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27 C h a p t e r 4 This chapter provides a description of the data used in the analysis, the methodology used to address the primary research hypotheses, and the statistical analysis results. Results from secondary analyses are also discussed. The discussions in this chapter refer to figures and tables presented here and to figures and tables presented in Appendix A. Database Description From the video reviews, data were collected ⢠For 145 NDS and 275 non-NDS drivers; ⢠At 44 signalized intersection left-turn pairs; ⢠At 14 two-way stop-controlled intersections; ⢠In four states: Florida, Indiana, North Carolina, and Washington; ⢠For 758 left-turning maneuvers by NDS drivers; and ⢠For 3,350 events, where an event is defined as either an accepted or rejected gap, by either an NDS or non-NDS driver. The analyses focused on the following measurements (or dependent variables) defined in Chapter 3: ⢠Gap length (duration, in seconds), denoted as follows: 4 Available gaps refer to all measured accepted and rejected gaps (all drivers). 4 Accepted gaps refer to all gaps accepted by an NDS or non- NDS driver for which the gap length could be measured (i.e., the gap end time was observed). Approximately half of the accepted gaps (54%) had no observable gap end time and, therefore, no measured gap length. ⢠Postencroachment time (seconds) for accepted gaps with a measured gap length. To address the two main hypotheses stated at the begin- ning of this report, the potential effect of the following factors on the above measurements was investigated in this study: ⢠Hypothesis 1 (effect of offset on critical gap length): Offset categoryâseven categories for signalized intersections and four categories for two-way stop-controlled intersections. ⢠Hypothesis 2 (effect of sight obstruction on critical gap length): Presence of a vehicle in the opposing left-turn lane. Basic Site, Driver, Trip, and Gap Descriptives Site characteristics of the 44 signalized intersection left-turn pairs are shown in Table A.1 (Columns 1 through 9) and in Table A.2 (Columns 1 through 8) for the 14 two-way stop- controlled intersections. The last three columns in each table provide the number of NDS drivers who drove through each intersection and the number of trips made by NDS and non- NDS drivers. It should be noted that some NDS drivers have made a left turn at more than one intersection or intersection type, and multiple turns at the same intersection, over the course of the NDS period. As a result, the total number of driversâwhen summed across various subgroups of the data (e.g., age group, gender, intersection type, offset category)â does not necessarily add up to 145 in the various tables shown in this report. Number of trips, events, and accepted gaps for NDS and non-NDS drivers are shown, separately for each offset cate- gory, in Table 4.1. The number of NDS drivers, non-NDS drivers, and total events were substantially lower for two-way stop-controlled intersections than signalized intersections, although the number of measured accepted gaps was compara- ble between the two intersection types. This is not unexpected since traffic volumes are generally lower at unsignalized inter- sections than at signalized intersections. In addition, the distri- bution of left-turn offsets was not as good for stop-controlled intersections as for signalized intersections. Specifically, no Statistical Analysis
28 intersections were found for either of the positive-offset catego- ries or for the offset category of -1 ft to -5 ft; a substantial majority of trips were observed at intersections with left-turn lane offset between -11 ft and -15 ft. This limited the poten- tial for identifying differences between offset categories in the analysis. NDS driver age (one of four age groups) and number of trips, accepted gaps, and events are shown, separately for each offset category, in Table 4.2. The distribution of driver age was highly skewed toward older drivers for stop-controlled inter- sections, again, limiting the potential for identifying differ- ences in behavior between age groups for these intersections. To assess how evenly the data used in the analysis are distrib- uted across intersection type and offset category, across NDS driver demographics (age and gender), and across the type of gap (accepted or rejected), a number of bar charts were drawn; these are shown in Appendix A in the following sequence: ⢠Number of sites by state, offset category, and intersection type (Figure A.1); ⢠Number of drivers by state, age group, and gender (Fig- ure A.2); ⢠Number and type of gaps by state and offset category for signalized intersections (Figure A.3); and ⢠Number and type of gaps by state and offset category for two-way stop-controlled intersections (Figure A.4). Figure A.1 shows that the greatest number of sites and the most complete distribution over the offset categories of interest was found for sites in Florida. North Carolina also had a good distribution of offset categories. Only a limited number of sites were found in the other statesâthree sites in Washington and two sites in Indiana. Figure A.2 shows a good mix of drivers by gender and age, especially in the Florida data. Figure A.3 and Figure A.4 show that substantially more events were observed at signalized intersections than at two-way stop-controlled inter- sections; this reflects that traffic volumes are generally higher at signalized intersections. Figure A.3 and Figure A.4 also show that both accepted and rejected gaps were observed across the full range of offset categories. Naturally, more rejected gaps than accepted gaps were observed, since a left-turning driver may potentially reject several gaps at an intersection but can accept only one. Table 4.1. Trip and Event Statistics by Intersection Type and Offset Category Offset Category Total Events Number of Drivers Number of Trips Number of Measured Accepted Gaps NDS Non-NDS NDS All NDS All Signalized Intersections (a) -16 ft or less 196 5 8 19 27 13 19 (b) -11 ft to -15 ft 100 15 20 54 74 8 11 (c) -6 ft to -10 ft 225 24 19 46 64 16 28 (d) -1 ft to -5 ft 594 35 30 79 108 41 56 (e) 0 ft 618 39 62 149 211 57 95 (f) 1 ft to 3 ft 234 21 50 76 126 20 35 (g) 4 ft to 6 ft 98 21 20 29 49 14 25 All signalized 2,065 160 209 452 659 169 269 Two-Way Stop-Controlled Intersections (a) -16 ft or less 45 4 2 19 21 3 5 (b) -11 ft to -15 ft 932 21 53 194 241 112 149 (c) -6 ft to -10 ft 201 9 8 66 73 34 40 (e) 0 ft 107 10 3 27 30 13 13 All two-way stop- controlled 1,285 44 66 306 365 162 207 All Intersections 3,350 204 275 758 1,024 331 476
29 be long. An accepted gap was considered âlongâ when no oncoming opposing vehicles were present in the forward- facing camera at the time the left-turning vehicle began the turning maneuver, or when the rear camera showed that no opposing through vehicle passed through the intersection for at least 12 s after the turn was made. Video reviewers observed traffic patterns at the signal through the rear-facing camera after the turn was made to attempt to ensure that situations in which the left-turn signal turned redâthus ending the gap shortly after the turn was madeâwere not marked as long gaps. Slightly more than half of the nonmeasured accepted gaps (308 of 548) were marked as long. The research team then considered methods for includ- ing the unmeasured gaps that were estimated to be long in the analysis. To do so, a gap length would have to be assigned to these gaps. The research team considered two options: (a) setting the missing gap length equal to the 85th-percentile measured accepted gap length within an offset category, and (b) assigning them a random length from the tail of the distri- bution of measured accepted gap lengths within an offset cate- gory (i.e., distributing the unmeasured but estimated long gaps along the upper 15% tail of the distribution of the measured accepted gaps). However, in both cases, a large proportion of the total data used in the analysis would then be estimated (308 of 784 observations), and the original analysis results (without the truncated gap length) would be substantially skewed toward the longer gaps. This is especially problematic when consider- ing that the remaining gaps not included in the analysis (the Truncated Gap Lengths Many observations collected from the video reviews did not yield a measured gap length when the driver accepted the gap; therefore, those observations were not included in the analysis. As shown in Table 4.1, gap length was measured for just under half of the accepted gaps observed in the videos (476 of 1,024). For the remaining accepted gaps, no gap length was measured because the gap end time could not be observed due to one or more of the following conditions: ⢠The rear-facing camera image quality or camera position did not provide visibility of oncoming through traffic after the left turn was made for a sufficient amount of time