CHAPTER 5

Case A CMF Development and Results

This chapter describes the methodology used to develop the case A CMFs and presents key findings from the analysis of the ATSPM data and crash data. Additionally, it describes the developed case A CMFs along with the way they can be utilized by agencies to estimate the safety effects of converting arterials from traditional signal timing to ATSPM-based signal timing.

Case A CMF – Analysis Methodology and Findings

This section presents the CMFs that describe the change in safety on several arterial street corridors for which an ATSPM system was implemented and then used to manage the signal system. The presentation includes a description of the study design, a description of the crash history of each corridor, a brief review of the statistical analysis methods used, and a summary of the computed CMFs.

Case A CMF – Study Design

This section provides a brief overview of the study design that was used to develop case A CMFs. The following topics are addressed in separate subsections:

• Study Objective and Method
• Terminology
• CMF Development Approach
• Study Sites
• Database Structure

Study Objective and Method

The objective of the case A CMF study was to develop a set of CMFs that collectively describe the association between ATSPM deployment and the change in traffic safety on an arterial street. The set of CMFs are specific to two crash severity categories (fatal-and-injury crashes combined, property-damage-only crashes), two traffic time periods (i.e., peak hours, non-peak hours), and two facility types (i.e., signalized intersections, segments). The premise is that ATSPM deployment will improve system manager awareness of current system performance, which will trigger changes to the signal operation. If the manager is aware of these CMFs, then the changes made will also reflect consideration of traffic safety.

A before-after-with-yoked-comparison-site study method was used to develop the proposed set of CMFs. Data were collected for a “before ATSPM system deployed” period and an “after ATSPM system deployed” period at each of six arterial streets for which ATSPMs are currently being used to manage the signal system operation. Additionally, similar data were also collected at six arterial streets that do not have an ATSPM deployment. Each of these streets was matched to one of the ATSPM-deployed-streets and served as a comparison (or control) site to account for changes in safety that are unrelated to the ATSPM deployment.

The FI crash severity category discussed in this chapter includes fatal (K), incapacitating injury (A), and non-incapacitating injury (B), and possible injury (C) crashes. This approach for modeling FI crash frequency is in contrast to that used by some researchers who have developed models for other severity combinations (e.g., models for predicting the frequency of the K, A, and B categories combined).

Terminology

A site for case A CMFs is defined to be one signal system consisting of a section of arterial street (both travel directions) that is comprised of multiple consecutive segments, with each segment bounded by a signalized intersection. A site includes N signalized intersections, where N typically varies from 5 to 15.

A segment is defined as a length of street between two adjacent signalized intersections. Segment length is measured from the center of one signalized intersection to the center of the next signalized intersection. A treatment site is a study site that has ATSPM-supported signals during the “after” period (but not during the “before” period). A comparison site is a study site that does not have ATSPM-supported signals during either the “before” or “after” periods.

CMF Development Approach

Crash data were acquired for the “before” and “after” analysis periods. To account for crash exposure, AADT volume data were also acquired for the two analysis periods. Crash frequency (with linear volume adjustment) before and after ATSPM installation was compared to quantify the change in crash frequency associated with ATSPM installation. The change in crash frequency was computed for each site and reported as a CMF value. The methods described by Hauer (1997) were used to compute the CMF values.

The data time period used for the study included at least three consecutive years of data for the “before” period and at least two years of data for the “after” period. The data time period coincided with the most recent years for which crash data were available at each site. An acclimation period was used to separate the before and after periods. This period was intended to minimize the potential for including an ATSPM novelty effect in the computed CMF values.

