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26 was conducted in order to accurately estimate the effect of this Thus, this AMF (or series of AMFs) is related to any treat- treatment on overall "crash harm." Based on a recent report ment that is associated with a changed mean speed. Appendix F from FHWA (72), the comprehensive cost per crash is $47,333 provides the details associated with this evaluation. for angle crashes and $26,735 for rear-end crashes. Assuming that the overall severity of non-angle crashes is quite similar to Data Used that of rear-end crashes, the economic analysis revealed a reduction of about $11,800 per intersection-year in the over- The data used in this reanalysis were supplied by Elvik all crash harm due to this treatment. from his earlier study (74). His research team had extracted data on mean speed change and the related crash-frequency Replace Single Red Signal Head with Dual Red change from 97 published international studies containing Signal Heads 460 results. Each result contained information on mean speed and crash frequency before treatment and mean speed A second red signal head was added to the existing head at and crash frequency after treatment. Some studies included eight intersections in Winston-Salem. The EB analysis indicates information on mean speed and crash frequency for a set of a slight, but not statistically significant, increase in both right- comparison locations where no treatment was installed. Each angle and total crashes after installation. Given the limited sam- result also included study details such as the type of study ple of sites that were evaluated, these results suggest that the (e.g., simple before/after or time series), the country where installation of double red signal heads does not appear to be an the study was conducted, the type of location (urban/rural) effective strategy for reducing total or angle crashes. and the road system. The country data were important since a secondary objective of this reanalysis was to determine if the Speed Change and Crashes results from non-U.S. studies could be applied to U.S. roads. The research team then reexamined each of the study Description of Treatment and Crash Types results and clarified possible errors through a series of con- of Interest versations with Elvik. The research team also calculated The objective of this analysis was to develop an AMF that revised estimates of standard errors of the crash and speed would relate speed change caused by a treatment to a change in changes based on the study types, using procedures that will crash frequency for a certain level of crash severity (i.e., fatal, be used in the upcoming Highway Safety Manual. injury, no-injury). Thus, if one could estimate the effect of a treatment on mean speed, the AMF would then translate this Methodology change in mean speed to an estimated change in crash fre- quency. With this speed change AMF, if the change in mean The final dataset was then used to examine the power speed can be anticipated so can the potential safety effect. If the model results and to develop alternative model forms. One change in mean speed can be measured, the future safety effect alternative model form was based on the "maneuver time can be estimated without waiting for crashes to materialize. The needed to avoid a crash," which is a function of initial speed treatments could theoretically include "passive" treatments and the distance to an obstacle or vehicle. The other alterna- such as changes in speed limits or increased speed enforcement tive model form was based on the underlying physics of speed (i.e., "passive" in the sense that the driver can choose to react or versus crash frequency and crash injury. The two alternative not react to the treatment) and "active" treatments that could model forms were then compared and used to develop a final include changes to the roadway such as residential traffic- set of proposed AMFs. calming speed tables (i.e., "active" in the sense that the driver is "forced" to reduce speed by the treatment). Results A study by Nilsson (73) hypothesized a "power model" relating the ratio of before-treatment and after-treatment crash Like the results of the earlier study (74), both alternative frequency to the ratio of before-treatment and after-treatment models indicated that the data supported the existence of a rel- mean speed raised to some power, with the power changing atively strong relationship between speed change and change for different crash severities. Elvik et al. (74) further developed in fatal and non-fatal injury crash frequency. The relationship this power model using a large set of data extracted from pub- with property-damage-only (PDO) crashes was not distinct. lished research reports. The objective of the reanalysis of the Both of the alternative model forms indicated that the speed- Elvik et al. data done in this research was to determine if such versus-crash relationship in the foreign studies was similar to a relationship exists, and if so, whether the power model or that in the U.S. studies. Quality of fit statistics indicated that some alternative model form best describes the relationship be- both model forms were slightly more accurate than the power tween speed changes and crash frequency. model. As expected, the two alternative models produced