to observe the next opposing vehicle go through the intersection. ⢠The geometry of the intersection obscured the visibility of the conflict area soon after the left turn was made. ⢠A following left-turning vehicle (or opposing right-turning vehicle) blocked sight of the intersection before the next opposing through vehicle passed through the intersection. ⢠The signal turned red for the opposing through traffic before the next opposing through vehicle entered the intersection. ⢠No opposing through vehicles were present after the left turn was made within the limits of the rear-facing cameraâs range of visibility. For accepted gaps where the end gap time could not be observed in the video, video reviewers had the option to check a box indicating whether the accepted gap was estimated to Table 4.2. NDS Driver and Trip Statistics by Intersection Type and Offset Category Age Category (years) Number of Drivers Number of Trips Number of Measured Accepted Gaps Number of Events Signalized Intersections 16 to 20 years 25 99 43 454 21 to 25 years 35 120 30 212 26 to 65 years 34 115 44 355 66+ years 24 118 52 586 All signalized 118 452 169 1,607 Two-Way Stop-Controlled Intersections 16 to 20 years 12 76 31 159 21 to 25 years 11 40 10 145 26 to 65 years 8 32 18 77 66+ years 11 158 103 658 All two-way stop-controlled 42 306 162 1,039 All Intersections 160 758 331 2,646
30 Repeated Measures The NDS data provide an opportunity to know how many of the total turning maneuvers at any given intersection, or within any given offset category, were made by the same driver during the study period, as well as how many study intersections a given NDS driver was observed passing through. All statis- tical analyses documented in this report assumed statistical independence of the observations. In other word, the fact that a given NDS driver could have driven through a given inter- section multiple times was not accounted for statistically in the logistic regression models. Table 4.3 summarizes statistics of repeat visits by NDS drivers at intersections within a given offset range, separately for each intersection type. For these counts, researchers assumed that non-NDS drivers for which rejected and accepted gaps were observed were all unique. The table shows that, for example, at signalized intersections with a left-turn offset of -16 ft or less, 12 drivers each made one trip through one of the intersections in that category, while one driver made 15 trips through inter- sections in that category. In the -11-ft to -15-ft offset category, 27 drivers each made one trip through one of the intersections in that category, one driver made 17 trips through intersections in that category, and seven drivers (35 total drivers minus the 28 previously accounted for) made the remaining 30 trips (74 trips minus the 44 already accounted for). Although many drivers made left turns at an intersection multiple times as shown in this table, these observations cannot 240 accepted gaps not measured and not estimated to be long) likely had shorter gap lengths that could have potentially bal- anced that skew toward the longer gaps. For accepted gaps that were not estimated to be long, the research team considered methods for estimating the length of the gap based on the distance of the next visible oppos- ing through vehicle seen in the forward-facing camera at the time of left-turn initiation. However, the research team did not believe there were any reasonable methods available to make this estimation within an acceptable level of error, given the following: ⢠The speed of the opposing vehicle was unknown. ⢠The exact location of the oncoming vehicle becomes more dif- ficult to determine the farther away it is from the intersection. ⢠The potential existed for these vehicles to change course (turn into a driveway or the left-turn lane) or for other vehicles to pull out of a driveway ahead of them and shorten the gap. For these reasons, researchers decided to base the analysis only on gaps with observed begin and end gap times. While the distribution of measured accepted gaps may not be truly representative of the distribution of all accepted gaps, the criti- cal gaps estimated in the analysis are similar to those reported in the literature, indicating that the exclusion of gaps that could not be measured is unlikely to have substantially biased the results. Table 4.3. Repeated Trips by a Single NDS Driver by Offset Category Offset Category Number of All Drivers Number of Trips for All Drivers Highest Number of Repeats for an NDS Driver Number of Drivers Who Made Single Visits Signalized Intersections (a) -16 ft or less 13 27 15 12 (b) -11 ft to -15 ft 35 74 17 27 (c) -6 ft to -10 ft 43 64 12 36 (d) -1 ft to -5 ft 65 108 13 50 (e) 0 ft 101 211 36 85 (f) 1 ft to 3 ft 71 126 28 64 (g) 4 ft to 6 ft 41 49 3 35 Two-Way Stop-Controlled Intersections (a) -16 ft or less 6 21 8 3 (b) -11 ft to -15 ft 74 241 46 59 (c) -6 ft to -10 ft 17 73 31 11 (e) 0 ft 13 30 5 7
31 ⢠Available gap length by offset category (4) for two-way stop- controlled intersections (Figure 4.2); ⢠Accepted gap length by offset category (7) for signalized inter- sections (Figure 4.3); and ⢠Accepted gap length by offset category (4) for two-way stop-controlled intersections (Figure 4.4). Each box plot includes the following descriptive statistics: number of gaps, minimum and maximum gap lengths, mean and median gap lengths, and standard deviation. These distribution plots show that available gap length is rel- atively evenly distributed across offset categories. The research team was concerned that the magnitude of available gap lengths might be confounded with offset category; this would have made the study of the effect of offset on gap-acceptance behavior difficult. However, as shown in these figures, this concern did not arise. These plots also show that the distribution of gap length is skewed positive, with a number of gap lengths reaching as much as 16 s for signalized intersections and 30 s for two-way stop- controlled intersections. The data shown in these plots are the primary data used for analysis and encompass all NDS drivers. be considered repeated measures in the true statistical sense. Repeated measures assumes that, other than time, all other con- ditions affecting gap acceptance remain the same. Here, the driver is making decisions about an entirely different set of available gaps every single time he or she arrives at the inter- section. In addition, conditions such as weather, lighting, reason for the trip, and other considerations may vary from trip to trip, which could influence the driverâs behavior. For these reasons, a repeated measures analysis was not pursued with these data. Available and Accepted Gap Length Distributions: All Left-Turning Situations The first research question to investigate is whether vary- ing offsets have an effect on driversâ gap acceptance. Before analysis, the distribution of available and accepted gap lengths was assessed across the various offset categories for each intersection type. Box plots were drawn for the following combinations: ⢠Available gap length by offset category (7) for signalized intersections (Figure 4.1); Signalized Intersections Red dot = mean; Horizontal line = median; Colored box = mid 50% of data; Blue circle = extreme value (a) -16 ft or less (b) -15 to -11 ft (c) -10 to -6 ft (d) -5 to -1 ft (e) 0 ft (f) 1 to 3 ft (g) 4 to 6 ft 0 2 4 6 8 10 12 14 16 18 A va ila bl e ga p le ng th (s ec ) Offset category N 140 Min 0.3 Mean 2.5 Median 1.6 Max 15.9 Std Dev 2.6 26 1.6 4.4 3.1 12.6 3.2 134 0.2 2.9 2.3 12.8 2.1 500 0.1 2.4 1.6 14.7 2.4 367 0.2 3.4 2.5 15.7 2.9 99 0.3 3.5 2.7 15.2 2.7 55 0.5 3.2 2.2 11.7 2.5 Figure 4.1. Distribution of available gap length by offset category for signalized intersections.
32 Two-Way Stop-Controlled Intersections Red dot = mean; Horizontal line = median; Colored box = mid 50% of data; Blue circle = extreme value (a) -16 ft or less (b) -15 to -11 ft (c) -10 to -6 ft (e) 0 ft 0 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0 22.5 25.0 27.5 30.0 A va ila bl e ga p le ng th (s ec ) Offset category N Min Mean 2.5 Median 1.2 Max Std Dev 24 0.0 14.5 3.5 652 0.1 3.0 1.8 29.7 3.3 151 0.3 3.6 2.3 19.8 3.6 67 0.2 3.1 2.3 11.7 2.6 Figure 4.2. Distribution of available gap length by offset category for two-way stop-controlled intersections. Signalized Intersections Red dot = mean; Horizontal line = median; Colored box = mid 50% of data; Blue circle = extreme value (a) -16 ft or less (b) -15 to -11 ft (c) -10 to -6 ft (d) -5 to -1 ft (e) 0 ft (f) 1 to 3 ft (g) 4 to 6 ft 0 2 4 6 8 10 12 14 16 18 A cc ep te d ga p le ng th (s ec ) Offset category N Min Mean 8.1 Median 7.2 Max Std Dev 13 3.5 15.9 3.4 8 2.2 7.4 7.3 12.6 4.1 16 3.0 6.6 5.8 12.8 3.1 41 0.9 7.7 7.6 14.3 3.6 57 2.7 7.9 7.4 15.7 3.3 20 2.3 7.9 7.5 15.2 2.9 14 1.1 6.2 6.4 11.7 3.0 Figure 4.3. Distribution of accepted gap length by offset category for signalized intersections.