One set of CMFs was developed for each study site. Each set of CMFs separately examines the change in crash frequency associated with different severity categories, time periods, and facility type settings. These settings include: two crash severity categories (fatal-and-injury crashes combined, property-damage-only crashes), two traffic time periods (i.e., peak hours, non-peak hours), and two facility types (i.e., signalized intersections, segments). The specific CMFs developed are identified in the following list:

• CMF for fatal-and-injury (FI) crashes (all time periods and facility types combined),
• CMF for property-damage-only (PDO) crashes (all time periods and facility types combined),
• CMF for peak traffic time periods (all severities and facility types combined),
• CMF for non-peak traffic time periods (all severities and facility types combined),
• CMF for signalized intersections (all severities and time periods combined),
• CMF for segments intersections (all severities and time periods combined), and
• CMF for all severities, time periods, and facility types combined.

The development of one CMF for each factorial combination of study site, severity, time period, and facility type (e.g., a CMF for FI crashes at signalized intersections during peak traffic periods) was considered but the crash sample size for each site at this level of disaggregation was too small to produce statistically valid CMFs.

Two traffic time periods were evaluated to assess whether the safety effect of ATSPM operation was sensitive to traffic demand level and signal coordination. The two periods focused on the peak and non-peak traffic periods. One analysis period consisted of the collective set of peak hours of the typical week (e.g., 7:00-9:00 am and 4:00-6:00 pm). The second analysis period consisted of the collective set of non-peak hours of the typical week.

Study Sites

The treatment and comparison sites are described in Table 27. Each treatment site is paired with one comparison site. The matched pair of sites are identified by a common number in column 2 of the table. For example, the “1. US 29” treatment site is paired with the “1. US 221” comparison site.

Table 27. Study sites for case A CMF development.

^a – AADT volume represents a segment-length weighted average for the site.

^b – TWLTL: two-way left-turn lane; RC: raised-curb median; U: undivided cross section.

^c – Treatment and comparison sites are matched by number (i.e., treatment site 1 is matched to comparison site 1).

^d – VDOT: Virginia Department of Transportation; UDOT: Utah Department of Transportation; GDOT: Georgia Department of Transportation.

The data time period was established to coincide with the operating agency’s active use of ATSPMs to manage the signal operation at a treatment site. The date of active use is listed in column 2 of Table 28. The “before” time period was set to end prior to the date of active use. The start of the “after” period was set to occur 6 to 12 months after the end of the “before” period. This time lag is used as an acclimation period to minimize the potential for including an ATSPM novelty effect in the computed CMF values. The data time period for each comparison site was set to equal that for its associated treatment site.

Table 28. Data time periods for case A CMF development.

Database Structure

A crash database was assembled for each site. Twelve databases were assembled in total (i.e., one database for each of the six treatment sites and one database for each of the six comparison sites). Each database is structured as a flat file (using an Excel workbook). Each observation in the database describes one crash. The crashes included in the database are those that occurred on the associated site during the corresponding data time period. Each crash in the database is described by a set of variables. Collectively, these variables describe the crash events, roadway conditions, driver conditions, and vehicle conditions associated with each crash.

Table 29 lists the key crash variables needed for CMF development. The crash data was requested to include at least these variables. The researchers used these variables to determine the count of crashes for the FI and PDO severity categories, signalized intersection and segment categories, and the peak- and non-peak-traffic time periods. They were also used to identify and remove crashes that occurred on ice-covered roadways or in parking lots, as well as those that were related to work zone presence.

Table 29. Crash data variables ‒ Case A CMF.

^a – Key variables listed; typically, a larger number of crash, roadway, driver, and vehicle variables were acquired.

The crash data needed for case A CMF development included all crashes that occurred within the boundaries of each arterial street study site during the data time period. They include the N-1 segments, the cross-street legs of each of the N signalized intersections (for a distance back 500 ft), and the external major-street leg at the first and last signalized intersection (for a distance back 500 ft).

In addition to the crash data, the researchers assembled AADT volume data for each study site. The goal was to obtain one AADT volume for each segment of the site for each year of the data time period. It was found that AADT volume was not available for each segment but, rather, only for one or two segments within or external-but-near-to the study site. As a result, the researchers interpolated the AADT volume for intermediate segments. Also, the AADT volume for a given year was not available at a few sites, so the missing volume was estimated by interpolation or extrapolation using the preceding or subsequent year values.

