Evaluation of Dynamic Speed Feedback Signs on Curves: A National Demonstration Project

CHAPTER 6. SPEED ANALYSIS

This chapter describes the speed metrics used to assess the effectiveness of the DSFS system. Speed results across sites are also summarized. Given data were collected for three locations at each of the 22 sites, results for individual sites are reported in appendix A. In addition, nighttime versus daytime speeds were compared for several sites, and passenger vehicle versus heavy truck speeds were compared for several sites. This was done to assess whether differences existed that should be considered, and no major differences were noted. This is also noted in appendix A.

SPEED METRICS

The change in speed from each after data collection period was compared with the before period. A negative result indicates that speeds were reduced from the before to the after period.

A number of speed metrics were calculated for the direction of travel toward the sign. They include average speed; SD of speed; 50th percentile speed; 85th percentile speed; and number of vehicles traveling 5, 10, 15, or 20 mph or more over the posted or advisory speed limit. For simplicity in setting up the pneumatic road tubes, the traffic counters were set up to record both directions of traffic on the two-way roadway. Results were reduced by lane and are presented only for traffic traveling in the direction of the DSFS.

Average or mean speed is the average of all spot speeds at the location in question. Mean speed was calculated using the equation in figure 45.

Figure 45. Equation. Calculation of mean speed.

Where:
= arithmetic average or mean of observed values.
x_i = ith individual value of statistic.
N = sample size, number of values x_i.

SD indicates the amount of variability for a given speed. It can be used to show how speeds are dispersed around the mean. Higher SDs indicate greater variability in the data.

The 50th percentile speed is the speed at which 50 percent of the vehicles are traveling or below. The 85th percentile speed is the speed at which 85 percent of the vehicles are traveling or below. For example, if the 85th percentile speed is 55 mph, 85 percent of the vehicles were observed at a speed of 55 mph or less.

The fraction of vehicles traveling at or above the posted speed limit or advisory speed by a certain threshold amount was also calculated. If an advisory speed was present, the fraction of vehicles traveling 5, 10, 15, and 20 mph or more over the advisory speed was calculated. If no advisory speed was present, the fraction of vehicles traveling 5, 10, 15, and 20 mph or more over the posted speed limit was calculated. This metric provides a measure of the number of vehicles traveling at high speeds. In many cases, agencies are more concerned with reducing the number of drivers traveling at excessive speeds than with simply reducing average speeds.

The mean, SD, 85th percentile, minimum and maximum speeds, and percent of vehicles traveling at or above 5, 10, 15, and 20 mph over the posted speed limit or advisory speed were calculated at each location for each data collection period. Mean speeds were compared at the 95-percent confidence level using a t-test (assuming unequal variances). The percent of vehicles traveling at 5, 10, 15, and 20 mph above the posted speed limit or advisory speed (before periods) were compared with those of after periods. A z-test was used to detect differences between two population proportions at the 95-percent confidence level (Ott and Longnecker 2001). (See the equation in figure 46.)

Figure 46. Equation. z-test.

Unless indicated otherwise, difference in means and percents over the posted or advisory speed were statistically significant at the 95-percent level of significance.

The percent change between the fraction of vehicles exceeding the posted or advisory speed before and after installation of the signs was also calculated using the equation in figure 47.

Figure 47. Equation. Percent change in fraction of vehicles exceeding posted/advisory speed after installation of signs.

Where:
FR_(before,x) = fraction of vehicles exceeding the posted or advisory speed by x mph for before period x.
FR_{(after,x, i)} = fraction of vehicles exceeding the posted or advisory speed by x mph for after period i.
C_p = percent change.

For example, if the fraction of vehicles traveling 5 mph or more over the posted speed limit was 0.413 for the before period, and the fraction of vehicles traveling 5 mph or more at 1 month after installation is 0.083, the percent change is (0.413 - 0.083)/0.413 = 0.799. Therefore, 79.9 percent fewer vehicles exceeded the posted or advisory speed by 5 mph or more after the sign had been in place for 1 month. The percent change was the metric used to assess differences in the fraction of vehicles that exceeded the posted or advisory speed by 5, 10, 15, or 20 or mph.

ADT was computed for each site. Total volume was averaged by the number of days of data (i.e., total volume for a 48-h count was divided by 2). ADT is presented only for the upstream site given volume was not expected to vary over the study section.

SUMMARY OF SPEED ANALYSIS

Data were collected at 22 sites for four time periods (before, 1 month after, 12 months after, and 24 months after). Data were also collected at three different locations at each site as described in chapter 6. This resulted in a significant amount of information. Consequently, results for individual sites by time period and location are provided in appendix A. Results across sites were summarized and are presented in the following sections.

Results of Mean and 85th Percentile Speed Analysis at Point of Curvature

Table 27 through table 35 summarize results by curve. The change in mean and 85th percentile speed from the before period speed to specific after period speed, in mph, are shown. The percent change (as defined in the Speed Metrics section of this chapter) in the fraction of vehicles exceeding the posted or advisory speed is also presented.

These tables provide the curve identification number, sign type, road name, and posted speed limit for each curve. An S for Sign Type indicates a speed display sign, and a C designates a curve display sign. When an advisory curve speed was displayed, the advisory speed is shown as well.

Table 27 through table 29 show changes in the speed metrics at the PC for data collected about 1 month after installation of the DSFS systems. Changes in mean speeds range from a decrease of 5.6 mph at site AZ-6 to an increase of 3.3 mph at site FL-32. Changes in 85th percentile speeds at the PC 1 month after installation ranged from a decrease of 8 mph to an increase of 4 mph.

Table 27. Summary of results at the PC 1 month after sign installation (part 1).

C = Curve display sign
S = Speed display sign

Table 28. Summary of results at the PC 1 month after sign installation (part 2).