33 the view of oncoming vehicles for the left-turning NDS driver is quite high. For all available gaps, the percentage of oppos- ing left-turn drivers that create a sight obstruction for NDS drivers is 86% for all negative-offset categories combined; for accepted gaps, it is 71%. Both the percentage of events in which sight distance is blocked and the likelihood that an opposing left-turning vehicle will restrict sight distance for the left-turning driver being studied are substantially smaller for the zero- and positive-offset categories. For example, at sig- nalized intersections with an offset between -6 ft and -10 ft, a driverâs view is blocked by an opposing left-turn vehicle during 45% of the gaps evaluated, while at intersections with offsets between 0 ft and 6 ft, a driverâs sight is restricted by an opposing vehicle only about 3% of the time. The table also shows that the percentage of accepted gaps in which the driverâs view is blocked was, in general, much lower than the same per- centage of all available gaps, especially at left-turn lanes with negative offsets at signalized intersections. For example, while a driverâs view was blocked during 30% of evaluated gaps at signalized intersections with an offset of -16 ft or less, this percentage dropped to only 7% when considering only gaps that were accepted. This indicates that drivers tended to wait Available and Accepted Gap Length Distributions Under Sight Obstruction The second research question to investigate is whether the pres- ence of a sight obstructionâdue to the presence of a driver in the opposing left-turn laneâaffected gap acceptance. Out of all cases where gap length could be recorded in the videos (1,669 events across both intersection types), a vehicle in the opposing left-turn lane was blocking the NDS driverâs view in 326 cases (approximately 20% of all cases studies). Table 4.4 shows the following statistics for obstructed and nonobstructed sight-distance situations, by intersection type and offset cate- gory, separately for available and accepted gaps: ⢠Percentage of events in which an opposing left-turning vehi- cle is present; ⢠Percentage of events in which driverâs view is obstructed by an opposing left-turn vehicle; and ⢠Ratio of the two percentages. The table shows that for all negative-offset categories, the likelihood that an opposing left-turning vehicle will restrict Two-Way Stop-Controlled Intersections Red dot = mean; Horizontal line = median; Colored box = mid 50% of data; Blue circle = extreme value (a) -16 ft or less (b) -15 to -11 ft (c) -10 to -6 ft (e) 0 ft 0 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0 22.5 25.0 27.5 30.0 A cc ep te d ga p le ng th (s ec ) Offset category N Min Mean 10.4 Median 10.6 Max Std Dev 3 6.2 14.5 4.1 112 2.3 8.6 7.8 29.7 4.1 34 3.3 8.8 8.5 19.8 4.0 13 2.8 7.5 7.5 11.7 2.8 Figure 4.4. Distribution of accepted gap length by offset category for two-way stop-controlled intersections.
34 durations of rejected gaps represent crash risks judged unac- ceptable by the left-turning driver. The analysis of choice is therefore regression analysis in which the distributions of the accepted and rejected gap durations are analyzed to establish the critical gap duration (tc). The critical gap is defined as the gap that is equally likely to be accepted or rejected. The logistic regression analysis consists of modeling the relationship between the probability of accepting or rejecting a gap of a given length and the length of the gap and the left- turn offset distance. The basic relationship can be expressed in the form of a logistic function as follows: ( )= = + ( )â β +β +β 1 1 1 (4.1) 0 1 P Y X e X Ii i where P(Y = 1|X) = probability of accepting a gap of given length X; X = gap length (seconds); Ii = indicator variable for the categorical offset parameter (covariate); b0 = overall intercept; b1 = common slope on X; until their view was no longer obstructed before accepting a gap. Thus, even before analysis of the lengths of the accepted gaps, the data in Table 4.4 suggest that driver gap-acceptance behavior is affected by left-turn lane offset. Figure A.5 (signalized intersections) and Figure A.6 (two- way stop-controlled intersections) illustrate the distribution of postencroachment time for accepted gaps by offset category and whether sight distance is obstructed. Statistical Methodology This research sought to answer two main questions: (1) does the amount of left-turn lane offset affect gap-acceptance behavior (specifically the critical gap length)? and (2) does the presence of an opposing left-turn driver affect driver behavior when turning left at an intersection? The statistical analysis approach chosen in this study is driven by the two main measurements recorded from the videos: the duration (recorded in seconds) of each available gap and an indication of its acceptance or rejection by the left- turning driver. The durations of accepted gaps represent crash risks judged acceptable by the left-turning driver, while the Table 4.4. Sight Obstruction Statistics Offset Category Available Gaps Accepted Gaps Only Percentage of Events When Opposing Vehicle Is Present Percentage of Events When Driverâs View Is Blocked Ratio of Driverâs Sight Blocked to Opposing Vehicle Present Percentage of Events When Opposing Vehicle Is Present Percentage of Events When Driverâs View Is Blocked Ratio of Driverâs Sight Blocked to Opposing Vehicle Present Signalized Intersections (a) -16 ft or less 34.7 30.1 86.8 7.4 7.4 100.0 (b) -11 ft to -15 ft 25.0 12.0 48.0 23.0 8.1 35.3 (c) -6 ft to -10 ft 48.0 44.9 93.5 32.8 25.0 76.2 (d) -1 ft to -5 ft 26.1 23.6 90.3 24.1 18.5 76.9 (e) 0 ft 26.5 3.9 14.6 21.3 4.7 22.2 (f) 1 ft to 3 ft 35.5 3.0 8.4 34.9 3.2 9.1 (g) 4 ft to 6 ft 21.4 3.1 14.3 30.6 4.1 13.3 Two-Way Stop-Controlled Intersections (a) -16 ft or less 4.4 0.0 0.0 9.5 0.0 0.0 (b) -11 ft to -15 ft 7.8 6.4 82.2 8.7 7.5 85.7 (c) -6 ft to -10 ft 23.9 18.9 79.2 9.6 8.2 85.7 (e) 0 ft 9.3 0.0 0.0 3.3 0.0 0.0 All Intersections Combined Negative offset 20.9 17.9 85.6 15.8 11.2 70.8 Zero offset 24.0 3.3 13.8 19.1 4.1 21.7 Positive offset 31.3 3.0 9.6 33.7 3.4 10.2
35 All analyses were performed separately for signalized and two-way stop-controlled intersections, using PROC LOGISTIC and PROC PROBIT, two statistical procedures of SAS Ver- sion 9.3 (SAS Institute 2013). In general, a 10% significance level was used to test for the significance of the regression coefficients. However, all confidence intervals were calculated as two-sided 95% confidence intervals. analysis results for Critical Gap Lengths Three basic types of logistic regression models were developed: 1. Model Type 1 to test for the effect on the probability of gap acceptance of offset category at signalized intersectionsâ seven offset categoriesâand at two-way stop-controlled intersectionsâfour offset categories. 2. Model Type 2 to test for the effect of sight obstruction on the probability of gap acceptance, separately for each offset category at signalized intersectionsâfive offset categories (zero and negative offsets only due to small sample sizes in the two positive-offset categories). 3. Model Type 3 to test for the effect of sight obstruction on the probability of gap acceptance at signalized intersections (all seven offset categories combined)âand at two-way stop- controlled intersections (all four offset categories combined). Analysis Results for Critical Gap by Left-Turn Offset: Signalized Intersections The results of model Type 1 logistic analysis applied to gaps and gap lengths observed at 44 approach pairs at signalized intersec- tions are presented here. The following results were obtained: ⢠The total number of events is 1,671, with 269 accepted and 1,402 rejected gaps. ⢠The interaction term between gap length and offset category is significant at the 10% level (p-value = 0.06). ⢠Offset is significant at the 10% level (p-value = 0.09). ⢠The slopes of the seven regression curves are not parallel. The seven regressions curves are plotted in Figure 4.5. From the model, the critical gap length, t50, and its 95% confidence interval were estimated, separately for each offset category. The results, along with the number of accepted and rejected gaps in each offset category, are shown in Table 4.5 and plotted in Figure 4.6. The critical gap estimates and their confidence intervals were then compared to identify which pair of offset categories is statistically significantly different. The comparisons and test results are shown in Table 4.6. The pairs of offset categories that are statistically significantly different are shown in bold: ⢠-16 ft or less (7.5 s) from 1 ft to 3 ft (5.0 s) and from 4 ft to 6 ft (4.7 s); bi = parameter representing the deviation of offset category Ii intercept from the overall intercept, i = 1 to k, where k is the number of offset cat- egories in the model; and b0, b1, bi = regression coefficients estimated by maximum likelihood method. By calculating the logit of P [i.e., the (natural) log odds of the outcome] and modeling it as a linear function of the gap length, Equation 4.1 is then linearized to read: ln 1 (4.2)0 1logit P P P X Ii i( )( ) = â = β + β + β The model in Equation 4.2 assumes that the regression lines in the groups defined by offset categories are parallel. This assumption of parallel slopes is first tested by including an interaction term between offset category and gap length into the model in Equation 4.2 as follows: ln 1 (4.3)0 1logit P P P X I Xi i i( )( ) = â = β + β + β + δ where di = parameter representing the deviation of offset category Ii slope from the common slope, b1. The decision of whether to consider a parallel or nonparal- lel lines logit model is made based on the following modeling outcomes: ⢠If the interaction term is not statistically significant, then a parallel lines logit model is assumed (Equation 4.2). ⢠If the interaction term is statistically significant but the off- set term is not, then a parallel lines logit model is assumed (Equation 4.2). ⢠If both the interaction and the offset terms are statistically significant, then a nonparallel lines logit model is assumed (Equation 4.3). Either model then allows for estimating a number of gap lengths of interest, in particular, the gap length corresponding to a probability of 0.5 (i.e., the critical gap length, t50). The ultimate use of the logit model is to estimate the effect of offset on critical gap length, t50. The overall offset effect is estimated by the significance level associated with the offset factor in the model, in other words, the significance of the coefficients bi associated with the indicator variable Ii. From the logit regression models, the critical gaps, t50, and their 95% confidence intervals are estimated at each level of offset. These confidence intervals are then compared in a pairwise fashion to assess which offset category differs statistically from which other offset category with respect to critical gap. This final comparison is performed using a visual hypothesis testing method modified to take into account sample sizes and vari- ability of the data modeled in each group (Smith 1997).