Case A CMF ‒ Database Assembly

This section describes the activities undertaken to assemble the crash database for each study site. The following topics are addressed in this section:

• Crash Data Verification
• Crash Data Screening
• Crash Assignment
• Crash Data Summary

The crash data for each site was requested from contacts with the operating agency associated with each study site. Thereafter, the provided data were imported into an Excel database for assembly.

Crash Data Verification

To ensure the crash data provided by the three transportation agencies did not include anomalies or missing data, the research team conducted the following checks:

• Time intervals with no crashes: The team verified that one or more crashes were represented during each month of the data time period for each study site.
• Roadway segments with no crashes: The team verified that one or more crashes were represented on each road segment of each study site.
• Duplicate crash records: The team verified that there were no duplicate crash records in the database for each study site.

Crash Data Screening

The count of crashes that occurred within the boundaries of each arterial street study site during the data time period are listed in the last column of Table 30.

Table 30. Crash types removed from the database ‒ Case A CMF.

^a – Crash counts for each site correspond to the data time period shown in Table 28.

^b – The study site boundary is described in the text associated with Figure 5.

Prior to the analysis of the crash counts, crashes that are unrelated to the application of ATSPM operation were removed from the database. Specifically, the crashes that were removed were those that occurred on ice-covered roadways or in parking lots, as well as those that were related to work zone presence. The count of the removed crashes is shown in Table 30. This process resulted in the removal of 4.3% of crashes for treatment sites and 5.7% of crashes for comparison sites. As can be observed below, the majority of the removed crashes were due to work zones.

Crash Assignment

This section describes the techniques used to identify crashes associated with two crash categories. One category is “facility type” (i.e., signalized intersection and segment). The two types are mutually exclusive and are used to categorize all crashes in the database. In other words, every crash in the database was assigned to either a signalized intersection or a segment.

A second crash category to which crashes were assigned is “system” (i.e., on system and off system). On-system crashes denote crashes that are most likely to be influenced by ATSPM operation. The two types are mutually exclusive and are used to categorize all crashes in the database.

The assignment technique was based on consideration of the crash variables listed in Table 29. The specific variables used for the assignment varied among states because each operating agency’s crash data included slightly different variables (or similar variables but with different values). The assignment technique for each database source is described in the following subsections.

Crash Assignment for Virginia Data

If one or more of the conditions in the preceding list apply, then the crash is categorized as “Intersection.” It is then defined as “Intersection – unsignalized” unless one or more of the following conditions apply:

• Traffic Control Type variable indicates “traffic signal”, or
• Distance to the nearest signalized intersection on the subject arterial street is 250 feet or less.

If one or more of the conditions in the preceding list apply, then the crash is defined as “Intersection-signalized”.

• Defined as “Intersection - signalized” and the distance to the nearest signalized intersection on the subject arterial street is 250 feet or less, or
• Roadway ID variable indicates the crash is located on the subject arterial street.

Based on these conditions, off-system crashes are typically located on the streets intersecting the subject arterial street. For those streets that intersect at an unsignalized intersection, all crashes on the intersecting street are “off system.” For those streets that intersect at a signalized intersection, all crashes on the intersecting street more than 250 feet from the associated signalized intersection are “off system”. A crash on the subject arterial street is also considered “off system” if it is more than 500 feet before the first signalized intersection or more than 500 feet beyond the last signalized intersection.

Crash Assignment for Utah Data

If one or more of the conditions in the preceding list apply, then the crash is categorized as “Intersection.” It is then defined as “Intersection – unsignalized” unless one or more of the following conditions apply:

• Distance to the nearest signalized intersection on the subject arterial street is 250 feet or less, or
• Traffic Control Device variable indicates “traffic control signal”, or
• Traffic Control variable indicates “signal”.

If one or more of the conditions in the preceding list apply, then the crash is defined as “Intersection-signalized”.

