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

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166 A P P E N D I X G This appendix presents the companion tables to the four cross-sectional generalized linear model (GLM) analyses inves- tigating the effect of shoulder rumble strip offset. • Table G-1 presents the GLM results to investigate the effect of shoulder rumble strip placement (edgeline vs. non-edge- line) on SVROR FI crashes based on all site types; it is the companion table to Table 42. • Table G-2 presents the GLM results to investigate the overall effect of shoulder rumble strip placement on SVROR FI crashes across all sites in all states; it is the companion table to Table 43. • Table G-3 presents the GLM results to investigate the effect of shoulder rumble strip offset (at three levels) on SVROR FI crashes based on all site types; it is the companion table to Table 44. • Table G-4 presents the GLM results to investigate the com- bined effect of shoulder rumble strip offset and recovery area on SVROR FI crashes based on all site types; it is the companion table to Table 45. Number of sites, number of site-years, offset, and offset × recovery area statistics for each model are provided in the corresponding Tables 42 through 45. Table G-1: The statistics shown for each roadway type and state (combined or single) include: • 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 • Overdispersion parameter: estimate and standard error Each regression model is represented by the following equation: Expected total crashes mi yr a b lnADT c R = + × + ×exp HR d RS PlacementOut + ×( ) GLM Analysis Results for Effect of Shoulder Rumble Strip Offset and Recovery Area on Safety where a (i.e., intercept), b, and c are the coefficients whose estimates are shown in Table G-1. The companion coefficients for rumble strip placement, d, at two levels (edgeline vs. non- edgeline) as compared to no RS, are shown in Table 42. Table G-2: The statistics shown for all sites and states combined include the estimate for: • Intercept • ADT (on natural log scale) • Outside RHR • Overdispersion parameter The single regression model is represented by the following equation: where a (i.e., intercept), b, and c are the coefficients whose estimates are shown in Table G-2. The variable IRoadway type×State is an indicator variable with value 1 for a particular roadway type × state combination in the table, and zero otherwise. The companion coefficients for rumble strip placement, d, at two levels (edgeline vs. non-edgeline) as compared to no RS, are shown in Table 43. Table G-3: The statistics shown for each roadway type and state (combined or single) include: • 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 • Overdispersion parameter: estimate and standard error Each regression model is represented by the following equation: Expected total crashes mi yr a b lnADT c R = + × + ×exp HR d OffsetOut + ×( ) Expected total crashes mi yr a b lnADT c R = + × + ×exp HR d RS Placement I Out Roadway type Stat + ×( ){ × × e }

noisrepsidrevORHRedistuOTDAnltpecretnI Roadway type State Estimate SE Estimate SE p–value Estimate SE p–value Estimate SE Urban freeways PA –6.92 1.15 0.67 0.11 <.0001 0.20 0.07 Combined –8.76 1.46 0.79 0.15 <.0001 0.21 0.11 0.0622 0.19 0.06 MO –7.02 1.79 0.67 0.18 0.0002 0.20 0.07 Rural freeways PAa Combined –7.25 1.47 0.59 0.16 0.0003 0.30 0.10 0.0024 0.44 0.09 MN –9.73 1.47 0.90 0.15 <.0001 0.20 0.07 MO –15.06 3.93 1.55 0.42 0.0002 0.58 0.20 Rural multilane divided highways (nonfreeways) PA –0.05 0.28 0.57 0.32 Combined –5.46 0.77 0.31 0.10 0.0014 0.41 0.06 <.0001 0.84 0.13 MN –4.49 1.20 0.25 0.15 0.09 1.15 0.33 MOa Rural two–lane roads PAa Combined –5.38 0.79 0.31 0.10 0.003 0.41 0.06 <.0001 0.86 0.14 Rural two-lane roadsb MN –3.83 1.20 0.17 0.15 0.28 1.21 0.46 a LM algorithm did not converge. b Excludes 53 Minnesota nontreatment cross-sectional sites. Table G-1. GLM estimates for SVROR FI crashes based on all sites—rumble strip placement analysis.