36 the turning vehicle closer to the opposing through lanes of traffic and, therefore, shorten the travel distance (and time) required to clear the intersection. In addition, it should be noted that the provision of positive offset reduces or elimi- nates the potential for opposing left-turn vehicles to block their respective driverâs view of opposing through vehicles, which allows drivers to more comfortably accept shorter gaps. Analysis Results for Critical Gap by Left-Turn Offset: Two-Way Stop-Controlled Intersections The results of model Type 1 logistic analysis applied to gaps and gap lengths observed at 14 approach pairs at two-way ⢠-10 ft to -6 ft (6.5 s) from 1 ft to 3 ft (5.0 s); ⢠-5 ft to -1 ft (7.0 s) from 1 ft to 3 ft (5.0 s) and from 4 ft to 6 ft (4.7 s); and ⢠0 ft (6.2 s) from 1 ft to 3 ft (5.0 s). The analysis of critical gap by offset category for signalized intersections shows that, in general, the critical gap is lon- gest for intersections with negative-offset left-turn lanes and shortest for those with positive-offset left-turn lanes. This is to be expected given that the intersection geometry of a left- turn lane with negative offset requires the turning vehicle to travel a farther distance during the turning maneuver to clear the intersection. Positive-offset left-turn lanes bring Figure 4.5. Predicted probability of accepting gap as function of gap length and offset category for signalized intersections. Table 4.5. Critical Gap Estimates by Offset Category for Signalized Intersections Offset Category Critical Gap Estimate (s) 95% Confidence Limits (s) Number of Accepted Gaps Number of Rejected GapsLower Upper (a) -16 ft or less 7.5 6.0 10.2 19 169 (b) -15 ft to -11 ft 6.1 4.4 12.0 11 26 (c) -10 ft to -6 ft 6.5 5.6 8.0 28 161 (d) -5 ft to -1 ft 7.0 6.2 8.1 56 485 (e) 0 ft 6.2 5.7 6.9 95 404 (f) 1 ft to 3 ft 5.0 4.5 5.7 35 108 (g) 4 ft to 6 ft 4.7 3.8 6.3 25 49 All 269 1,402
37 Figure 4.6. Critical gaps and 95% confidence intervals by offset category for signalized intersections. Offset category (g) 4 to 6 ft (f) 1 to 3 ft (e) 0 ft (d) -5 to -1 ft (c) -10 to -6 ft (b) -15 to -11 ft (a) -16 ft or less Critical gap (sec) 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10 11 12 Signalized Intersections Blue dot=Estimate; Black circles=Lower and Upper 95% CL Table 4.6. Comparison of Critical Gap Estimates Between Offset Categories for Signalized Intersections Comparison Between: Statistically Significantly Different? Comparison Between: Statistically Significantly Different?Offset Category 1 Offset Category 2 Offset Category 1 Offset Category 2 (a) î²16 ft or less (b) -15 ft to -11 ft No (c) î²10 ft to î²6 ft (d) -5 ft to -1 ft No (c) -10 ft to -6 ft No (e) 0 ft No (d) -5 ft to -1 ft No (f) 1 ft to 3 ft Yes (e) 0 ft No (g) 4 ft to 6 ft No (f) 1 ft to 3 ft Yes (d) î²5 ft to î²1 ft (e) 0 ft No (g) 4 ft to 6 ft Yes (f) 1 ft to 3 ft Yes (b) -15 ft to -11 ft (c) -10 ft to -6 ft No (g) 4 ft to 6 ft Yes (d) -5 ft to -1 ft No (e) 0 ft (f) 1 ft to 3 ft Yes (e) 0 ft No (g) 4 ft to 6 ft No (f) 1 ft to 3 ft No (f) 1 ft to 3 ft (g) 4 ft to 6 ft No (g) 4 ft to 6 ft No Note: The pairs of offset categories that are statistically significantly different are shown in bold.
38 From the model, the critical gap length, t50, and its 95% confidence interval were estimated, separately for each offset category. The results, along with the number of accepted and rejected gaps in each offset category, are shown in Table 4.7 and plotted in Figure 4.8. Since offset was not statistically significant in the logit analy- sis, the critical gap estimates and their confidence intervals were not compared to identify which pair of offset categories is sta- tistically significantly different. Clearly, none of the pairwise comparisons are statistically significant as evidenced by the widely overlapping confidence intervals in Figure 4.8. The number of observations available for two-way stop- controlled intersections was substantially lower than that for signalized intersections. In general, all offset categories showed stop-controlled intersections are presented. The following results were obtained: ⢠The total number of events is 1,126 with 207 accepted and 919 rejected gaps. ⢠The interaction term between gap length and offset category was not significant at the 10% level; thus, a parallel lines logit model was assumed. ⢠Offset is not significant (p-value = 0.94). The four regressions curves are plotted in Figure 4.7. Note that the research team could not identify any two-way stop- controlled intersections with positive offsets, reducing the offset categories to four. Figure 4.7. Predicted probability of accepting gap as function of gap length and offset category for two-way stop-controlled intersections. Table 4.7. Critical Gap Estimates by Offset Category for Two-Way Stop-Controlled Intersections Offset Category Critical Gap Estimate (s) 95% Confidence Limits (s) Number of Accepted Gaps Number of Rejected GapsLower Upper (a) -16 ft or less 4.8 3.4 6.2 5 24 (b) -15 ft to -11 ft 5.2 4.9 5.5 149 690 (c) -10 ft to -6 ft 5.2 4.7 5.9 40 128 (e) 0 ft 5.3 4.4 6.2 13 77 All 207 919
39 intersections than for positive- and zero-offset intersections. In fact, there were few observations at positive-offset left-turn lanes in which an opposing vehicle restricted sight distance. A second analysis of critical gap was conducted to determine whether sight obstruction had an effect on critical gap for each of the negative- and zero-offset categories. (The positive-offset category was not included in this analysis because there were only six accepted gaps across three signalized intersections when sight distance was restricted.) Because of the limited number of observations at two-way stop-controlled intersections, this analysis was performed only for signalized intersections. The results of model Type 2 logistic analysis applied to gap acceptance and gap lengths observed at 33 approach pairs at signalized intersections with negative or zero offset are pre- sented here. These analyses were done separately for each of the five offset categories. The following results were obtained: ⢠The interaction term between gap length and sight obstruc- tion was not significant at the 10% level in any of the five analyses, thus, parallel lines logit models were assumed. ⢠The statistical significance and p-values associated with sight obstruction for the five offset categories are as follows: 4 (a) -16 ft or less: not significant (p-value = 0.23); 4 (b) -15 to -11 ft: not significant (p-value = 0.23); 4 (c) -10 ft to -6 ft: significant (p-value = 0.02); 4 (d) -5 ft to -1 ft: not significant (p-value = 0.24); and 4 (e) 0 ft: not significant (p-value = 0.24). The five pairs of regression curves are plotted in Figures 4.9 through 4.13. similar critical gaps at two-way stop-controlled intersections. Larger sample sizes would be needed to better distinguish the gap acceptance behavior among these categories. Analysis Results for Critical Gap by Presence of Sight Obstruction, Separately for Each Offset Category: Signalized Intersections Only The safety concern related to the amount of left-turn lane off- set is not so much the amount of offset itself (although, as dis- cussed above, this does affect the distance traveled during the turning maneuver and, therefore, the gap length required for safe turning) but, instead, the possibility that a left-turn driverâs view of potentially conflicting opposing through vehicles will be restricted by the presence of left-turning vehicles in the oppos- ing left-turn lane. As the left-turn lanes become more negatively offset, opposing drivers are more directly in each otherâs line of sight to oncoming opposing traffic. Conversely, as left-turn lanes are more positively offset, the opposing left-turn driver is moved to the right of the field of view of the primary study driver and away from the line of sight to oncoming opposing traffic. The literature and common sense suggest that restricted sight distance should both increase the average gap length accepted by drivers, as they are more hesitant to accept a gap they cannot fully see, and increase the instances in which drivers accept a gap that they normally would reject because they can- not properly assess the gap length due to the sight restriction. As Table 4.4 shows, the proportion of events for which an opposing left-turning vehicle restricts the sight distance of the primary left-turn driver is much higher for negative-offset Figure 4.8. Critical gaps and 95% confidence intervals by offset category for two-way stop-controlled intersections. Offset category (e) 0 ft (c) -10 to -6 ft (b) -15 to -11 ft (a) -16 ft or less Critical gap (sec) 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 Two-Way Stop-Controlled Intersections Blue dot=Estimate; Black circles=Lower and Upper 95% CL
40 Figure 4.9. Predicted probability of accepting gap as function of gap length and presence of sight obstruction for signalized intersections with offsets of î²16 ft or less. Figure 4.10. Predicted probability of accepting gap as function of gap length and presence of sight obstruction for signalized intersections with offsets between î²15 ft and î²11 ft.