Crash Assignment for Georgia Data

If one or more of the conditions in the preceding list apply, then the crash is categorized as “Intersection.” It is then defined as “Intersection – unsignalized” unless one or more of the following conditions apply:

• Traffic Control Type variable indicates “traffic signal”, or
• Distance to the nearest signalized intersection on the subject arterial street is 250 feet or less.

If one or more of the conditions in the preceding list apply, then the crash is defined as “Intersection-signalized”.

A variable named Intersection-Related is included in the Georgia crash data. Its value is “true” (indicating the crash is related to the intersection operation) or “false”. This variable was considered for use in the facility type assignment. However, this use was abandoned when it was discovered that the variable value was “true” for every crash in 2022 and 2023 at all four Georgia study sites. Many of the “true” values were associated with crashes whose other variable values indicated a non-signal-related crash. In contrast, for the years 2017 to 2020, the Intersection-Related variable had values that varied from “true” to “false”, with each group having logical values for other variables having “intersection-relationship” information.

Crash Data Summary

This section summarizes descriptive statistics for crash data for the treatment sites and the comparison sites. Initially, traffic volume and crash rate statistics are summarized for each study site. Then, the crash frequency associated with the before and after time periods is tabulated and discussed. This discussion examines the change in crash frequency at each site as well as the change in crash frequency for three subset pairs. The three subsets include two crash severity categories (fatal-and-injury crashes combined, property-damage-only crashes), two traffic time periods (i.e., peak hours, non-peak hours), and two facility types (i.e., signalized intersections, segments).

Traffic Volume Time Trend

The trend in segment traffic volume over time is illustrated in Table 31. The values shown correspond to the data time period at each site and include the acclimation period. Looking across all sites, there is a trend toward relatively stable volumes for the period 2016 to 2019, with a few sites having a slight increase in volume, a few sites having no change, and a few sites having a slight decrease. In 2020, the volumes drop significantly at all sites, likely due to the COVID pandemic’s impact on travel. The volume levels begin to increase after 2020 but are still below pre-COVID levels at several sites by 2022 and 2023. This volume variation will likely have an influence on crash frequency at each site and was incorporated in the before-after statistical analysis.

Table 31. Segment traffic volume – Case A CMF.

^a – AADT volume represents a segment-length weighted average for the site.

Crash Rate Summary

The count of “segment” crashes at each study site is listed in Table 32. Segment crashes represent all crashes that are not identified as “intersection-signalized” using the crash assignment rules described in a previous section. As such, segment crashes include crashes associated with unsignalized intersection and driveway facilities.

Table 32. Segment crash characteristics – Case A CMF.

^a – Segment exposure is “mvm”: million vehicle miles; total for all segments of study site.

^b – Crash counts (for both before and after) for each site correspond to the data time period shown in Table 28.

^c – “Segment” crashes represent all crashes that are not assigned to a signalized intersection.

An examination of the crash rates in the last three columns of Table 32 indicates a wide variation in rates among the study sites, especially among the treatment sites. For treatment sites, the “total” (i.e., all severities combined) crash rate varies from 0.50 to 3.04 crashes/mvm. For comparison sites, the total crash rate varies from 1.08 to 2.28 crashes/mvm. A similarly wide range exists in the FI crash rate for treatment sites, relative to the comparison sites, so the issue is unlikely due to differences in reporting threshold among states.

The most notable crash rate extremes are those for treatment sites 1, 2, and 4. The crash rate for sites 1 and 2 are relatively small, so they were examined to determine if there were “missing” crashes (i.e., crash events whose record was not in the data obtained from the operating agency). During this examination, it was noted that the percentage of “possible injury” (i.e., “C”) crashes was only about 3 percent at treatment sites 1 and 2. At the other study sites, the percentage of “possible injury” crashes ranged from 17 to 23 percent (which is typical of the severity distribution found for most arterial street segments). Other than this anomaly, no evidence of missing crashes could be found at treatment sites 1 and 2.

