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There are different methods for developing CMF for a treatment:
A before-after analysis considers and compares the safety performance (e.g. crash count, etc.) of one or several sites before and after the implementation of a treatment. This happens over a time period (before to after conditions)
A cross-sectional analysis takes one or several sites with treatment already applied to them and compare their safety performance with similar sites without any treatments. This happens at the same time (there is no before/after conditions)
[To be continued]
Another important issue that exists with regards to implementing countermeasures is the effect of combined treatments on the same locations, especially when they target the same crash type. Multiplying the CMFs of the two or more countermeasures implemented in the same location may overestimate the effect of combined treatments, as in such conditions, each treatment may not affect the expected number of crashes to its full potential, because the crashes are also being affected by other treatments. (This issue is another story about when do/do not multiply the CMFs, that I will write about somewhere else.)
If we know the CMF value of a treatment and the historical number of crashes (N), the reduced number of crash by applying that treatment would be simply determined by the product of CMF and N. On the other hand, Crash Reduction Factor (CRF) shows the reduction in crashes after treatment, i.e. (1 - CMF) x 100.
In estimating the CMF for any treatment, we need data for both before- and after-treatment conditions, but after-treatment conditions do not always exist. In such cases, an expected number of crash for the after condition can be used, which is calculated from the before conditions' data. This is a challenge in the process of developing the CMF for a treatment as we cannot just simply use the before- condition crash statistics for the after- conditions. There are many factors that affect the occurrence of crashes and crashes are somehow random in nature too. This randomness results in a bias in crash estimation, called regression to the mean (RTM), which is a whole separate animal in statistics and has to be dealt with, when estimating expected crash number for the after- condition.
Just like any other statistical process, when we talk about expected value, standard deviation (error) also shows up to indicate how confident we are in our calculations: the smaller the standard error, the better our estimations.
What is this? A crash modification factor? How would you modify a crash, as if it is a crash scene for a movie?!
The Crash Modification Factor (CMF) is a factor that indicates how much the number of crashes will be reduced (modified).
Assume that 50 crashes have occurred in the last five years on a curve with no signs. Now a treatment (e.g. installing Chevron signs on a curve) is applied on the road (curve) and in the next five years there is only 20 crashes recorded. If we think that installing the treatment caused this reduction in the number of crash at that point, then we may say that this treatment has a CMF of 20/50 = 0.40. It is obvious that if a CMF is higher than 1, it means an increase in crash after implementing a countermeasure treatment.
Sometimes, a CMF is presented as a function, when the safety effect of a treatment is not uniform for all the sites with different characteristics, which is true for many situations. Still, the concept is the same, but this time the CMF considers the specific site's characteristics. Generally, safety is a complex matter and nothing can be assumed linear in this arena, but engineers always make simplifying assumptions to ease the design of nature.
CMFs can be defined for specific types of crashes, specific crash severity, or specific site conditions (rural roadway, urban intersection, etc). That is because not all treatments prevent all different types of crashes; for example, installing rumble strips has nothing to do with angle crashes, so the CMF developed for a treatment may only be applied to a portion of the historical crashes occurred at the treatment site.
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