <.0001 –0.03 0.09 0.758 0.12 0.04Rural freeways PA –10.16 2.32 1.04 0.24 <.0001 –0.12 0.12 0.316 0.06 0.07 Combined –7.71 1.24 0.72 0.13 <.0001 0.23 0.07 0.001 0.01 0.11 0.956 0.22 0.04 MN –9.18 1.27 0.90 0.14 <.0001 0.11 0.07 0.131 0.07 0.09 0.474 0.09 0.04 MO –14.93 3.71 1.59 0.40 <.0001 0.05 0.20 0.799 0.38 0.12 Rural multilane divided highways (nonfreeways) PA 0.28 0.24 –0.54 0.27 0.045 0.40 0.22 Combined –7.16 0.77 0.65 0.09 <.0001 0.31 0.05 <.0001 –0.32 0.12 0.006 0.50 0.06 MN –6.45 1.10 0.53 0.14 0.0002 0.31 0.06 <.0001 –0.14 0.10 0.155 0.24 0.08 MO –8.37 1.95 0.61 0.25 0.013 0.71 0.19 0.0002 –0.51 0.75 0.501 0.51 0.11 Rural two-lane roads PA –5.44 0.86 0.61 0.10 <.0001 –0.18 0.22 0.415 0.37 0.08 a Statistics are bolded when p ≤ 0.10. Table F-1. GLM estimates for TOT crashes based on all site types. Table F-2. GLM estimates for FI crashes based on all site types.

Table F-3. GLM estimates for SVROR crashes based on all site types. Table F-4. GLM estimates for SVROR FI crashes based on all site types. Intercept lnADT Outside RHR Rumble stripsa Overdispersion Roadway type State Estimate SE Estimate SE p-value Estimate SE p-value Estimate SE p-value Estimate SE Urban freeways PA –6.79 0.90 0.72 0.09 <.0001 –0.04 0.08 0.625 0.19 0.04 Combined –5.94 1.57 0.65 0.16 <.0001 –0.10 0.07 0.175 0.25 0.04 MO –5.41 2.31 0.61 0.23 0.009 –0.07 0.07 0.357 0.23 0.04 Rural freeways PA –3.42 2.40 0.29 0.25 0.256 0.26 0.14 0.057 –0.02 0.13 0.875 0.26 0.07 Combined –7.11 1.08 0.62 0.11 <.0001 0.39 0.08 <.0001 0.35 0.12 0.004 0.39 0.05 MN –8.74 1.21 0.83 0.13 <.0001 0.17 0.08 0.035 0.33 0.12 0.006 0.24 0.05 MO –12.64 2.98 1.26 0.32 <.0001 0.34 0.22 0.128 0.53 0.16 0.001 0.45 0.12 Rural multilane divided highways (nonfreeways) PA –0.59 6.16 0.12 0.65 0.855 –0.27 0.17 0.117 0.17 0.14 Combined –5.24 0.83 0.37 0.10 0.0002 0.42 0.05 <.0001 –0.35 0.17 0.037 0.72 0.07 MN –3.82 0.83 0.10 0.10 0.353 0.50 0.08 <.0001 0.18 0.13 0.180 0.51 0.13 MO –0.33 0.18 –0.09 0.79 0.906 1.23 0.18 Rural two-lane roads PA –2.64 0.89 0.28 0.11 0.008 –0.60 0.22 0.008 0.49 0.09 a Statistics are bolded when p ≤ 0.10. Intercept lnADT Outside RHR Rumble stripsa Overdispersion Roadway type State Estimate SE Estimate SE p-value Estimate SE p-value Estimate SE p-value Estimate SE Urban freeways PA –6.92 1.15 0.67 0.11 <.0001 0.02 0.10 0.862 0.20 0.07 Combined –8.53 1.48 0.76 0.15 <.0001 0.22 0.11 0.042 –0.15 0.08 0.078 0.19 0.06 MO –6.75 1.85 0.65 0.19 0.001 –0.13 0.10 0.173 0.20 0.07 Rural freeways PA –9.99 2.78 0.89 0.29 0.002 0.29 0.16 0.076 –0.14 0.16 0.383 0.17 0.10 Combined –7.19 1.48 0.58 0.16 0.0004 0.32 0.10 0.001 0.05 0.14 0.738 0.45 0.09 MN –9.50 1.49 0.88 0.15 <.0001 0.12 0.14 0.398 0.22 0.08 MO –15.15 3.96 1.56 0.42 0.000 0.17 0.21 0.422 0.59 0.20 Rural multilane divided highways (nonfreeways) PA –0.07 0.28 –0.40 0.28 0.156 0.58 0.32 Combined –5.46 0.77 0.32 0.10 0.001 0.41 0.06 <.0001 –0.47 0.16 0.004 0.85 0.13 MN –4.50 1.19 0.26 0.15 0.084 0.04 0.17 0.840 1.16 0.33 MO –8.46 2.18 0.40 0.24 0.094 0.95 0.15 <.0001 –0.90 1.38 0.515 0.19 0.14 Rural two-lane roads PA –2.96 0.94 0.25 0.12 0.035 –0.47 0.24 0.054 0.57 0.14 a Statistics are bolded when p ≤ 0.10.