The crash data for treatment site 4 was also examined to find an explanation for its relatively high crash rate. A visual examination of the physical location of each segment crash (using a GIS layer) indicated that there were clusters of crashes on both the major road legs at several of the larger signalized intersections. These clusters tended to be located in the range of 350 to 500 ft back from the intersection. It is possible that these crashes are related to the adjacent signalized intersection but mis-coded by the operating agency. It is worth noting that this anomaly is found in the crash data for only one of the four sites associated with this agency. No change to the crash assignment process for this agency’s data could be devised that would address this issue and could be consistently applied to all four sites, without creating other anomalies.

The count of “intersection-signalized” crashes at each study site is listed in Table 33. In general, about 60 to 70 percent of the crashes at each site are “intersection-signalized” crashes. Based on the crash assignment process, “intersection-signalized” crashes can be located on the subject arterial street or on a cross street.

Table 33. Signalized intersection crash characteristics – Case A CMF.

^a – Signal exposure is “mev”: million entering vehicles; total for all signalized intersections within study site.

^b – Crash counts (for both before and after) for each site correspond to the data time period shown in Table 28.

An examination of the crash rates in the last three columns of Table 33 indicates a wide variation in rates among the study sites. Notably, the crash rates for treatment sites 1 and 2 are much lower than that of the other study sites and lower than the crash rate for typical signalized intersections of 1.0 to 1.1 crashes/mev (Hagenauer et al., 1982). This anomaly was also noted for segment crashes. Based on an examination of the crash data for these two sites, no evidence of missing crashes could be found.

Before-After Crash Frequency

Table 34 to Table 37 summarize the crash data for the before and after periods at each study site. Table 34 summarizes the “overall” crashes (i.e., all crash severity categories, facility types, and traffic time periods combined) for each site. Each of the remaining three tables summarizes the crashes for one of the three CMF pairings (i.e., CMFs for two severity categories, two facility types, and two traffic time periods).

The last two columns of Table 34 list the overall crash frequency for each study site. The crash frequency for all but one site (i.e., treatment site 6) is shown to have decreased from the before to the after period. This decrease may be partly due to the decrease in traffic volume that was previously noted in the discussion of Table 31. If the decrease in crash frequency at a treatment site is larger than that of its comparison site, then the associated CMF for this pair will be less than 1.0 and indicate a reduction in crash frequency is associated with ATSPM operation. The analytic comparison of the two changes in crash frequency and calculation of CMF values is described in the next section.

The crash frequency for treatment site 6 is shown in Table 34 to have increased in the after period, relative to the before period. It was previously noted in the discussion of traffic volume that the traffic volume for the after period at this site was smaller than that for the before period so the trend in crash frequency is unlikely to be explained by the change in traffic volume. The crash data for this site was further examined to determine if there was some artifact of the data that could explain the observed increase in crash

frequency. As discussed previously, it was noted that the variable “intersection-related” in the crash data was set to “true” for every crash in years 2022 and 2023 (but not in previous years). However, no evidence was found from this examination of the crash data that could explain the trend in Table 34.

Table 34. Before-after crash data; all severities, facility types, and hours – Case A CMF.

^a – Trt.: treatment site; Comp.: comparison site.

^b – Crash counts for each site correspond to the data time period shown in Table 28.

^c – Underlined values identify sites where the after-period crash frequency is smaller than that for the before period.

Table 35 lists the crash counts and frequencies for FI and PDO crashes. A review of the FI crash frequencies indicates the after-period crash frequency for eight of the twelve sites is smaller than that for the before period. The PDO crash frequencies decreased for all but one site. A closer examination of the data indicates that the reduction in overall crash frequency noted for Table 34 may be largely due to the reduction in PDO crashes.

There was no change in the crash reporting threshold for Virginia or Georgia during the data time period. However, Utah did raise this threshold during this period. Specifically, in May of 2019, Utah raised the reporting threshold for PDO crashes from $1000 to $2500. This change likely explains some of the reduction in PDO crashes for the UDOT sites.