*Not statistically significant at 95-percent level of significance
C = Curve display sign
S = Speed display sign

Table 29. Summary of results at the PC 1 month after sign installation (part 3).

*Not statistically significant at 95-percent level of significance
C = Curve display sign
S = Speed display sign

Table 30 through table 32 provide changes in the speed metrics at the PC for data collected about 12 months after installation of the DSFS systems. Decreases in mean speeds range from 6.5 mph to an increase of 0.6 mph. Decreases in 85th percentile speeds range from a decrease of 8 mph to an increase of 1 mph. Signs were functioning for all 22 sites for the 12-month after period.

Table 30. Summary of results at the PC 12 months after sign installation (part 1).

*Not statistically significant at 95-percent level of significance
C = Curve display sign
S = Speed display sign

Table 31. Summary of results at the PC 12 months after sign installation (part 2).

*Not statistically significant at 95-percent level of significance
C = Curve display sign
S = Speed display sign

Table 32. Summary of results at the PC 12 months after sign installation (part 3).

*Not statistically significant at 95-percent level of significance
C = Curve display sign
S = Speed display sign

Table 33 through table 35 show changes in speed metrics at the PC for the 24-month after period. Results are shown for 18 sites. Signs at two sites in Oregon and two sites in Texas had various issues between the 12- and 24-month after periods. Given a number of other signs had already been repaired, it was determined there were not sufficient project resources to make additional trips to perform maintenance at those sites.

As shown, at the 24-month after period, decreases in mean speeds ranged from 0.8 to 5.7 mph, with one site experiencing an increase in mean speed of 0.5 mph. Decreases in 85th percentile speeds ranged from 1 to 6 mph, with one site having an increase in 85th percentile speed of 1 mph.

Table 33. Summary of results at the PC 24 months after sign installation (part 1).

*Not statistically significant at 95-percent level of significance
C = Curve display sign
S = Speed display sign

Table 34. Summary of results at the PC 24 months after sign installation (part 2).

*Not statistically significant at 95-percent level of significance
C = Curve display sign
S = Speed display sign

Table 35. Summary of results at the PC 24 months after sign installation (part 3).

C = Curve display sign
S = Speed display sign

Decreases in mean and 85th percentile speeds were plotted to show the distribution of change. Figure 48 shows the percent of sites experiencing decreases in mean speeds of a certain magnitude at 1, 12, and 24 months. Figure 49 provides change in 85th percentile speed of a certain magnitude.

As shown, at 1 month, 2 of the 21 sites had increases in mean speeds between 1 and 4 mph, 9 of the sites (43 percent) experienced virtually no change in mean speeds, 5 sites (24 percent) experienced decreases of 1 to 4 mph, and 5 sites had decreases between 4 and 7 mph.

Changes in 85th percentile speeds for the 1-month after periods are shown in figure 49. As indicated, two sites (10 percent) experienced increases between 1 and 7 mph, four sites (19 percent) had little change in 85th percentile speeds, seven sites (33 percent) had decreases between 1 and 4 mph, six sites (29 percent) had decreases of 4 to 7 mph, and two sites (10 percent) had decreases of more than 7 mph.

At 12 months after installation of the signs, no sites experienced significant increases in mean speeds as shown in figure 50. Three of the 22 sites (14 percent) had little change, 15 sites (68 percent) had decreases of 1 to 4 mph, and 4 sites had decreases from 4 to 7 mph. As indicated in figure 49, no sites had increases in 85th percentile speeds at 12 months while 3 of the 22 (18 percent) had little change, 10 sites (45 percent) had decreases of 1 to 4 mph, 6 sites (27 percent) had a decreases of 4 to 7 mph, and 2 sites (9 percent) had decreases of 7 mph or more.

Figure 48 and figure 49 also show results for 24 months after installation of the signs. Data were available for 18 sites given maintenance and vandalism issues had occurred at 4 sites so that data were not collected for them at the 24-month after period.

Figure 48. Chart. Percent of sites experiencing a change in mean speed of a certain magnitude at the PC.

Figure 49. Chart. Percent of sites experiencing a change in 85th percentile speed of a certain magnitude at the PC.

As shown in figure 48, at 24 months, no signs had significant increases in mean speeds, while three sites had little change in mean speeds. The majority (13 sites or 72 percent) had decreases of 1 to 4 mph while 2 sites (11 percent) had a decrease between 4 and 7 mph. As shown in figure 49, at the 24-month after period, 1 site (6 percent) had no relevant changes in 85th percentile speed, 14 sites (83 percent) had decreases of 1 to 4 mph, and 2 sites (11 percent) had decreases of 4 mph or more.

Results of Percent Change in Vehicles Exceeding Posted or Advisory Speed at Point of Curvature

Figure 50 through figure 53 show changes in the percent of vehicles traveling at 5 mph or more, 10 mph or more, 15 mph or more, and 20 mph or more over the posted speed or advisory speed at the PC. Researchers compared the fraction of vehicles a certain threshold over the advisory speed if present; if not present, the posted speed limit was used.

Figure 50 shows the change in percent of vehicles traveling 5 mph or more over the posted or advisory speed at 1, 12, and 24 months.

Figure 50. Chart. Changes in percent of vehicles traveling 5 or more mph over posted limit or advisory speed at the PC.

Data for vehicles traveling 5 mph or more over the posted or advisory speed are fairly consistent over the 1-, 12-, and 24-month after periods. As shown, 5 to 10 percent of sites had reductions of 70 percent or more, and about 15 percent of sites had decreases from 35 to 70 percent. The majority of sites for all time periods had decreases up to 35 percent. A small number of sites had little change, with up to 10 percent having increases up to 25 percent and about 5 percent with increases of more than 25 percent.