Table F-5. GLM estimates for TOT crashes based on before and after sites and nontreatment cross-sectional sites. Table F-6. GLM estimates for FI crashes based on before and after sites and nontreatment cross-sectional sites. Intercept lnADT Outside RHR Rumble stripsa Overdispersion Roadway type State Estimate SE Estimate SE p-value Estimate SE p-value Estimate SE p-value Estimate SE Urban freeways PA –9.30 1.23 1.03 0.12 <.0001 –0.05 0.06 0.372 0.22 0.03 Combined –8.83 1.75 1.01 0.18 <.0001 0.07 0.07 0.363 0.21 0.03 MO –5.38 2.63 0.68 0.26 0.010 0.11 0.07 0.113 0.19 0.03 Rural freeways PA –1.03 2.32 0.17 0.24 0.492 0.06 0.15 0.677 0.14 0.05 Combined –5.46 1.30 0.60 0.14 <.0001 0.24 0.08 0.003 0.25 0.08 0.004 0.29 0.03 MN –7.44 1.46 0.82 0.17 <.0001 0.14 0.08 0.086 0.15 0.12 0.185 0.12 0.03 MO –6.59 3.18 0.82 0.34 0.014 0.24 0.11 0.028 0.42 0.08 Rural multilane divided highways (nonfreeways) PA –1.11 4.54 0.22 0.49 0.656 –0.30 0.31 0.337 0.26 0.13 Combined –5.96 0.87 0.64 0.10 <.0001 0.23 0.04 <.0001 –0.06 0.14 0.680 0.59 0.04 MN –5.16 1.09 0.49 0.13 0.000 0.34 0.05 <.0001 0.16 0.09 0.058 0.31 0.06 MO –4.79 2.05 0.65 0.24 0.007 –0.17 0.93 0.858 0.99 0.12 Rural two-lane roads PA –4.55 0.80 0.57 0.10 <.0001 –0.28 0.19 0.145 0.36 0.06 a Statistics are bolded when p ≤ 0.10. Intercept lnADT Outside RHR Rumble stripsa Overdispersion Roadway type State Estimate SE Estimate SE p-value Estimate SE p-value Estimate SE p-value Estimate SE Urban freeways PA –10.24 1.50 1.05 0.14 <.0001 –0.23 0.10 0.019 0.29 0.05 Combined –9.51 1.58 0.97 0.16 <.0001 –0.04 0.09 0.631 0.12 0.04 MO –9.70 2.26 0.99 0.23 <.0001 –0.01 0.10 0.888 0.13 0.04 Rural freeways PA –5.19 3.37 0.52 0.35 0.134 –0.09 0.15 0.555 0.08 0.08 Combined –7.49 1.52 0.70 0.17 <.0001 0.23 0.09 0.007 0.05 0.17 0.766 0.29 0.06 MN –8.70 1.48 0.87 0.15 <.0001 –0.20 0.18 0.278 0.08 0.05 MO –15.91 3.83 1.70 0.41 <.0001 0.02 0.21 0.929 0.38 0.12 Rural multilane divided highways (nonfreeways) PA –1.02 9.61 0.14 1.03 0.893 –0.58 0.29 0.045 0.41 0.22 Combined –6.86 0.75 0.63 0.09 <.0001 0.28 0.05 <.0001 –0.16 0.13 0.244 0.54 0.06 MN –5.99 1.06 0.47 0.13 0.000 0.31 0.06 <.0001 0.07 0.15 0.648 0.28 0.10 MO –8.46 1.91 0.63 0.24 0.010 0.70 0.19 0.000 –0.44 0.76 0.567 0.50 0.11 Rural two-lane roads PA –5.44 0.86 0.61 0.10 <.0001 –0.18 0.22 0.415 0.37 0.08 a Statistics are bolded when p ≤ 0.10.