168 where a (i.e., intercept), b, and c are the coefficients whose estimates are shown in Table G-3. The companion coefficients of offset distance, d, at three levels as compared to no RS, are shown in Table 44. Table G-4: The statistics shown for each roadway type and state (combined or single) include: • 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 • Overdispersion parameter: estimate and standard error Each regression model is represented by the following equation: Expected total crashes mi yr a b lnADT c R = + × + ×exp HR d Offset RAOut + × ×( ) where a (i.e., intercept), b, and c are the coefficients whose estimates are shown in Table G-4. The companion coeffi- cients, d, for the combination offset × recovery area, at five levels as compared to no RS with narrow shoulders, are shown in Table 45. Tables G-1 through G-4: For states that treat both sides of a divided highway as separate sites (i.e., Missouri and Pennsylvania), the RHR variables 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 models for rural two-lane roads represents the average RHR for both sides of the roadway. No GLM results are shown in those cases where the algo- rithm did not converge. Empty cells in those cases where the GLM algorithm did converge indicate that the corresponding coefficient estimate is not statistically significant at the 0.15 level or that the coefficient’s sign is not in the expected direction. Roadway type State Intercept (or state effect) lnADT Outside RHR Overdispersion Urban freeways PA –3.70 0.62 0.07 MO –4.29 0.66 0.12 Rural freeways PA –6.82 0.87 0.27 MN –6.00 0.82 0.07 MO –11.11 1.42 0.13 Rural multilane divided highways (nonfreeways) PA –2.14 0.38 0.39 MN –0.93 0.06 0.43 MO –6.01 0.45 0.98 Rural two–lane roads PA –3.01 0.25 –0.0008 0.29 Table G-2. GLM estimates for SVROR FI crashes based on all sites— overall rumble strip placement analysis.

noisrepsidrevORHRedistuOTDAnltpecretnI Roadway type State Estimate SE Estimate SE p–value Estimate SE p–value Estimate SE Urban freeways PA –5.85 1.21 0.60 0.11 <.0001 0.18 0.07 Combined –0.54 0.26 0.07 MO –7.02 1.79 0.67 0.18 0.0002 0.20 0.07 Rural freeways PA –0.54 0.24 0.11 Combined –6.59 1.49 0.60 0.16 0.0003 0.29 0.10 0.004 0.43 0.09 MN –9.73 1.47 0.90 0.15 <.0001 0.20 0.07 MO –15.11 3.91 1.55 0.42 0.0002 0.58 0.20 Rural multilane divided highways (nonfreeways) PA 0.81 0.00 0.48 0.30 Combined –5.45 0.78 0.34 0.11 0.0021 0.39 0.07 <.0001 0.81 0.12 MN –4.50 1.33 0.25 0.19 0.1774 1.14 0.33 MO –0.65 0.75 0.23 Rural two–lane roads PA –0.89 0.59 0.15 noisrepsidrevORHRedistuOTDAnltpecretnI Roadway type State Estimate SE Estimate SE p-value Estimate SE p-value Estimate SE Urban freeways PA –6.92 1.15 0.67 0.11 < .0001 0.20 0.07 Combined –8.73 1.51 0.78 0.16 < .0001 0.21 0.12 0.068 0.19 0.06 MO –6.74 1.77 0.65 0.18 0.0004 0.20 0.07 Rural freeways PAa Combined –7.36 1.56 0.60 0.17 0.001 0.29 0.10 0.003 0.43 0.09 MN –8.90 1.47 0.82 0.15 < .0001 0.19 0.07 MO –15.06 3.93 1.55 0.42 0.0002 0.58 0.20 Rural multilane divided highways (nonfreeways) PAa Combined –5.48 0.77 0.31 0.10 0.001 0.42 0.06 <.0001 0.84 0.13 MN –4.32 1.20 0.23 0.15 0.123 1.13 0.33 MOa Rural two-lane roads PAa a GLM algorithm did not converge. Table G-3. GLM estimates for SVROR FI crashes based on all sites—offset analysis. Table G-4. GLM estimates for SVROR FI crashes based on all sites—combined rumble strip offset and recovery area.