Table 37 lists the crash counts and frequencies for crashes during peak and non-peak traffic hours. A review of the crash frequencies during the peak hours indicates the after-period crash frequency for all twelve sites is smaller than that for the before period. The crash frequencies for the non-peak hours decreased for ten of the sites. As noted previously, the decrease may be partly due to a decrease in traffic volume (as was discussed in a previous section). Treatment site 6, which has been noteworthy in the discussion of previous tables, is the only site experiencing an increase in crash frequency during the non-peak traffic hours.

Table 37. Before-after crash data by time period; all severities and facility types – Case A CMF.

^a – Trt.: treatment site; Comp.: comparison site.

^b – Crash counts for each site correspond to the data time period shown in Table 28.

^c – Underlined values identify sites where the after-period crash frequency is smaller than that for the before period.

^d – Peak traffic hours occurred during 7:00-9:00 am and 4:00-6:00 pm.

Case A CMF ‒ Before-After Study Statistical Analysis Methods

This section summarizes the statistical analysis methods used to evaluate site compatibility and to compute the CMF values. The following topics are addressed in this section:

• Test of Comparability of Treatment and Comparison Site
• Treatment Effect at One Site
• Test for Similarity of Treatment Effect at Multiple Sites

Test of Comparability of Treatment and Comparison Site

The purpose of including a comparison site (or sites) in the before-after analysis of a treatment site is to account for year-to-year changes in crash risk at the treatment site that are not related to implementation of the treatment. In this manner, the comparison site crash history is used to predict the after-period crash frequency at the treatment site had the treatment not been implemented. This predicted frequency is then compared to the observed after-period crash frequency to quantify treatment effectiveness.

A comparison site (or site group) must be comparable to the treatment site to ensure that the predicted after-period crash frequency is accurate. One measure of this comparability is the similarity of the year-to-year variation in crash frequency between the treatment and comparison sites during the before period. The similarity between the treatment and comparison site crash history can be quantified by performing a test

of comparability. The test of comparability developed by Hauer (1997) was used to evaluate the six treatment-and-comparison site pairs identified in Table 27.

This test computes one odds ratio for each of years 2 through m of an m-year before period. A treatment- and-comparison site pair is considered “suitably comparable” if the average odds ratio is subjectively near 1.0 and its confidence interval includes the value of 1.0. The odds ratio for year i (i = 2 to m) is computed using the following equation:

where,

For assessing the comparability of the site pairs identified in Table 27, a site pair was considered “suitably comparable” when (a) the average odds ratio was between 0.88 and 1.14, and (b) the 95th percentile confidence interval included 1.0. If either criterion was not satisfied, then the comparison site was not statistically suitable for comparison and the treatment site was evaluated using a before-after evaluation with linear traffic volume adjustment. In summary, one of the following two methods were used to compute each CMF, depending on the outcome of the test of comparability:

1. If test is passed: before-after with yoked comparison site and linear traffic volume adjustment.
2. If test is not passed: before-after with linear traffic volume adjustment.

Treatment Effect at One Site

CMF Calculation Method 1

For CMF Calculation Method 1 (i.e., yoked comparison site with linear volume adjustment), the site-specific CMF was computed using the following procedure. This procedure is based on the method developed by Hauer (1997).

Step 1. Compute Reference Year Crash Frequency

The AADT volume information is used in the following equations to compute the crash frequency for the before and after time periods at the treatment and comparison sites. The AADT volume for one predetermined reference year at the treatment site or the comparison site is used in each equation. The reference year is often chosen as the first year of the before period for the treatment site; however, this is not a requirement, and the CMF value will not be affected by the choice of year or site type.

CMF Calculation Method 2

For CMF Calculation Method 2 (i.e., only linear volume adjustment), the site-specific CMF was computed using the following procedure. This procedure is based on the method developed by Hauer (1997).

Step 1. Compute Reference Year Crash Frequency

The AADT volume information is used in the following equations to compute the crash frequency for the before and after time period at the treatment site. The AADT volume for one predetermined reference year at the treatment site is used in each equation. The reference year is often chosen as the first year of the before period; however, this is not a requirement, and the CMF value will not be affected by the choice of year.

where all variables are as previously defined.