Figure 51 shows data for the proportion of vehicles traveling 10 mph or more over the posted speed limit or advisory speed. The majority of sites (41 to 55 percent, depending on time period) had decreases of up to 35 percent in the fraction of vehicles traveling 10 mph or more over the posted or advisory speed while 23 to 35 percent of sites had decreases between 35 and 70 percent. Finally, about 10 percent of sites for 1 month, 14 percent for 12 months, and 6 percent for 24 months had decreases of 70 percent or more. At 1 month, 14 percent of sites and at 12 months, 5 percent of sites had increases up to 25 percent in the fraction of vehicles traveling 10 mph or more over the posted or advisory speed. Six percent of vehicles had increases of more than 25 percent for the 24-month after period. Up to 12 percent of sites had no change.

Figure 51. Chart. Changes in percent of vehicles traveling 10 or more mph over posted limit or advisory speed at the PC.

Figure 52 shows changes in the fraction of vehicles traveling 15 mph or more over the posted or advisory speed. Less than 6 percent of sites for any analysis time period had increases or no change in the fraction of vehicles traveling 15 mph or more over the posted or advisory speed. Twenty-four percent of vehicles at 1 month, 18 percent at 12 months, and 41 percent at 24 months, had decreases of up to 35 percent in the percentage of vehicles traveling 15 mph or more over the posted or advisory speed. The majority of sites (43 percent and 64 percent) for 1 and 12 months after and 29 percent for 24 months after had decreases between 35 and 70 percent. Up to 19 percent of sites had decreases of more than 70 percent.

Figure 53 shows results for changes in the percent of vehicles traveling 20 mph or more over the posted or advisory speed. The majority of vehicles (35 percent) at 24 months had decreases up to 35 percent in the fraction of vehicles traveling 20 mph or more over the posted or advisory speed. About 9 and 14 percent of sites experienced decreases in that range for the 1- and 12-month after periods.

The majority of sites (38 percent) for 1 month and (41 percent) for 12 months had decreases of 35 to 70 percent in the vehicles traveling 20 mph or more over the posted or advisory speed. Between 19 and 32 percent of sites had decreases in the fraction of vehicles traveling 20 mph or more over the posted or advisory speed. A few sites (14 percent for 1 month and about 5 percent for 12 and 24 months) had increases of more than 25 percent. About 5 percent had increases up to 25 percent, and about 6 to 9 percent had no change. About 20 percent of sites at 1 and 24 months and about 30 percent of sites at 12 months had decreases in the percent of vehicles traveling 20 mph or more over the posted or advisory speed.

Figure 52. Chart. Changes in percent of vehicles traveling 15 or more mph over posted limit or advisory speed at the PC.

Figure 53. Chart. Changes in percent of vehicles traveling 20 or more mph over posted limit or advisory speed at the PC.

As noted, significant reductions in the number of vehicles traveling over the posted or advisory speeds occurred for all of the after periods at the PC. In most cases, the majority of sites had reductions in the fraction of vehicles exceeding the posted or advisory speed between 35 and 70 percent. This was the case for all of the speed thresholds (5, 10, 15, and 20 mph or more over). In addition, reductions of greater than 70 percent were noted for all time periods and thresholds except for one. This indicates the signs were effective in reducing high-end speeds, as well as average and 85th percentile speeds.

Results of Mean and 85th Percentile Speed Analysis at the Center of the Curve

Table 36 through table 44 summarize overall results by curve at the CC. The changes in mean and 85th percentile speeds from the before period speed to the specific after period speed, in mph, are shown. The percent change (as defined in Speed Metrics) in the fraction of vehicles exceeding the posted or advisory speed is also presented.

These tables provide the curve identification number, sign type, road name, and posted speed limit for each curve. An S for Sign Type indicates a speed display sign, and a C designates a curve display sign. When an advisory curve speed was displayed, the advisory speed is shown as well.

Table 36 through table 38 show results at the CC for individual sites at the 1-month after period. Speed reductions were generally larger at the CC than at the PC. Changes in mean speeds ranged from a decrease of 10.9 mph to an increase of 2.8 mph. Changes in 85th percentile speeds ranged from a decrease of 12 mph to an increase of 6 mph. Data are presented for 21 of the 22 sites. At the 1-month after period, a sign had been knocked down at one of the Texas sites and had not been repaired when data were collected.

Table 36. Summary of results at the CC 1 month after sign installation (part 1).

*Not statistically significant at 95-percent level of significance
C = Curve display sign
S = Speed display sign

Table 37. Summary of results at the CC 1 month after sign installation (part 2).

*Not statistically significant at 95-percent level of significance
C = Curve display sign
S = Speed display sign

Table 38. Summary of results at the CC 1 month after sign installation (part 3).

*Not statistically significant at 95-percent level of significance
C = Curve display sign
S = Speed display sign

As noted, most sites had significant decreases in the fraction of vehicles traveling 5, 10, 15, or 20 mph or more over the posted or advisory speed. Reductions up to almost 100 percent were reported for the fraction traveling 5, 10, or 15 mph or more over the posted or advisory speed. One site had a 211-percent reduction, and another site had a 161-percent reduction in the fraction of vehicles traveling 20 mph or more over the posted or advisory speed limit.

Table 39 through table 41 provide results for the CC for 12 months after installation of the signs. Results are presented for all 22 sites. Changes in mean speeds ranged from a decrease of 7.9 mph to an increase of 3.7 mph. Changes in 85th percentile speeds ranged from a decrease of 9 mph to an increase of 3 mph.

Table 39. Summary of results for the CC 12 months after sign installation (part 1).

*Not statistically significant at 95-percent level of significance
C = Curve display sign
S = Speed display sign

Table 40. Summary of results for the CC 12 months after sign installation (part 2).