41 Figure 4.11. Predicted probability of accepting gap as function of gap length and presence of sight obstruction for signalized intersections with offsets between î²10 ft and î²6 ft. Figure 4.12. Predicted probability of accepting gap as function of gap length and presence of sight obstruction for signalized intersections with offsets between î²5 ft and î²1 ft.
42 stop-controlled intersections are presented here. The following results were obtained: ⢠The interaction term between gap length and sight obstruc- tion was not significant at the 10% level in either of the two analyses; thus, parallel lines logit models were assumed. ⢠The statistical significance and p-values associated with sight obstruction for the two intersection types are as follows: 4 Signalized intersections: significant sight obstruction effect (p-value = 0.02); and 4 Two-way stop-controlled intersections: significant sight obstruction effect (p-value = 0.03). The two pairs of regression curves are plotted in Figure 4.15 and Figure 4.16. From the two models, the critical gap length, t50, and its 95% confidence interval were estimated, separately for each sight obstruction (yes/no) and intersection type. The results, along with the number of accepted and rejected gaps for each com- bination, are shown in Table 4.9 and plotted in Figure 4.17. Although sight obstruction has an overall significant effect on gap-acceptance probability over the range of available gaps in the study, the comparisons of the critical gaps between sight obstruction and no sight obstruction are inconclusive (i.e., there is not enough evidence to prove statistical significance of the difference between the two estimates.) This might seem contradictory at first, but it should be noted that the logis- tic regression predicts probability of acceptance (y-axis) as a function of gap length (x-axis). Inverse regression is used to From the five models, the critical gap length, t50, and its 95% confidence interval were estimated, separately for each offset category and sight obstruction (yes/no). The results, along with the number of accepted and rejected gaps for each com- bination, are shown in Table 4.8 and plotted in Figure 4.14. With the exception of the offset range of -15 ft to -11 ft, which had the smallest number of observations, the critical gap was larger when a driverâs sight distance was obstructed by an opposing left-turn vehicle than when it was not obstructed. In addition, the difference in critical gaps was greater for inter- sections with negative offsets than for those with zero offset. The only statistically significant effect of sight obstruction was found at intersections with offsets between -10 ft and -6 ft. Because of the low number of events in which the left- turning driverâs view of oncoming traffic was restricted, the differences are not statistically significant for most of the off- set categories. For this reason, the offsets were collapsed for a third analysis to show that overall, the critical gap is longer for drivers whose view is obstructed by the presence of a left- turning driver than for drivers who have no sight obstruction. This analysis was conducted for signalized and two-way stop- controlled intersections separately and is discussed next. Analysis Results for Critical Gap by Presence of Sight Obstruction and Intersection Type, Across All Offset Categories The results of model Type 3 logistic analysis applied to gap acceptance and gap lengths observed at signalized and two-way Figure 4.13. Predicted probability of accepting gap as function of gap length and presence of sight obstruction for signalized intersections with zero offset.
43 Table 4.8. Critical Gap Estimates by Offset Category and Presence of Sight Obstruction for Signalized Intersections Offset Category Is Sight Distance Obstructed? Critical Gap Estimate (s) Significant Difference Between Obstruction and No Obstruction? Number of Accepted Gaps Number of Rejected Gaps 95% Confidence Limits (s) Lower Upper (a) -16 ft or less Yes 9.4 6.0 15.2 No 2 57 No 7.3 5.8 9.9 17 112 (b) -15 ft to -11 ft Yes 4.8 1.7 10.7 No 3 6 No 6.5 4.5 12.3 8 20 (c) î²10 ft to î²6 ft Yes 7.8 6.3 10.0 Yes 7 85 No 5.6 4.6 7.1 21 76 (d) -5 ft to -1 ft Yes 7.7 6.2 9.6 No 10 119 No 6.8 6.0 7.9 46 366 (e) 0 ft Yes 7.7 5.2 10.3 No 2 14 No 6.2 5.7 6.8 93 390 (f) 1 ft to 3 fta Yes â â â â 0 3 No â â â 35 105 (g) 4 ft to 6 fta Yes â â â â 2 1 No â â â 23 48 All zero and negative offsets 209 1,245 All offsets 269 1,402 a Not included in the analysis. Offset Category No Yes No Yes No Yes No Yes No Yes Critical gap (sec) 0 4 8 12 16 (a) (b) (c) (d) (e) Sight Obstructed? Signalized Intersections Blue dot=Estimate; Black circles=Lower and Upper 95% CL Figure 4.14. Critical gaps and 95% confidence intervals by offset category and presence of sight obstruction for signalized intersections.
44 Figure 4.16. Predicted probability of accepting gap as function of gap length and presence of sight obstruction for two-way stop-controlled intersectionsâall offsets combined. Figure 4.15. Predicted probability of accepting gap as function of gap length and presence of sight obstruction for signalized intersectionsâall offsets combined.
