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35 Where 4.3.2 Univariate Disaggregate Analysis = Calibrated intercept and In the univariate disaggregate analysis, key findings are as b1, b2 , ... bn = Estimated effects on of factors or variables follows: x1, x2 , ... xn. The safety benefits of PRPMs on nighttime crashes With this model form, categorical variables were desirable increases as traffic volumes increase, decreases as degree to ascertain conditions that favor PRPM installation. Thus, of curvature increases, and decreases as roadway width for variables such as degree of curvature and AADT, ranges and shoulder width decrease. had to be assigned an ordinal value. This assignment of ordi- There is a correlation between traffic volumes and road- nal values was an iterative process considering the number of way design parameters (e.g., roadway width and shoul- crashes in a range, the variation in crashes per mile-year der width) that could mask safety effects and that neces- within and among ranges, and the observations from the uni- sitates the more formal multivariate modeling described variate exploratory analysis. in the next section. Stepwise linear regression was performed using the SASTM statistical analysis software package (41), estimates of , and values of factors for individual sites. Statistically 4.3.3 Multivariate Modeling of the Index nonsignificant variables at the 90-percent degree of confi- of Effectiveness (site) dence were eliminated. The absence of a variable in the final Table 4-2 shows the results of the multivariate modeling model does not imply that the variable does not affect the of site. The model includes variables relating to AADT and safety impact of PRPM because a statistically nonsignificant degree of curvature only. These variables are significant at effect could result from correlation with other variables, a a 95-percent confidence level. Other variables relating to lack of variation in the data, or a sample that is too small. In PRPM design (e.g., spacing), other delineation measures (e.g., addition, the generally small size of the composite safety chevrons), and roadway geometry (e.g., lane widths and effects of PRPMs strongly indicates that one is unlikely to shoulder widths) were also considered, but were found not to detect many factors that affect the safety effect of PRPMs. improve the model significantly. The sample size for the modeling for two-lane roadways consisted of 925 miles. 4.3 RESULTS OF ANALYSES It was necessary to group data for modeling because seg- FOR TWO-LANE ROADWAYS ments tended to be short. This tendency to be short resulted in considerable variations in individual values of , models with 4.3.1 Composite Analysis nonsignificant parameter estimates, and a poor overall fit when ungrouped data were used. The data used for modeling Table 4-1 shows the results of the composite safety evalu- were combined when sites shared a set of characteristics (e.g., ation of snowplowable PRPMs on nonintersection segments all urban, no curvature, AADT < 20,000). The data were fur- of two-lane roadways. Statistically significant results (at the ther grouped by segment lengths, the count of nighttime col- 95-percent confidence level) are shown in bold. Key findings lisions in the after period, and the expected after period colli- are as follows: sions without PRPM over all sites. Using these groupings, a value was obtained. The model was estimated with the char- Illinois shows significant increases in total crashes acteristics of each group as individual data points, with (9.1 percent), daytime crashes (17.9 percent), wet weather weights applied for the total length of the segments in a group. crashes (15.5 percent), and dry weather crashes (8.7 per- To facilitate the grouping, ranges for variables such as cent) after the nonselective implementation of PRPMs. degree of curvature and AADT had to be assigned an ordinal New Jersey shows a significant decrease in head-on value. This was accomplished with the use of an iterative crashes (19.6 percent) after the nonselective implemen- process to determine the best ranges by considering the num- tation