Table F-7. GLM estimates for SVROR crashes based on before and after sites and nontreatment cross-sectional sites. Table F-8. GLM estimates for SVROR FI crashes based on before and after sites and nontreatment cross-sectional sites. Intercept lnADT Outside RHR Rumble strips a Overdispersion Roadway type State Estimate SE Estimate SE p-value Estimate SE p-value Estimate SE p-value Estimate SE Urban freeways PA –7.26 1.11 0.77 0.11 <.0001 –0.10 0.11 0.339 0.19 0.05 Combined –5.16 2.02 0.58 0.21 0.005 –0.10 0.08 0.214 0.26 0.04 MO –5.15 3.12 0.58 0.31 0.063 –0.06 0.08 0.453 0.26 0.05Rural freeways PA 0.18 0.08 –0.14 0.18 0.450 0.16 0.08 Combined –7.12 1.25 0.64 0.13 <.0001 0.33 0.09 0.0003 0.51 0.14 0.0002 0.42 0.06 MN –8.58 1.41 0.86 0.14 <.0001 0.30 0.10 0.002 0.20 0.06 MO –13.09 3.08 1.31 0.34 <.0001 0.33 0.22 0.137 0.51 0.16 0.002 0.46 0.12 Rural multilane divided highways (nonfreeways) PA –0.46 6.31 0.11 0.67 0.874 –0.26 0.17 0.141 0.18 0.14 Combined –5.23 0.83 0.38 0.10 0.0002 0.41 0.05 <.0001 –0.30 0.22 0.177 0.73 0.08 MN –3.60 0.85 0.06 0.11 0.578 0.52 0.08 <.0001 0.11 0.18 0.523 0.46 0.16 MO –0.32 0.18 –0.06 0.79 0.940 1.21 0.17 Rural two-lane roads PA –2.64 0.89 0.28 0.11 0.008 –0.60 0.22 0.008 0.49 0.09 a Statistics are bolded when p ≤ 0.10. Intercept lnADT Outside RHR Rumble stripsa Overdispersion Roadway type State Estimate SE Estimate SE p-value Estimate SE p-value Estimate SE p-value Estimate SE Urban freeways PA –6.95 1.39 0.67 0.13 <.0001 –0.10 0.13 0.43 0.18 0.08 Combined –6.61 1.89 0.63 0.19 0.001 –0.19 0.10 0.05 0.21 0.07 MO –8.20 2.37 0.79 0.24 0.001 –0.15 0.11 0.18 0.22 0.08 Rural freeways PA –1.86 3.25 0.14 0.34 0.680 –0.25 0.20 0.21 0.17 0.13 Combined –7.07 1.79 0.57 0.20 0.004 0.30 0.12 0.014 0.14 0.20 0.50 0.52 0.11 MN –8.15 1.71 0.74 0.18 <.0001 –0.16 0.19 0.40 0.16 0.09 MO –16.48 3.99 1.70 0.43 <.0001 0.11 0.21 0.60 0.60 0.21 Rural multilane divided highways (nonfreeways) PA –0.04 0.29 –0.24 0.20 0.23 0.59 0.32 Combined –5.39 0.80 0.31 0.10 0.003 0.41 0.06 <.0001 –0.50 0.20 0.01 0.86 0.14 MN –3.83 1.22 0.17 0.16 0.286 –0.26 0.25 0.30 1.26 0.47 MO –8.49 2.16 0.41 0.24 0.087 0.94 0.15 <.0001 –0.84 1.43 0.56 0.19 0.14 Rural two-lane roads PA –2.96 0.94 0.25 0.12 0.035 –0.47 0.24 0.05 0.57 0.14 a Statistics are bolded when p ≤ 0.10.