45 unobstructed view versus 7.7 s for drivers with an obstructed view resulting from the presence of a left-turning driver (dif- ference of 2.1 s). Analysis of Short Gap Lengths and Postencroachment Times The analyses in the preceding sections show that, on average, drivers wait to accept longer gaps where left-turn lanes are negatively offset and when their view of opposing vehicles is obstructed. However, the shortest accepted gaps may also be taken in these conditions. That is, while many drivers wait for longer gaps when they do not have a good view of the available compare critical gaps. Estimates and their confidence limits corresponding to a 0.5 probability (y-axis) are computed on the gap length axis (x-axis). Therefore, the steeper the curves, the more difficult it becomes to prove statistically significant differences on the x-axis by reverse regression. This analysis showed that the critical gaps for the two sight obstruction conditions are not statistically significantly dif- ferent. However, in both cases, the critical gap when the view is obstructed is longer than when the view is unobstructedâ by 1.1 s at signalized intersections and by 1.3 s at two-way stop-controlled intersections. These differences are some- what smaller than those found by Yan and Radwan (2007). Their research showed a critical gap of 5.6 s for drivers with Table 4.9. Critical Gap Estimates by Intersection Type and Presence of Sight Obstruction: All Offsets Combined Traffic Control Type Is Sight Distance Obstructed? Critical Gap Estimate (s) Significant Difference Between Obstruction and No Obstruction? Number of Accepted Gaps Number of Rejected Gaps 95% Confidence Limits (s) Lower Upper Signalized Yes 7.5 6.6 8.5 No 26 285 No 6.4 6.0 6.9 243 1,117 All 269 1,402 Two-way stop Yes 6.4 5.3 7.6 No 15 66 No 5.1 4.8 5.4 192 853 All 207 919 Figure 4.17. Critical gaps and 95% confidence intervals by intersection type and presence of sight obstructionâall offsets combined. Control Type No Yes No Yes Critical gap (sec) 4 6 85 7 9 Signalized Two-Way Stop Sight Obstructed? Blue dot=Estimate; Black circles=Lower and Upper 95% CL
46 traffic was obstructed by an opposing left-turning vehicle was low; this does not warrant a comparison of the differences in postencroachment times on the short end of the distribution between accepted gaps with and without sight obstructions. When considering all accepted gaps, Table 4.10 shows that the 1st-, 10th-, and 15th-percentile accepted gaps were shorter at negative-offset left-turn lanes than at zero- or positive-offset left-turn lanes at both signalized and stop-controlled inter- sections. Similarly, Table 4.11 shows that a higher percentage of accepted gaps had postencroachment times less than 2, 3, and 4 s at signalized intersections with negative offsets than at zero or positive offsets. These findings suggest that while the 50th-percentile accepted gap length is generally longer at negative-offset left-turn lanes than at zero- or positive-offset left-turn lanes, there is also a higher likelihood that drivers gaps, a few drivers may accept gaps that are shorter than they would otherwise choose because they cannot see how short the gap is. The research team investigated this possibility in two ways: 1. For each of the six combinations of offset (negative, zero, and positive) and sight obstruction (yes or no), the 1st-, 5th-, 10th-, and 15th-percentile accepted gap lengths were estimated for comparison (Table 4.10). 2. The percentage of accepted gaps with a postencroachment time less than 4, 3, 2, or 1 s were calculated for each of the six offset and sight obstruction combinations (Table 4.11). Both Table 4.10 and Table 4.11 show that the number of accepted gaps for which the subject vehicleâs view of approaching Table 4.10. 1st-, 5th-, 10th-, and 15th-Percentile Accepted Gap Lengths With and Without Sight Obstruction by Offset Category Offset Category All Accepted Gaps Accepted Gaps with Sight Obstruction Number of Observations Percentile Number of Observations Percentile 1st 5th 10th 15th 1st 5th 10th 15th Signalized Intersections Negative 114 -1.33 0.34 2.28 2.71 22 -0.66 2.56 2.64 2.97 Zero 95 0.02 2.15 2.97 3.58 2 5.66 5.66 5.66 5.66 Positive 60 -1.50 1.17 3.00 3.53 2 6.84 6.84 6.84 6.84 Two-Way Stop-Controlled Intersections Negative 196 2.14 2.42 2.85 3.38 16 2.42 2.42 2.77 3.67 Zero 13 1.76 1.76 3.97 3.97 0 â â â â Table 4.11. Percentage of Accepted Gaps With Postencroachment Times Less Than 1, 2, 3 and 4 Seconds With and Without Sight Obstruction by Offset Category Offset Category All Accepted Gaps Accepted Gaps with Sight Obstruction Number of Observations Percentage of Observations with Postencroachment Time Less Than: Number of Observations Percentage of Observations with Postencroachment Time Less Than: 1 s 2 s 3 s 4 s 1 s 2 s 3 s 4 s Signalized Intersections Negative 114 6 9 18 36 22 5 5 18 32 Zero 95 1 3 11 21 2 0 0 0 0 Positive 60 3 7 10 20 2 0 0 0 0 Two-Way Stop-Controlled Intersections Negative 196 0 1 11 19 16 0 0 13 19 Zero 13 0 8 8 15 0 â â â â
47 Driver age categories were designed to match SHRP 2âs age categories shown on the NDS data website. However, some age groups were combined to provide a large enough sample size for comparison. The following plots are shown in Appendix A: ⢠Figures A.7 through A.10: Signalized intersections, avail- able and accepted gap lengths, by offset category and age group, and by offset category and gender. ⢠Figures A.11 through A.14: Two-way stop-controlled inter- sections, available and accepted gap lengths, by offset cat- egory and age group, and by offset category and gender. ⢠Figures A.15 and A.16: Signalized intersections, post- encroachment time for accepted gap, by offset category and age group, and by offset category and gender. ⢠Figures A.17 and A.18: Two-way stop-controlled inter- sections, postencroachment time for accepted gap, by offset category and age group, and by offset category and gender. These plots illustrate that, in this database, none of the driver demographics are confounded with offset categories with respect to available or accepted gap length or postencroachment time. In other words, the plots show that (1) all drivers (all ages and both genders) are equally exposed to available gaps across the entire range of gap length without a trend across offset cat- egories; (2) there is no pattern of older drivers accepting mostly long gaps while younger drivers accept mostly short gaps, across gender and all offset categories; and (3) there is no indication that certain age/gender groups have shorter postencroachment times than others. A much larger sample than the 145 NDS drivers included in this study would be needed to undertake a rigorous statistical analysis of the effect of these demographics on accepted gaps. Because sample sizes were small in each age and gender cat- egory when broken down by offset, the research team evalu- ated length of accepted gap and postencroachment time by age and gender with all offset categories combined. The analysis of length of accepted gap showed no statistically significant dif- ferences between age groups or genders and is not shown in this report. The distribution of postencroachment time by NDS driver age group and gender is shown in Figure 4.18 for all signal- ized intersections combined and in Figure 4.19 for all two-way stop-controlled intersections combined. A two-way analysis of variance (ANOVA) was performed to investigate whether gap- acceptance behavior, as measured by post encroachment time, varies between male and female drivers and among age groups. The interaction between age and gender was also tested. The interaction term between age group and gender in the ANOVA was not statistically significant for either intersection type (p-value of 0.60 for signalized intersections and 0.70 for two-way stop-controlled intersections); in other words, there is no evidence from these data that, for example, younger male drivers behave differently than, say, older female drivers. will accept shorter gaps at negative-offset intersections as well. It appears that on average, drivers at negative-offset left-turn lanes are more cautious and wait for longer gaps than drivers at other intersections, but they are also more likely to leave a short amount of clearance time between their turn and the arrival of the next opposing through vehicle than drivers at other intersections. Two possible explanations for this are (1) some drivers take short, risky gaps when their view is obstructed because they cannot properly assess the risk; and (2) drivers may hesitate before initiating a left turn when their sight is obstructed, resulting in less time between the turn and the arrival of the next opposing through vehicle. Secondary analyses The previous analysis sections examined the overall effect of offset distance on driver gap acceptance and whether that effect is further affected by the presence of a vehicle in the opposing left-turn lane. However, the potential influence of other factors, such as relevant intersection characteristics, human factor considerations, and driver demographics, are worth exploring as well. This section presents a number of secondary analyses, more exploratory in nature, on a number of topics, depending on the distribution of the data collected. These secondary analyses serve two purposes. First, the data needed to be checked to ensure that some of the documented influences (such as driver age, driver gender, weather conditions, and time spent waiting for a gap) on left-turn gap-acceptance behavior were not confounded with offset. For example, the data needed to show that a given offset category did not include mostly drivers from one age category or have substantially lon- ger time spent waiting for a gap than other offset categories. Second, it might be of interest to show researchers wanting to use NDS data in future research some of the various types of evaluations that could be conducted using the NDS data. Sev- eral of these secondary analyses are described next. Gender and Age From a human factors perspective, it is important to recognize the effect that driver demographics have on driving, especially left-turning, behavior. The literature suggests that the youngest drivers with the least experience and the oldest drivers, who are less likely to detect approaching vehicles and who make poor speed and gap estimates once vehicles are detected, are the least comfortable judging gaps for left-turn maneuvers (Parsonson et al. 1999). The research team wanted to show differences, if any, in accepted gap length and post encroachment time by age category and gender but also wanted to show that the effects of these factors are not confounded with offset categoryâthat is, that any given offset category does not contain mostly one category of drivers.