C = Curve display sign
S = Speed display sign

Table 41. Summary of results for the CC 12 months after sign installation (part 3).

*Not statistically significant at 95-percent level of significance
C = Curve display sign
S=Speed display sign

Table 42 through table 44 provide changes in speed metrics for the 24-month after period. Data are presented for 18 sites given 4 sites were no longer functioning. One site had an increase in mean speed of 2.0 mph while the remaining sites had decreases from 0.8 to 7.0 mph. Two sites experienced increases (1 and 2 mph) in 85th percentile speeds, and two sites had no change. The remaining sites had decreases in 85th percentile speed from 1 to 8 mph.

Table 42. Summary of results at the CC 24 months after sign installation (part 1).

*Not statistically significant at 95-percent level of significance
C = Curve display sign
S = Speed display sign

Table 43. Summary of results at the CC 24 months after sign installation (part 2).

C = Curve display sign
S = Speed display sign

Table 44. Summary of results at the CC 24 months after sign installation (part 3).

C = Curve display sign
S = Speed display sign

The following figures show the distribution of results. Figure 54 shows the percent of sites experiencing changes in mean speeds of a certain magnitude. As indicated, the majority of sites had decreases in mean speeds from 1 to 4 mph.

Figure 54. Chart. Percent of sites experiencing a change in mean speed of a certain magnitude at the CC.

At 1 month, 2 of the 21 sites (10 percent) had increases in mean speeds that were greater than 1 to 4 mph, 5 of the sites (24 percent) experienced virtually no change in mean speeds, and 11 sites (52 percent) experienced decreases of 1 up to 4 mph. Finally, three sites (15 percent) had decreases of 4 mph or more.

Similar results occurred for the 12-month and 24-month after periods. At 12 and 24 months, about 14 percent of sites had increases between 1 and 4 mph. Eighteen percent of sites for the 12 month after period and 6 percent for 24 months after had little change. The majority of sites (55 and 72 percent) had decreases in mean speeds from 1 to 4 mph. At 12 months, 9 percent of sites and 6 percent of sites had decreases between 4 and 7 mph, respectively. About 5 percent of sites for both the 12- and 24-month after periods had decreases of more than 7 mph.

Figure 55 shows the change in 85th percentile speeds at the CC at 1, 12, and 24 months. Overall, the majority of sites for all after periods had decreases in mean speeds from 1 to 4 mph.

Figure 55. Chart. Percent of sites experiencing a change in 85th percentile speed of a certain magnitude at the CC.

At 1 and 24 months, two sites (about 10 percent) had increases that were more than 1 mph while, at 12 months, four sites (18 percent) saw an increase. Between 6 and 14 percent of sites experienced little change in 85th percentile speeds depending on the after periods.

Thirteen sites (62 percent) at 1 month, 10 sites (45 percent) at 12 months, and 10 sites (56 percent) at 24 months had decreases from 1 to 4 mph. Two sites (10 percent) at 1 month, four sites (18 percent) at 12 months, and three sites (17 percent) at 24 months had decreases from 4 to 7 mph. One site (about 5 percent) for each after period experienced a decrease from 7 to 10 mph, and 1 site (5 percent) at 1 month after had decreases in 85th percentile speeds that were more than 10 mph.

Results of Percent Change in Vehicles Exceeding Posted or Advisory Speed at Center of the Curve

Figure 56 through figure 59 show changes in the percentage of vehicles traveling at 5, 10, 15, or 20 mph or more over the posted speed limit or advisory speed at the CC. The figures show the percentage of sites that experienced a change within a particular range. Data are fairly consistent over the 1-, 12-, and 24-month after periods.

As shown in figure 56, 18 percent and 6 percent of sites had increases in the fraction of vehicles traveling 5 mph or more over the posted or advisory speed at the 12- and 24-month after periods, and 5 percent of sites at the 1-month after period had no change. The majority of sites (67 percent for 1 month, 59 percent for 12 months, and 65 percent for 24 months) had decreases up to 35 percent in the fraction of vehicles traveling 5 mph or more over the posted or advisory speed. About 24 percent of sites had reductions between 35 and 70 percent, and about 5 percent of sites had reductions of 70 percent or more.

Figure 56. Chart. Changes in percent of vehicles traveling 5 or more mph over posted limit or advisory speed at the CC.

Figure 57 provides results for the percentage of vehicles traveling at 10 mph or more over the posted speed or advisory speed at the CC. Five to 9 percent of sites at 1 and 12 months, respectively, had increases up to 25 percent, and 10 percent and 5 percent of sites had no change for the 1- and 12-month after periods, respectively. Most sites had reductions in the fraction of vehicles traveling 10 mph or more over the posted or advisory speed up to 35 percent or between 35 and 70 percent.

About 29 percent of sites at 1 month and 41 percent of sites at 12 and 24 months experienced reductions in the fraction of vehicles traveling 10 mph or more over the posted or advisory speed. Thirty-six to 41 percent of sites had reductions between 35 and 70 percent. Finally, about 20 percent of sites at 1 month, 9 percent at 12 months, and 12 percent at 24 months had reductions in the fraction of vehicles traveling 10 mph or more over the posted or advisory speed.

Figure 57. Chart. Changes in percent of vehicles traveling 10 or more over posted limit or advisory speed at the CC.

Similarly, figure 58 shows changes in the fraction of vehicles traveling 15 mph or more over the posted or advisory speed. Five percent of sites at 12 months had increases of more than 25 percent, and 5 percent had no change for that same time period. Between 6 and 14 percent of sites had increases of up to 25 percent.