of PRPMs. ber of crashes within a range, the variation in crashes per New York shows a significant decrease in total crashes mile-year within and among ranges, and the observations (9.5 percent), nighttime crashes (13 percent), wet weather from the univariate analysis. crashes (20 percent), and wet weather nighttime crashes The degree of curvature variable is the degree of curve in (23.9 percent) after the selective implementation of degrees per 100 ft and is calculated as (18,000/3.14 radius), PRPMs (at sites selected on the basis of wet-night crash where radius is the radius of the curve in feet. Roadways with history). a degree of curvature less than 3.5 include gentle curves as Pennsylvania shows significant increases in head-on well as roadway tangent sections (i.e., where the degree of crashes (37.2 percent) and guidance-related crashes curvature equals 0). Table 4-3 shows the accident modifica- (19.7 percent) after the selective implementation of tion factors (AMFs) derived from the respective models in PRPMs (at sites selected on the basis of overall night- Table 4-2. An AMF, like the index of effectiveness, is an time crash experience). index of how much crash experience is expected to change

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36 TABLE 4-1 Results of safety evaluation of two-lane roadways (nonintersection crashes) with snowplowable PRPMs (selective and nonselective implementation)* Crash Type Illinois New Jersey New York Pennsylvania (Nonselective) (Nonselective) (Selective) (Selective) # Sites = 5347 # Sites = 779 # Sites = 226 # Sites = 5383 # Miles = 460.53 # Miles = 173.98 # Miles = 81.75 # Miles = 266.94 Obs 1 % Obs % Obs % Obs % 2 3 Exp s.e. Ch Exp s.e. Ch Exp s.e. Ch Exp s.e. Ch Total 1133 1.091 9.1 3508 1.032 3.2 1121 0.905 -9.5 1244 0.980 -2.0 1038 0.035 3399 0.027 1238 0.034 1270 0.030 Fatal and injury 292 1.071 7.1 1219 0.955 -4.5 424 1.020 2.0 231 1.017 1.7 272 0.065 1275 0.038 415 0.057 227 0.068 Daytime 592 1.179 17.9 2338 1.047 4.7 672 1.003 0.3 739 0.963 -3.7 502 0.051 2232 0.034 669 0.048 767 0.038 Daytime fatal 167 1.080 8.0 861 0.976 -2.4 293 1.074 7.4 133 0.978 -2.2 and injury 155 0.086 882 0.044 272 0.072 136 0.086 Nighttime 541 1.001 0.1 1148 0.991 -0.9 449 0.873 -12.7 505 1.039 3.9 540 0.045 1158 0.040 514 0.052 486 0.048 Nighttime fatal 156 1.106 10.6 350 0.899 -10.1 131 1.000 0.0 98 1.074 7.4 and injury 141 0.091 389 0.058 131 0.097 91 0.110 Dry 773 1.087 8.7 2601 1.05 5.0 764 1.047 4.7 798 0.978 -2.2 711 0.041 2476 0.032 729 0.048 816 0.037 Wet 284 1.155 15.5 876 0.972 -2.8 333 0.798 -20.2 440 1.047 4.7 246 0.072 900 0.045 417 0.05 420 0.053 Head-on 28 0.859 -14.1 180 0.804 -19.6 Sample size too small 120 1.372 37.2 -33 0.163 224 0.068 87 0.127 Wet-night Sample Sample Sample Sample 140 0.761 Sample Sample size too size too size too size too size too size too small small small small -23.9 small small 183 0.075 Guidance 397 1.018 1.8 Sample Sample Sample size too small 279 1.197 size too size too 19.7 small small 390 0.053 233 0.074 *A site is a homogeneous segment of road represented by a set of attributes (shoulder width, type, lane width, AADT, terrain, guide rails, horizontal alignment, etc.). Statistically significant results (at 95% confidence level) are shown in bold. 1 Obs = Observed crash frequency. 2 Exp = Expected crash frequency. 3 Ch = change. following the implementation of a measure such as PRPMs. effect (i.e., an increase in crashes). For example, according The AMF is the ratio between the number of crashes per unit to Table 4-2, at AADTs ranging between 15,000 and 20,000 of time expected after a measure is implemented and the on a roadway with a degree of curvature less than 3.5, the number of crashes per unit of time estimated if the imple- AMF is 0.757 (1.1573 - 0.4004), which translates into a mentation does not take place. An AMF less than 1 would 24.3-percent [100(1 - 0.757)] reduction. indicate a positive safety effect (i.e., a reduction in crashes), The results of the multivariate modeling of the index of while an AMF greater than 1 would indicate a negative safety effectiveness confirm the observations from the univariate