48 Figure 4.18. Distribution of postencroachment time for accepted gaps by NDS driver age group and gender at signalized intersections. Signalized Intersections Red dot = mean; Horizontal line = median; Colored box = mid 50% of data; Blue circle = extreme value Female Male Female Male Female Male Female Male -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 P o s t - e n c r o a c h m e n t t i m e ( s e c ) NDS driver gender 16-20 21-25 26-65 66+ Age group N 24 Min 3.3 Mean 6.5 Median 6.0 Max 12.6 Std Dev 2.7 19 2.0 6.8 6.2 14.6 3.2 23 1.0 5.8 5.5 12.3 2.7 7 3.8 7.2 6.8 13.9 3.4 31 0.9 5.5 5.6 10.1 2.6 13 -1.5 4.7 5.3 8.8 2.8 30 -1.1 7.1 6.8 12.3 3.1 22 -1.6 6.8 6.3 14.9 3.7
49 Figure 4.19. Distribution of postencroachment time for accepted gaps by NDS driver age group and gender at two-way stop-controlled intersections. Two-Way Stop-Controlled Intersections Red dot = mean; Horizontal line = median; Colored box = mid 50% of data; Blue circle = extreme value Female Male Female Male Female Male Female Male 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 P o s t - e n c r o a c h m e n t t i m e ( s e c ) NDS driver gender 16-20 21-25 26-65 66+ Age group N 19 Min 1.8 Mean 6.7 Median 6.5 Max 13.6 Std Dev 2.3 12 3.8 9.5 9.5 13.9 2.9 9 2.6 6.2 4.8 14.2 3.9 1 10.8 10.8 10.8 10.8 . 7 4.4 6.5 5.6 12.6 2.8 11 3.3 7.3 8.3 10.4 2.2 49 2.1 7.3 7.1 13.0 2.7 56 4.0 10.0 9.0 24.8 4.7
50 was red at the time of arrival in the queue, this time spent at the red light was included in the time spent waiting for a gap. The literature suggests that drivers who wait longer than 30 s for a gap tend to become impatient and select a shorter, riskier gap. Figure A.19 (signalized intersections) and Figure A.20 (two- way stop-controlled intersections) illustrate the relationship between accepted gap length and time spent waiting to accept the gap. Similarly, Figure A.21 (signalized intersections) and Figure A.22 (two-way stop-controlled intersections) illustrate the relationship between postencroachment time of accepted gaps and time spent waiting to accept the gap. None of these plots provides sufficient evidence to conclude that drivers who spend more time waiting for a suitable gap accept a smaller, riskier gap. Weather and Lighting Conditions It is expected that in poor weather conditions, drivers will wait for longer gaps and proceed more slowly through the intersection. Darkness may affect accepted gap length as well, as gap length may be more difficult to judge. However, the data in this study were heavily skewed toward trips made in daylight and under dry conditions: ⢠93% of the events were observed under dry conditions versus 7% under rainy or snow/icy conditions combined. The ANOVA models were then estimated without the inter- action term, with the following results: ⢠At signalized intersections 4 There is no statistically significant difference in post- encroachment times between male and female NDS drivers, all age groups combined (p-value of 0.93). 4 Postencroachment time varies significantly among age groups, both genders combined (p-value of 0.05). ⢠At two-way stop-controlled intersections 4 Postencroachment time varies significantly between male and female drivers, all age groups combined (p-value less than 0.0001). 4 There is no statistically significant difference in post- encroachment times among age groups, both genders combined (p-value of 0.18). Least square mean postencroachment times and their 95% confidence limits are presented in Table 4.12. Time Spent Waiting for Gap The length of time a vehicle spent waiting for a suitable gap was calculated as the time between when the left-turning driver arrived in the queue (or at the stop bar if there was no queue) and when the driver began the turning maneuver. If the signal Table 4.12. Postencroachment Times by NDS Gender and Age Group Across All Intersections, by Intersection Type Age Group/ Gender Number of Turns Postencroachment Time (s) Statistically Significant Comparisons at 5% LevelMean 95% Confidence Limits (s) Signalized Intersections 16â20 yr 43 6.6 5.7 7.5 21â25 yr 30 6.1 5.0 7.3 26â65 yr 44 5.3 4.4 6.2 Significant difference (p = 0.008) 66î± yr 52 6.9 6.1 7.8 Female 108 6.3 5.7 6.8 Male 61 6.2 5.4 7.0 Two-Way Stop-Controlled Intersections 16â20 yr 31 8.1 6.8 9.4 21â25 yr 10 7.7 5.4 10.0 26â65 yr 18 6.7 5.1 8.4 66î± yr 105 8.7 8.0 9.3 Female 84 6.5 5.6 7.4 Significant difference (p < 0.0001) Male 80 9.1 8.1 10.1
51 Presence of a Following Vehicle The presence of a following vehicle has the potential to make left-turn drivers accept a gap as soon as possible so as not to prolong the wait time of the driver behind them. Table 4.14 shows the percentage of all events (rejected and accepted gaps) and all accepted gaps in which a follow- ing vehicle was present while the left-turn driver evaluated a given gap. Mean and median gap lengths for each condition are presented by offset for comparison. For many of the off- set categories, it appears that drivers do accept slightly shorter ⢠84% of the events were observed in daylight versus 16% in the remaining lighting conditions (dark with streetlights: 9%; dark without streetlights: less than 1%; dawn/dusk: 7%). Figure A.23 (weather conditions) and Figure A.24 (light- ing conditions) illustrate the distribution of events by offset categories across all intersections (signalized and two-way stop-controlled combined). The highly skewed distribution of events across both weather and lighting conditions did not warrant a meaningful analysis of the effect of these two con- ditions on gap-acceptance behavior. Vehicle Type The type or size of vehicle making a left turn, as well as the type or size of oncoming vehicle, may influence the length of gap a driver feels comfortable accepting. Table 4.13 shows the combinations of NDS vehicle type and oncoming vehicle type or gap-closing event (gaps may end when the left-turn signal turns red before the next opposing through vehicle arrives) for the 331 measured gaps accepted by NDS drivers. The table shows that nearly 80% of these gaps were accepted by passenger vehicles. Pickup trucks and vans were virtually unrepresented in this data set. Therefore, a comparison of the gap-acceptance behavior by the drivers of different vehi- cle types was not conducted. Similarly, because only eight gaps were accepted in front of an oncoming heavy vehicle, no analysis was performed by oncoming vehicle type. Table 4.13. Combinations of NDS Vehicle Type and Gap-Closing Vehicle Type or Event for Accepted Gaps NDS Vehicle Type Vehicle Type or Event that Closes Gap Passenger Car Heavy Vehicle Red Signal Indication Not Recorded Passenger car 234 4 7 10 Pickup truck 3 0 0 2 SUV cross- over 59 4 6 1 Van/ minivan 1 0 0 0 Table 4.14. Event and Gap Statistics in Presence of Following Vehicle Offset Category Percentage of All Events with Following Vehicle Percentage of Accepted Gaps with Following Vehicle With Following Vehicle Without Following Vehicle Mean Accepted Gap (s) Median Accepted Gap (s) Mean Accepted Gap (s) Median Accepted Gap (s) Signalized Intersections (a) -16 ft or less 42.4 21.1 7.9 7.9 7.8 7.2 (b) -11 ft to -15 ft 11.1 14.8 11.0 11.0 6.2 5.0 (c) -6 ft to -10 ft 24.5 28.3 6.5 5.8 7.2 6.3 (d) -1 ft to -5 ft 34.3 32.9 7.1 6.7 8.6 8.1 (e) 0 ft 29.6 24.8 8.7 7.5 7.7 7.2 (f) 1 ft to 3 ft 36.1 30.3 7.3 6.5 8.2 7.7 (g) 4 ft to 6 ft 44.3 27.6 5.4 3.9 6.7 6.8 Two-Way Stop-Controlled Intersections (a) -16 ft or less 0.0 0.0 â â 10.4 10.6 (b) -11 ft to -15 ft 15.8 9.3 6.5 5.9 9.0 8.1 (c) -6 ft to -10 ft 6.6 7.6 7.8 6.7 8.9 8.7 (e) 0 ft 7.4 11.1 2.8 2.8 7.9 7.9
52 the distribution of postencroachment time for accepted gaps by the posted speed limit of the opposing approach. The plots do not indicate a decreasing trend in the times drivers leave between the execution of their turning maneu- ver and the arrival of the next opposing vehicle and decreas- ing posted speed limit on the opposing approach increases. It should be noted that sample sizes are small in many off- set categories, especially for the two-way stop-controlled intersections. Left-Turn Signal Phasing Drivers making left turns at an approach with permissive/ protected phasing may be more willing to wait for a longer gap than drivers at a left-turn signal with only permissive phasing, knowing that if no suitable gap is available, they will eventually be given a protected green indication. Figure 4.22 shows the distribution and basic statistics of accepted gap length, sepa- rately for each type of signal phasing. Similarly, Figure 4.23 shows the distribution and basic statistics of postencroach- ment time for accepted gaps separately for each type of signal phasing. The above stated assumption could not be validated gaps when a vehicle behind them is waiting to turn. However, the number of gaps accepted by NDS drivers while a following turning vehicle was present, separately for each offset category, was small. Across all intersection types and offset categories, a vehicle was waiting behind the left-turn NDS driver in only approximately 25% of events. This situation did not warrant a statistical analysis of the effect of the presence of a following vehicle on accepted gap length. Opposing Vehicle Speed The posted speed limit of the opposing approach was available for each left-turning maneuver observed in the study. In the absence of measured opposing vehicle speeds, the posted speed limit of the opposing approach was used as a surrogate for opposing vehicle speed. Conceivably, as the speed of approach- ing vehicles increases, so does the level of difficulty left-turning drivers may have in judging an acceptable gap. This potential relationship was investigated by examining the distribution of postencroachment time for accepted gaps by the various opposing speed limits. Figure 4.20 (signalized intersections) and Figure 4.21 (two-way stop-controlled intersections) show Signalized Intersections Red dot = mean; Horizontal line = median; Colored box = mid 50% of data; Blue circle = extreme value 20 30 35 40 45 55 -2 0 2 4 6 8 10 12 14 16 18 20 22 Po st -e n c ro ac hm e n t t im e (se c) fo r ac ce pt ed g ap s Opposing Approach Posted Speed Limit (mph) N Min .1 Mean 6.0 Median 4.2 Max 13.9 Std Dev 6 2 4.7 104 0.0 6.0 5.5 14.9 2.8 43 -1.6 5.6 5.5 10.2 2.9 71 -1.1 6.8 6.2 19.9 4.1 30 2.2 5.7 5.4 12.3 2.8 15 -1.3 6.6 7.2 14.6 4.8 Figure 4.20. Distribution of postencroachment time for accepted gaps by posted speed limit on opposing approach at signalized intersections.