Five percent of sites at 1 month, 18 percent at 12 months, and 35 percent at 24 months had reductions up to 35 percent in the percentage of vehicles traveling 15 mph or more over the posted or advisory speed. The majority of sites (48 percent for 1 month and 41 percent for the 12- and 2-month after periods) had decreases from 35 to 70 percent. Eighteen to 33 percent had reductions of more than 70 percent in the fraction of vehicles traveling 15 mph or more over the posted or advisory speed.

Figure 58. Chart. Changes in percent of vehicles traveling 15 or more mph over posted limit or advisory speed at the CC.

Figure 59 also shows results for the percent of vehicles exceeding the posted or advisory speed by 20 mph or more. One or two sites showed increases in the percent of vehicles exceeding the speed limit by 20 mph or more for the 1- and 12-month after periods, respectively. Two sites for the 24-month after period had increases from more than 1 to 10 percent. Five to nine sites (23 to 53 percent) had decreases from 35 to 70 percent.

As noted, large reductions in the number of vehicles traveling over the posted or advisory speed occurred for all of the after periods at the CC. The majority of sites had reductions up to 35 percent in the fraction of vehicles traveling 5 mph or more over the posted or advisory speed. The majority of sites had decreases up 70 percent in the fraction of vehicles traveling 10 mph or more over the posted or advisory speed. Most sites had reductions of 35 percent or more in the fraction of vehicles traveling 15 or 20 mph or more over the posted or advisory speed. These results indicate the signs were effective in reducing high-end speeds as well as average and 85th percentile speeds.

Figure 59. Chart. Changes in percent of vehicles traveling 20 or more mph over posted limit or advisory speed at the CC.

SUMMARY OF RESULTS BY SIGN TYPE

Results at Point of Curvature

Drivers may respond differently to different sign messages. In addition, different signs may be more effective in different situations. Given only 22 sites were included in this project, testing a range of signs with different driver messages was beyond the project scope. In addition, given the project intent was not to compare different sign types, the experiment was not designed for comparison.

However, there was some value in evaluating the data by sign type to assess whether there was evidence of differences that may lead to further research. As a result, data were disaggregated by sign type, and general comparisons were conducted. As indicated, the experiment was not set up to test differences by sign type, and the sample size is low. Consequently, caution should be used in interpreting the results.

Table 45 provides the average changes in speeds overall by after analysis period at the PC. As shown, the change in mean speed at the 1-month after period was a decrease of 1.8 mph. The average decrease in mean speed at the 12-month after period was even greater than the 1-month after period with a decrease of 2.57 mph. The average speed decrease of 1.97 mph for the 24-month after period was similar to the 1-month period.

Table 45. Average change over sites at PC.

The average mean speeds of sites with speed signs were higher than those with curve signs at 1 and 12 months, while the average mean speeds for sites with curve signs were slightly higher for the 24-month after period.

The changes in 85th percentile speeds for all sites was a decrease of about 2.2 mph for the 1- and 24-month after periods while the average decrease was 2.9 mph for the 12-month after period. The average changes in 85th percentile speeds were 0.55 mph higher for speed signs than for curve signs at the 1-month after period, and 0.3 mph higher for both the 12- and 24-month after periods.

Also shown in table 45, sites on average had a decrease of 12 percent in the fraction of vehicles traveling 5 mph or more over the posted or average speed limit for the 1-month after period. The fraction of vehicles traveling 10 mph or more over the posted or advisory speed decreased by an average of 30 percent for the 1-month after period and 36 percent for the fraction of vehicles traveling 15 mph or more over the posted or advisory speed. Similarly, the average decrease in vehicles traveling 20 mph or more over the posted or advisory speed was 29 percent.

Results for the 12-month after period were somewhat higher, with average decreases of 19, 34, 36, and 50 percent for the fraction of vehicles traveling 5, 10, 15, and 20 mph or more over the posted or advisory speed, respectively.

Results for the 24-month after period were similar to the 1-month after period.

Sites with speed signs had greater reductions in the fraction of vehicles traveling 5 mph or more over the posted or advisory speed at 1 month after while greater reductions were noted for sites with curve signs at the 12- and 24-month after periods.

Sites with curve signs had slightly greater decreases in the fraction of vehicles traveling 10 mph or more over the posted or advisory speed for 1 and 12 months after and a significantly higher reduction for the 24-month after period.

Sites with speed signs had much greater reductions in the fraction of vehicles traveling 15 mph or more over the posted or advisory speed at the 12-month after period while sites with curve signs had much larger reductions at 24 months. At 1 month after, reductions were similar but slightly higher for sites with curve signs.

Finally, sites with curve signs had slightly higher reductions at 1 month and much higher reductions at 24 months for the fraction of vehicles traveling 20 mph or more over the posted or advisory speed. At 12 months, sites with speed signs had moderately higher reductions.

Figure 60 through figure 62 show the percentage of sites that had a change in average speed of a certain magnitude for each after period at the PC. Results are presented by type of sign (curve advisory versus speed sign).

Figure 60. Chart. Changes in mean speed at the PC by sign type about 1 month after sign installation.

At 1 month, about 10 percent of sites with both sign types had increases of more than 1 mph in average speeds. The majority of sites (58 percent) with curve signs had little change in average speeds while 22 percent of sites with speed signs had little change. Seventeen percent of sites with curve signs had decreases of 1 to 4 mph, and another 17 percent had decreases of more than 4 percent, while 33 percent of sites with speed signs had decreases of 1 to 4 mph, and 33 percent had decreases of more than 4 mph.

Figure 61 shows results at 12 months, 23 percent of sites with curve signs had little change in mean speeds while 62 percent of sites with curve signs and 78 percent of sites with speed signs had a decrease in average speeds of between 1 and 4 mph. Fifteen percent of sites with curve signs and 22 percent of sites with speed signs had decreases of 4 mph or more.

