Requisitos de autorización y funcionamiento de puestos de bolsa

A secondary performance matrix that was used in evaluating the confirmation lights was the violation time into red, which was defined as the time elapsed prior to a violation occurring. Studies have shown that RLR violations occurring more than two seconds after the red signal indication are more dangerous compared to violations occurring less than a second after the all- red phase (Fitzsimmons et al., 2007; Lum and Wong, 2003). During an all-red phase, vehicles that enter the intersection less than a second after the red indication normally clear the

intersection before vehicles currently stopped at the cross street get the green light to start. In such instances, drivers of vehicles in the cross street are not exposed to potential conflicts that could result in crashes. However, drivers who enter the intersection late may put themselves and other road users at risk. An analysis of a before-after effect on RLR violation time into red was conducted to determine whether confirmation lights have the potential to change driver behavior when a violation occurred. The null and alternate hypotheses were stated respectively as:

Ho : Confirmation lights have no effect on the frequency of RLR violation time into red

Ha: Confirmation lights have effect on the frequency of RLR violation time into red

6.5 Methodology

After the video data were reduced, RLR violations for left-turn and through-movement were combined and categorized into two groups. Group 1 consisted of all the RLR violations which occurred within two seconds after the onset of the red signal and group 2 consisted of the violations which occurred more than two seconds after the red indication. Two seconds was chosen because in the City of Lawrence, a minimum of 1.5 seconds is used for the all red interval. This means that any RLR violation after 1.5 seconds into red has a high probability of

108 resulting in a RLR crash. Due to the small sample size of the RLR violation time into red, 2x2 contingency tables were used for analyzing the data for each site category (treatment, spillover, and control sites). Table 22 shows an example of the 2x2 contingency table with the frequency of RLR violations, which occurred less than two seconds and after two seconds during the before and one month after study periods at the treatment sites.

Table 22. Contingency Table for RLR Violation Frequency at the Treatment Sites.

Study period _{2 seconds} Number of Violations Total > 2 seconds

Before 54 2 56

1 month after 17 2 19

Total 71 4 75

After developing the 2x2 contingency tables for each study site, a Chi Square Test of Independence was chosen as the statistical method to determine if there exists a relationship between the two nominal variables: violation times after red indication, and before-after violation period. The Chi Square statistic was chosen because it was the appropriate method to compare counts of categorical responses between the two independent groups (before and after study periods). This analysis was completed with the understanding that confirmation lights may have an effect on the frequency of dangerous RLR violations at signalized intersections. The formula for the Chi Square Test of Independence is shown in Equation 6.

∑ Eq. 6

Where = calculated Chi Square value

E = expected frequency of RLR violation

109 In order to find the Chi Square value, the expected frequency for each column i and row j in Table 22 was calculated using Equation 7.

Eq. 7

Where = the expected frequency for the cell in the ith row and the jth column,

= the total number of subjects in the ith row

= the total number of subjects in the jth column

= the total number of subjects in the table.

Table 23.shows the expected frequencies for the cells in Table 22.

Table 23. Expected Frequencies

Study Period _{2 seconds} Number of Violations Total > 2 seconds

Before 53.01 2.99 56.00

1 month after 17.99 1.01 19.00

Total 71.00 4.00 75.00

The Chi Square value was computed as follows: ∑ 6.6. Results

6.6.1 Chi Square Test for Before and 1 Month After Study

Table 24 shows the Chi Square Test result for the before and one month after study periods. As shown, the numbers of RLR violations which occurred within two seconds after the red

110 indication were higher than the number of violations which occurred more than two seconds after the red indication at all the study sites. It can be seen from Table 24 that, most of the before violations reduced substantially one month after installation of the confirmation lights. The Chi Square statistical analysis showed p-values greater than 0.05 indicating that there were no statistical significant changes in the before-after violation time into red at all the study sites. This means that the confirmation lights one month shortly after installation did not have any

significant effect on drivers’ behavior of entering the intersections early or late after the red signal was indicated.

Table 24. Chi Square Test for Before and 1 Month after Study

Site

Category Study Period

Number of Violations Chi-square

Value P-value

2 seconds into red >2 seconds into red

Treatment Before 54 2 1.36 0.24 1 month after 17 2 Spillover Before 52 7 0.04 0.84 1 month after 26 4 Control Before 31 6 2.48 0.12 1 month after 37 2

6.6.2 Chi Square Test for Before and 3 Months After Study

Table 26 shows the results of the Chi Square Test and their associated p-values for the before and three months after violation time into red at the treatment, spillover and the control sites. As previously discussed, more RLR violations occurred within two seconds after the red indication than the number of violations which occurred more than two seconds after the red indication. At all the study intersections, the statistical tests showed p-values greater than 0.05. This indicated that the confirmation lights did not have any effect on the frequency of RLR violation time into red at the 95 percent level of confidence. Considering the City of Lawrence, the control sites did not see any difference in the violation time into red before and after the confirmation lights were

111 installed. Overall, there was no change in the violation time into red after the installation of this countermeasure indicating that this countermeasure cannot change driver behavior when the violations occur.

Table 25. Chi Square Test for Before and 3 Months After Study

Site

Category Study Period

Number of Violations _Chi-square

Value P-value

2 seconds into red >2 seconds into red

Treatment Before 54 2 3.26 0.07 3 month after 39 6 Spillover Before 52 7 2.12 0.15 3 month after 61 3 Control Before 31 6 1.66 0.20 3 month after 49 4

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