53 Two-Way Stop-Controlled Intersections Red dot = mean; Horizontal line = median; Colored box = mid 50% of data; Blue circle = extreme value 30 35 40 45 50 55 0 5 10 15 20 25 Po st -e nc ro ac hm en t t im e (se c) fo r a cc ep ted ga ps Opposing Approach Posted Speed Limit (mph) N 3 Min .4 Mean 9.6 Median 8.8 Max 24.8 Std Dev 5 4 4.2 30 2.6 8.2 7.4 19.8 4.4 2 10.8 11.0 11.0 11.2 0.3 115 1.8 6.3 5.8 17.1 3.3 5 2.7 7.4 5.5 13.9 4.9 4 1.8 5.8 6.1 9.2 3.5 Figure 4.21. Distribution of postencroachment time for accepted gaps by posted speed limit on opposing approach at two-way stop-controlled intersections. Figure 4.22. Distribution of accepted gap length (seconds) by type of signal phasing. Signalized Intersections Red dot = mean; Horizontal line = median; Colored box = mid 50% of data; Blue circle = extreme value Permissive Permissive/protected -2 2 6 10 14 18 22 G ap le ng th (s ec ) Left-turn signal phasing N 172 Min 0.2 Mean 7.4 Median 6.6 Max 21.7 Std Dev 3.7 97 -1.4 6.8 6.7 17.2 3.8
54 Summary of results The analysis found that drivers accept longer gaps at intersec- tions with negative offset than with positive offset. This makes intuitive sense, given that the distance drivers must travel to complete the left-turn maneuver is longer at intersections with wider medians and negative-offset left-turn lanes. In addition, driversâ view of opposing through traffic is much more likely to be blocked at left-turn lanes with negative off- set. When a left-turning driverâs view of oncoming through vehicles is blocked by an opposing left-turn vehicle, drivers find it more difficult to judge gaps in opposing traffic and, therefore, take more time to do so, resulting in longer accepted gaps. Specifically, when the sight distance for a left-turning driver was restricted by an opposing left-turning vehicle, the critical gap time for drivers was 1.1 s longer at signalized inter- sections and 1.3 s longer at stop-controlled intersections than when sight distance was not restricted. An analysis conducted to examine this difference by offset category did not produce significant results, mainly because of the limited sample size. However, the results do indicate that opposing left-turning drivers cause sight obstructions for each other much more frequently at negative-offset left-turn lanes than at left-turn lanes with zero or positive offsets. In addition, the likelihood of sight distance being blocked by an opposing left-turn driver was slightly higher at zero offsets than at positive offsets. Thus, intersections with positive offset are likely to provide the most operational and safety benefit. The effects of gender and age on gap-acceptance behavior were considered. The data showed no patterns when evaluated with either plot. In fact, drivers at left turns with permissive/ protected phasing tended to have slightly shorter (0.6 s) post- encroachment times than drivers facing permissive-only phas- ing. However, these results may be misleading since gaps that were accepted on a protected left-turn signal phase were not included in the analysis (although the observations of their rejected gaps during the permissive phase were included). analysis of Near Crashes The research team requested from VTTI a list of all crash or near-crash events recorded in the NDS data at any of the study intersections used in the analysis. VTTI returned a list of six eventsâthree crashes and three near crashesâthat took place within 1,000 ft of one of the study intersections. None of the events were related to a left-turn maneuver at the intersection, and none of the events took place during one of the video segments reviewed for this research. During video data reduction, reviewers recorded any observed avoidance maneuver made by either the left-turning vehicle or the opposing vehicle during a left-turn maneu- ver. Of the 3,350 observed gaps, avoidance maneuvers were observed during only six of themâall at signalized inter- sections. One event was related to the presence of a crossing pedestrian. Of the remaining five events, four occurred after the turning driver had been waiting nearly a minute or longer for a suitable gap. Table 4.15 provides a description of each of the recorded avoidance maneuvers. Because the sample of avoidance maneuvers is so small, a formal analysis of their characteristics could not be conducted. Signalized Intersections Red dot = mean; Horizontal line = median; Colored box = mid 50% of data; Blue circle = extreme value Permissive Permissive/protected -2 2 6 10 14 18 22 Po st -e nc ro ac hm en t t im e (se c) Left-turn signal phasing N 172 Min -1.6 Mean 6.2 Median 5.5 Max 19.9 Std Dev 3.3 97 -1.5 6.1 5.8 16.5 3.6 Figure 4.23. Distribution of postencroachment time for accepted gaps by type of signal phasing.
55 was found. For most of the offset categories, the presence of a following driver resulted in a lower average accepted gap length and a lower median accepted gap length; however, sample sizes were small. Lighting and weather condition were not evaluated due to small sample sizes in one or more of the categories. Most trips considered in the research were completed during daylight (84%) and in dry conditions (93%). Similarly, the effect of vehicle type on turning behavior was not evaluated due to small sample sizes for many categories of vehicle type. An examination of crashes and near crashes recorded in the NDS data set at the study intersections found no safety con- cerns related to left-turning maneuvers. Avoidance maneu- vers by left-turning or opposing through drivers observed in the video data reduction process were rare (only six of 3,350 events) and showed no pattern. However, an evalu- ation of the shortest postencroachment times showed that drivers were more likely to leave a shorter time between their turn and the arrival of the next opposing through vehicle at intersections with negative left-turn lane offset. This may indicate a greater potential for left-turn right-angle crashes at negative-offset left-turn lanes. separately for each offset category; for example, older drivers did not tend to accept longer gaps than younger drivers, and men did not accept shorter gaps than women. However, the number of events recorded for specific combinations of driver age and offset condition was small. When age and gender were considered across all offsets combined, older drivers had signif- icantly longer postencroachment times than younger drivers at signalized intersections. The distribution of all available gaps (both rejected and accepted) for each offset category by driver age, and then by gender, indicated that these factors were not confounded, and that drivers in most categories experienced a similar distribution of available gaps to choose from. No obvious relationship between time spent waiting for a gap and length of accepted gap or postencroachment time was found in this study. The evaluation of the effect of oppos- ing driver speed (approximated by posted speed limit on the opposing approach) on postencroachment time of left- turning drivers was inconclusive as to whether drivers leave less time between the execution of their turning maneuver and the arrival of the next opposing vehicle as opposing speed increases. No effect of left-turn signal phasing (permissive/ protected versus permissive only) on postencroachment time Table 4.15. Summary of Avoidance Maneuvers Recorded During Video Data Reduction Intersection ID Offset (ft) Driver Age Driver Gender Opposing Left-Turning Vehicle Present? Sight Distance Obstructed? Time Spent Waiting for Gap (s) Event Description uid_4 -13 84 M Yes No 53.5 Just after light turns green, the NDS driver hesitates at beginning of gap and then pro- ceeds to cut off opposing traffic by turning in front of them (failure to yield). uid_48 -3 27 F No No 68.3 Opposing driver slowed slightly as left-turning NDS driver turned in front. uid_50 -8 65 M Yes Yes 94.2 Opposing driver slowed slightly as left-turning NDS driver turned in front. uid_51 0 19 M No No 81.5 Opposing driver is a right turner who stops to wait for the NDS driver to complete the turn before completing the right turn. uid_53 0 39 F No No 10.7 NDS driver begins to turn, then corrects back rightward to avoid oncoming car, then completes turn. uid_76 -11 23 M No No 5.3 NDS driver slows during left turn to avoid a pedestrian who is crossing in the crosswalk.