Figure 62 shows results for the 24-month after period. As noted the results are very similar to the 12-month after period.

Figure 61. Chart. Changes in mean speed at the PC by sign type about 12 months after sign installation.

Figure 62. Chart. Changes in mean speed at the PC by sign type about 24 months after sign installation.

Figure 63 through figure 65 illustrates the percent of sites with changes in 85th percentile speeds of a certain magnitude at each after period by sign type at the PC. Results are presented by sign type.

Figure 63 Chart. Changes in 85th percentile speed at the PC by sign type about 1month after sign installation.

Ten percent of sites for both sign types experienced increases in 85th percentile speeds of more than 1 mph. Approximately one-third of sites with curve signs experienced no change while one-third of sites with both sign types had decreases between 1 and 4 mph. One-quarter of sites with curve signs and more than 50 percent of sites with speed signs had decreases of more than 4 mph.

Figure 64 shows results for the 12-month after period. About 31 percent of sites with a curve sign showed little change in 85th percentile speed. The majority of sites with both types of signs (38 percent of sites with curve signs and 56 percent of sites with speed signs) had decreases in 85th percentile speeds between 1 and 4 mph. Thirty-one percent of sites with curve signs and 44 percent of sites with speed signs experienced decreases in 85th percentile speeds of 4 mph or more.

As shown in figure 65, at 24 months, 50 percent of curve sign sites had little change in 85th percentile speeds while 13 percent of speed sign sites had no change. Forty percent of curve sign sites had decreases in 85th percentile speeds that were 1 to 4 mph, and 75 percent of speed sign sites saw the same decrease. Ten percent of curve sign sites and 13 percent of speed sign sites had decreases of 4 mph or more.

Sites with speed signs appeared to be slightly more effective based on the data described in the previous sections. To test that assumption, the researchers conducted a statistical test to evaluate differences between sign types for both average speed differences and differences in 85th percentile speeds.

Figure 64 Chart. Changes in 85th percentile speed at the PC by sign type about 12 months after sign installation.

Figure 65 Chart. Changes in 85th percentile speed at the PC by sign type about 24 months after sign installation.

The data were not normally distributed, so the Wilcoxon-signed rank test, a non-parametric test, was used. Results at 1 month showed no statistically significant difference in either average speed (p = 0.39) or 85th percentile speed (p = 0.22).

Similarly, results for 12 months showed no statistically significant difference in either average speed (p = 0.20) or 85th percentile speed (p = 0.15). Results for the 24-month after period were similar, with no statistical difference in mean (p = 0.66) or 85th percentile speeds (0.29). However, results should be used with caution given the sample size is small. Consequently, there was no evidence to suggest that one sign type was more effective than the other was.

Results at the Center of Curve

Table 46 provides the average change in speed metrics over all sites by after analysis period at the CC. Results are shown for all sites as well as by sign type. As shown, the change in mean speed at the 1-month after period was a decrease of 2.1 mph. The average decrease in mean speed at the 12-month and 24-month after periods were smaller than the decrease at 1 month (1.7 and 1.8 mph). The average decrease in mean speed for sites with speed signs was greater than for sites with curve signs for all of the after periods.

Table 46. Average change over sites at CC.

The average change in 85th percentile speeds for all sites was a decrease of 2.5 mph for 1 month, 1.6 mph for 12 months, and 1.9 mph for 24 months. The average decrease in 85th percentile speed was slightly higher for the 1-month after period for speed sign sites versus curve sign sites while the decrease at 12 and 24 months was much higher for speed sign sites than for curve sign sites (2.27 versus 0.82 and 2.4 versus 1.25, respectively).

The average change in the fraction of vehicles traveling 5 mph or more over the posted or advisory speed was similar for both curve- and speed-sign sites at 1 month, with curve signs having a slightly higher reduction at 12 months and a moderately higher reduction at 24 months. Both sign types produced similar reductions in the fraction of vehicles traveling 10 mph or more over for all after periods. The reduction in the fraction of vehicles traveling 15 mph or more over the posted or advisory speed was much greater for sites with curve signs at the 1-month after period and was moderately higher for the 12-month after period. Sites with speed signs had greater reductions in the fraction of vehicles traveling 15 mph or more over the posted or advisory speed at 24 months. Results were similar for the fraction of vehicles traveling 20 mph or more over the posted or advisory speed with much greater reductions for curve signs than for speed signs at 1 and 12 months and much higher reductions for speed signs at 24 months.

The simple comparison of reductions in the fraction of vehicles traveling a certain threshold over the posted or advisory speed by sign type does not offer strong evidence that either sign type was more effective.

Figure 66 through figure 68 shows information for mean speeds at the CC by type of sign for 1 month, 12 months, and 24 months after installation of the signs.

Figure 66. Chart. Changes in mean speed at the CC by sign type about 1 months after sign installation.

At 1 month, about 10 percent of both the sites with curve and speed signs had increases of 1 mph or more, while 17 percent of sites with curve signs and 33 percent of sites with speed signs had little change in mean speed (defined as changes between -1 and 1 mph). The majority of sites with curve signs (67 percent) and 33 percent of sites with speed signs had decreases from 1 to 4 mph. A small number of sites with curve signs (8 percent) and 22 percent of sites with speed signs had decreases in mean speeds of 4 mph or more.

At 12 months (figure 67), 20 percent of sites with speed signs had increases in mean speeds of 1 mph or more. Almost one-third of sites with curve signs and 10 percent of sites with speed signs had little change in mean speeds. The majority of sites for both the curve signs (50 percent) and speed signs (60 percent) experienced decreases in mean speeds between 1 and 4 mph, while 17 percent of sites with curve signs and 10 percent of sites with speed signs had decreases of 4 mph or more.