The proportions p_B,i and p_A,i are used when a year of the before or after period is a partial year, such that the observed crashes represent only part of the year (and the remaining portion of the year is excluded from the analysis).

Step 2. Compute the Expected Crash Frequency

The expected crash frequency at the treatment site in the after period (N_e,T,A) is computed using the following equation:

where N_e,T,A = expected crash frequency for the after period for the treatment group had no treatment been implemented, crashes/yr; and all other variables are as previously defined. Note that Hauer (1997) uses a “ratio of durations” r_d in the calculation of N_e,T,A. This ratio is indirectly incorporated in the calculations by use of “crash frequency” (i.e., in Equation 14 and Equation 15) while yielding the same CMF value and associated standard error as obtained from Hauer’s procedure (which is based on “total crashes for the time period”).

Step 3. Compute the Variance of the Expected Crash Frequency

The variance of the variable N_e,T,A is computed using the following equation:

Step 4. Compute the CMF Value and CMF Standard Error

The CMF value and its standard error are computed using Equation 10 and Equation 11, respectively.

Step 5. Compute Confidence Interval

The confidence interval for the CMF is computed using the guidance in Step 6 of the procedure for Calculation Method 1.

Test for Similarity of Treatment Effect at Multiple Sites

When the same treatment is implemented at multiple sites, the expectation is that the treatment effect will be similar at each site. This outcome is indicated by each treated site having the same computed CMF value. However, the CMF values can vary among sites due to random crash events and, possibly, due to systematic influences. More specifically, the CMF value may vary among treated sites due to the influence of other factors on treatment effect—factors that vary among the sites. For example, consider several two-lane highway segments that have had their shoulders widened by 1 foot. The computed CMF values are found to vary from 0.88 to 0.98 among the sites. A statistical test of treatment effect similarity indicates that this variation in CMF values is larger than can be explained by random crash events. Further examination of the site conditions reveals that those sites with smaller CMF values have narrow traffic lanes and those with large CMF values have wide traffic lanes. This trend suggests that the effectiveness of shoulder widening may be influenced by the width of the adjacent traffic lane (i.e., shoulder widening is more beneficial when the traffic lane is narrow). In this situation, a CMF function could be developed to predict the CMF for “change shoulder width” as a function of lane width.

The Pearson χ² statistic can be used to test for the similarity of treatment effect across multiple sites (Griffin and Flowers, 1997). This statistic is calculated using the following equation.

with

and

where

all other variables are as previously defined.

The last two terms in Equation 20 are excluded when the Pearson χ² statistic is computed for a CMF based on Calculation Method 2.

The Pearson χ² statistic follows the χ² distribution with p – 1 degrees of freedom, where p is the number of observations (i.e., sites). This statistic is asymptotic to the χ² distribution for larger sample sizes.

The null hypothesis of this test is that the treatment effect at each site is the same. The computed Pearson chi-square value is compared with the χ² distribution to determine the associated probability that this value could be exceeded when the set of CMFs are truly similar. If this probability is less than 0.05, then there is

likely some systematic trend in the set of CMF values and the null hypothesis should be rejected. It is possible that a CMF function could be developed from the set of CMF values if the systematic influences can be identified. If the null hypothesis is not rejected, then the site-specific CMF values can be combined into an overall CMF value that is considered to represent a reliable predictor of treatment effect at future sites.

Case A CMF – Findings from Before-After Study

This section summarizes the findings from the before-after study of six signalized arterial streets at which ATSPM-operation was implemented. The statistical analysis methods described in the previous section were applied to the crash data assembled for six treatment sites and their paired comparison site. The discussion examines CMF values reflecting overall crashes at each site as well as CMF values for three subset pairs. The three subsets include two crash severity categories (fatal-and-injury crashes combined, property-damage-only crashes), two traffic time periods (i.e., peak hours, non-peak hours), and two facility types (i.e., signalized intersections, segments).