Figure 67. Chart. Changes in mean speed at the CC by sign type about 12 months after sign installation.

Figure 68 also shows changes in mean speeds by sign type for the 24-month after period. Both the curve and speed signs had increases of more than 1 mph in mean speeds, while 10 percent of curve signs had little change in mean speeds. Eighty percent of curve signs and 63 percent of speed signs had decreases between 1 and 4 mph. One-quarter of the speed signs had decreases of 4 mph or more at the 24-month after period.

Figure 68. Chart. Changes in mean speed at the CC by sign type about 24 months after sign installation.

Differences in 85th percentile speeds between sign types for data collected at the CC are shown in figure 69 through figure 71 for 1, 12, and 24 months after installation of the signs.

Figure 69. Chart. Changes in 85th percentile speed at the CC by sign type 1 month after sign installation.

Seventeen percent of sites with curve signs and 11 percent of sites with speed signs at 1 month after had increases in 85th percentile speeds that were more than 1 mph. Another 11 percent of sites with speed signs had no change in 85th percentile speeds (defined as a change between -1 and 1 mph).

The majority of sites for both sign types (75 percent for curve signs and 44 percent for speed signs) had decreases in 85th percentile speeds between 1 and 4 mph. A small number of sites with curve signs (8 percent) and 33 percent of sites with speed signs had decreases that were 4 mph or more.

At 12 months (figure 70) after, similar numbers of sites (17 percent for curve sign sites and 20 percent for speed sign sites) had increases in 85th percentile speeds that were more than 1 mph, while 17 percent of sites with curve signs and 10 percent of sites with speed signs experienced little change. The majority of sites (50 percent of curve signs and 40 percent of speed signs) also experienced decreases between 1 and 4 mph. Seventeen percent of sites with curve signs and 30 percent of sites with speed signs had decreases in 85th percentile speeds that were 4 mph or more.

Figure 70. Chart. Changes in 85th percentile speed at the CC by sign type 12 months after sign installation.

Figure 71 also shows changes in 85th percentile speeds for the 24-month after period. About 10 percent of sites for both curve and speed signs had increases of more than 1 mph and no change. Eight percent of curve signs and 63 percent of speed signs had decreases of 1 to 4 mph, and 10 percent of curve signs and 38 percent of speed signs had decreases of more than 4 mph.

Similar to results at the PC, sites with speed signs appeared to be slightly more effective based on the information provided in figure 66 through figure 71. A Wilcoxon-signed rank test was also used to evaluate differences between sign types for both average speed differences and differences in 85th percentile speeds.

Results for 1 month after showed no statistically significant difference in either average speed (p = 0.64) or 85th percentile speed (p = 0.11) by sign type. Similarly, results for 12 months after showed no statistically significant difference in either average speed (p = 0.63) or 85th percentile speed (p = 0.35). At 24 months, results showed no difference (p = 0.69) in mean or 85th percentile speed (p = 0.92). Results suggest that there is no evidence of a difference in effectiveness between sign types at the CC. However, results should be used with caution given the sample size is small.

Figure 71 Chart. Changes in 85th percentile speed at the CC by sign type 24 months after sign installation.

COMPARISON OF MEAN AND 85TH PERCENTILE SPEED CHANGES OVER TIME

Data were collected over a period of 2 years to assess whether regular drivers become habituated to the signs, which might lessen their effectiveness. Table 45 showed the average change in mean and 85th percentile speed at the PC. The average change in mean speed at 1 month was -1.82 mph and the average changes at 12 and 24 months (-2.57 and -1.97 mph, respectively) were greater than at the 1-month after period. The average change in 85th percentile speed at the PC was similar for the 1- and 24-month after periods (-2.19 and -2.17 mph, respectively) and the decrease was greater at 12 months (-2.86 mph) than at 1 month. These data anecdotally suggest that the signs remained effective over time.

To test that assumption, a Wilcoxon-signed rank test was used to evaluate differences among the 1-, 12-, and 24-month after periods. The Wilcoxon-signed rank test is a non-parametric test and was used given the data were not normally distributed. The test compares the absolute value of the differences among observations, which are ranked from smallest to largest.

The individual changes in mean and 85th percentile speeds for sites at the PC were compared using the Wilcoxon-signed rank test. Results of the analysis indicated no statistical difference between changes in mean speeds at the PC for any of the time periods. The following shows the test statistics:

• 1 and 12 months (p = 0.29).
• 1 and 24 months (p = 0.43).
• 12 and 24 months (p = 0.43).

Similarly, no statistically significant differences in the change in 85th percentile speeds at the PC were noted with the following test statistics:

• 1 and 12 months (p = 0.45).
• 1 and 24 months (p = 0.60).
• 12 and 24 months (p = 0.36).

As shown in table 46, the average changes in mean speeds at 1, 12, and 24 months at the CC were -2.08, -1.65, and -1.76 mph, respectively. The average changes in 85th percentile speeds at the CC were -2.52, -1.55, and -1.89 mph for the 1-, 12-, and 24-month after periods, respectively. In both instances, the average decreases in speeds at the CC at 1 month were slightly greater than for the 12- or 24-month after period.

To test whether the differences were statistically significant, the individual changes in mean and 85th percentile speeds for sites at the CC were compared using the Wilcoxon-signed rank test. As shown by the test statistics below, there were no statistically significant differences between changes in mean speed across sites over the three after periods:

• 1 and 12 months (p = 0.87).
• 1 and 24 months (p = 0.99).
• 12 and 24 months (p = 0.88).

Results were similar for changes in 85th percentile speeds at the CC. As indicated, there were no statistically significant differences in changes in 85th percentile speeds across sites:

• 1 and 12 months (p = 0.53).
• 1 and 24 months (p = 0.50).
• 12 and 24 months (p = 0.98).

As indicated, changes in mean and 85th percentile speeds appeared to be consistent across the three after periods. This suggests the signs may have a long-term impact on speed.

STUDY LIMITATIONS/EXPERIMENTAL CONSIDERATIONS FOR SPEED DATA COLLECTION

The data collection methodology selected to compare speeds before and after installation of the DSFS system was based on the team's and project monitor's assessment of what was considered common practice and what was both practical and economically feasible given project resources. However, the team acknowledges that there are certain limitations with field studies in general and in the data collection method selected.

Comparison of speeds before and after installation of a countermeasure can be challenging, given speeds can vary for a number of reasons independent of the treatment. Speeds can vary as a result of temporal or seasonal fluctuations, weather, driver expectation of enforcement, etc. The ideal method to control for temporal and seasonal fluctuations would have been to collect data continuously for an entire year before installation of the signs and then for the 2 years after. However, installation of semi-permanent data collection devices was not practical or economical.

The major emphasis of this research project was to develop crash modification factors (CMF) for DSFS systems. Treatment and control sites were selected for the crash analysis. Ideally, speed data would also have been collected at the control sites so that speed fluctuations independent of the treatment could be assessed. However, given the magnitude of data collection and reduction required for the speed study, resources were not available to collect speed data at the control sites. As a result, control sites were used only for the crash analysis. It was decided, therefore, to use a location upstream from each treatment site as a comparison location for that site for the speed study as described in chapter 5. The intent of the comparison location was simply to identify any unusual trends in speed that might have been occurring independent of the treatment. The comparison locations were not intended to be true "control" locations whereby some statistical analysis could be conducted to compare speed trends unrelated to the treatment.

The impacts of temporal and seasonal fluctuations were minimized as much as possible. Based on the assumption that travel patterns are reasonably consistent for a given time period over several years, data were collected during the same month each year to minimize the impact of seasonal fluctuations. In addition, data were collected only during weekdays and weekends, and holidays were avoided. Unusual events and adverse weather were also avoided, and it was assumed that enforcement was consistent from the before to the after periods.

Data were also collected and reduced using a minimum 48 h so that temporal fluctuations over the course of the day were accounted for. An interval of 24 h was used for about 15 percent of sites owing to various issues with data collection. Use of increments of 24 h ensures that no time periods are over-represented (i.e., each hour of the day was represented the same number of times). However, the team acknowledges these assumptions may not have been valid and that there are a number of other factors that may have affected the speed data.

To account for unknown factors in some measure, data were also collected at a location that was approximately 0.5 miles upstream of the curve to serve as a monitoring (comparison) location. This distance was selected because it was far enough upstream that the sign would not be visible to drivers. It was assumed that vehicles at this location would not have been influenced by the sign and data would represent normal driving. As a result, this location was used to monitor whether speeds had fluctuated independent of the DSFS system. The impact of increases or decreases in speeds at these monitoring locations is discussed for each individual site in appendix A.

Consideration was given to using statistical methods to account for any upstream changes. If the data were perfectly normally distributed, the data at the PC and CC could be adjusted to account for the changes upstream. However, the speed data were slightly non-normal, particularly in the tails of the distribution. And, of course, the study team's major interest in the speed data is the upper tail of the distribution because high speeds are of concern. The non-normal nature of the tails of the distribution did not affect the use of the t-test to compare means. It would have been possible to adjust the means at the PC and CC. However comparisons of the 85th percentile speed and the percentage of vehicles traveling 5, 10, 15, or 20 mph over the posted or advisory speed would have been influenced by differences in the tails of the distributions. As a result, it was not possible to adjust the distributions to account for changes. Given that an acceptable statistical method to account for any upstream changes was not available, these data are included as a qualitative assessment in the discussion of each of the test sites in appendix A.

Although the upstream data collection point (the monitoring, or comparison location) was typically far enough from the curve that it should not have affected driver behavior, in some cases, drivers may have been able to see the sign activated for drivers ahead of them. This may have had some impact at the monitoring location. The monitoring point could have been set further upstream. However, it was critical to avoid intersections and other access points where drivers could turn onto or off the system, so that the same drivers would pass over both the upstream monitoring and curve data collection locations.

Some other data collection methods may have better accounted for temporal and seasonal fluctuations. One method that accounts for speed trends when comparing before and after speeds is to track vehicles between points and then compare changes in individual vehicle speeds between those points (Donnell et al. 2006). This method can also be used to remove vehicles that turn onto or off a roadway just prior to a countermeasure. Vehicles between points can be tracked by collecting data using road tubes with synchronized counter times. Vehicles are then matched up between counter locations using headway and vehicle type.

In this study, data were collected at three locations at 22 curves for four time periods (before, 1 month after, 12 months after, and 24 months after), resulting in 264 datasets for seven States. Tracking vehicles using the counters and road tubes was considered but, given the scale of the data collection effort and available project resources, it was decided that the use of synchronized counters and road tubes was not feasible.

The use of video data recording was also considered. However, the costs to collect and process data were prohibitive. In addition, at many of the sites, it would have been impossible to place a camera unobtrusively in a location that would allow vehicles to be tracked over a significant distance during both day and night conditions.

Another methodological issue that needs to be discussed is the exact placement of the speed recorders. The recorders could have been placed anywhere before or within the curve. Ideally, it would have been desirable to identify the magnitude and the location of each driver's speed change. However, this cannot be done easily, given that each driver slows at a different point and each roadway varied in setting, and the location at which drivers begin to slow may be different for nighttime versus daytime. In addition, regardless of where drivers begin to slow, curve entry speed determines whether they can negotiate the curve successfully or not. As a result, it was decided that speeds at the PC and the CC accurately reflect operational conditions at the site and are therefore appropriate for a before/after experimental design.