Table 38 lists the overall CMF values for each of the six treatment sites. The CMF values for sites 2, 3, 5, and 6 were computed using Calculation Method 1 (i.e., before-after with yoked comparison site and linear traffic volume adjustment). The CMF values for sites 1 and 4 were computed with Calculation Method 2 (i.e., before-after with linear traffic volume adjustment). Method 2 was used for Sites 1 and 4 because their respective comparison site did not pass the test of comparability.

Table 38. Overall CMF values; all severities, facility types, and hours – Case A CMF.

^a – s.e.: standard error of CMF. Bold CMFs exclude 1.0 from the 95^th-percentile confidence interval.

^b – If null hypothesis is not rejected, the CMF for all sites combined is reported in the last row.

The comparison site for SR 266 (i.e., E 11400 S) was not found to satisfy the comparability test criteria. However, “E 11400 S” was found to experience a 26.4 percent reduction in the PDO crash rate in the “after” period corresponding to an increase in the crash reporting threshold. This change is consistent with the PDO crash rate reduction for the other comparison site in Utah. To account for this trend, the expected crash frequency in the after period for SR 266 was reduced to reflect a 26.4 percent reduction in PDO crashes. This adjustment is also made to the SR 266 results in the subsequent tables presented in this section.

The CMF values in Table 38 indicate a wide range in safety effects associated with the implementation of ATSPM operation. Crash frequency decreased by 20 percent at site 1 and increased by 33.6 percent at site 6. In contrast, site 3 experienced almost no change in crash frequency. The test of similarity of treatment effect indicates that the range of CMF values is too large to be explained by random variation in crash events. Rather, there is likely a systematic influence underlying the six CMF values. To this point, there is

a notable correlation between CMF value and operating agency. Specifically, the CMF value varies widely from agency to agency. Possible explanations for the wide variation are offered in the next paragraph.

An examination of the data was undertaken to determine whether any of the scenarios in the following list might explain the observed correlation and trends. However, the findings from this examination did not reveal an explanation for the wide range in CMF values.

• Differences in safety-related site characteristics within the group of sites (e.g., some sites have high intersection volume-to-capacity ratio and others have a low ratio; some sites have a divided cross section and others have an undivided cross section; some sites have a low speed limit and others have a high speed limit; some sites have a short cycle length and others have a long cycle length).
• A change in site character from the before to the after period that had a change in safety (e.g., change in speed limit).
• A change in signal operation (due to ATSPM management practice) at a site that can indirectly influence safety (e.g., increase in operating speed due to improved signal coordination; reduction in cycle length leading to an increase in the frequency of change intervals and stops; conversion from full-time protected left-turn operation to time-of-day protected left-turn operation).

Table 39 lists the CMF values for FI crashes and for PDO crashes. In general, the site-to-site variation in CMF values for both severity categories is similar to that shown in Table 38. When applied to FI crashes, the test of similarity indicated that there was sufficient variability in each CMF that it is possible that treatment has the same effect on FI crashes. However, the correlation between CMF value and operating agency is clearly present and the combined CMF may not be accurate in all cases.

Table 39. CMF values by crash severity; all facility types and hours – Case A CMF.

^a – s.e.: standard error of CMF. Bold CMFs exclude 1.0 from the 95^th-percentile confidence interval.

^b – If null hypothesis is not rejected, the CMF for all sites combined is reported in the last row.

The CMF values for facility type and time period are listed in Table 40 and Table 41, respectively. The correlation between CMF value and operating agency (first noted in Table 38) is present in these two tables.

Further investigation is needed to provide a better understanding of the wide variation in CMF values and the extent to which systematic factors may be influencing these values. There is a notable correlation between operating agency and CMF value. However, the investigation should explore the underlying site characteristics and ATSPM management practices to determine whether this correlation can be explained by quantifiable and logically causal factors. If some combination of factors can be shown to have a logical correlation with the CMF values, then a CMF function could be developed to support predictive safety assessments of proposed ATSPM-based strategies.