As safety is a primary concern to engineers, road users, and adjacent property owners, a major effort was undertaken to determine if speed limit changes undertaken by the participating States resulted in improved safety. To assess the safety impact, a before and after design with a comparison group and a check for comparability was employed. The analysis method and findings are presented in the following sections of this report.
As speed limits on the 100 experimental sections were posted on different dates, every effort was made to collect as much accident data as possible to prevent using fragmented time periods. To provide a proper comparison, the same before and after time period used at the experimental site was used at its corresponding comparison site. The accident data were sorted and tabulated using dBASE IV. The final data base contained over 20,000 accident records; however, after matching comparable before and after time periods at the experimental and comparison sites, considerably fewer records were included in the final analysis.
Shown in appendix E are the summaries of the total reported accidents and injury accidents by before and after time period for the experimental and comparison sites.
The evaluation design selected to estimate the effectiveness of the speed limit changes on accidents is the before and after design with a comparison group, and a check for comparability. With this design, multiple before and after accident counts are taken at both the experimental and comparison locations. The purpose of the multiple measurements is to determine if the control locations are, in fact, suitable comparisons for the experimental sites. The purpose of the comparison group is to account for changes in safety (such as weather conditions, driver characteristics, etc. ) between the before and after periods. The primary benefit of this design is that the comparison group controls for extraneous factors, and as multiple measurements are made over time, some relief from regression-to-the-mean ~~ is obtained.
Numerous statistical methods have been used for analyzing categorical accident data. Each method contains strengths and weaknesses. For example, the simple before and after design may be biased due to nonrandom errors introduced by unaccounted for factors that unevenly affect accidents in the before or after period. On the other hand, the use of a comparison group with a small number of accidents can also bias the results. Due to the strengths and weaknesses of various accident analysis methods, four different techniques were used to estimate the safety effects of the speed limit changes.
The first method, reported by Griffin, uses multiple before and after analysis with paired comparison ratios to estimate the overall safety effects at multiple treatment locations.[27,28] The second method is the classical cross-product ratio or odds ratio that estimates the safety effect based only on the total accident counts at the sites. Application of this method is also discussed by Griffin.
Because regression-to-the-mean is an important factor which can often lead to erroneous conclusions in accident analyses, the third analysis method employed the use of a new empirical Bayes method, EBEST (Empirical Bayes Estimation of Safety and Transportation), which adjusts for regression-to-the-mean bias and provides a more realistic estimate of the safety effects. The EBEST procedure requires a reference group and measurement of site exposure. Because the reference group available for use in this study was smaller than required for appropriate application of the method, the procedure was used primarily to approximate the amount of regression-to-the-mean bias in the data set.
The fourth analysis method is the before and after design which uses the weighted average logic to produce an overall estimate of safety effects at multiple treatment locations. This method does not use comparison sites to control for extraneous factors, thus, it was only used when the comparison groups were not comparable or the accident counts at the comparison sites were too small to conduct a meaningful analysis. The results obtained with this design may contain nonrandom errors such as changes in traffic volumes, weather conditions, accident reporting thresholds, and other factors. Thus, the safety estimates produced by this method may be invalid.
The before and after design with a comparison group and a check for comparability can be used to estimate the effects of a treatment on accidents at a single site or for a group of sites if the number of reported accidents is sufficiently large. In this study, the design was used to estimate safety effects for groups of sites. The design was not used to estimate the effect of posted speed limit changes on accidents at each individual experimental site because the small accident sample sizes at the majority of the sites were much less than that needed to use comparison sites. In other words, the comparison group must have a sufficient number of accidents, otherwise, it is better not to use it.
One of the major problems cited in using a comparison group in accident evaluation is having a small sample. In conducting the accident analyses comparison groups were not used if the number of accidents was less than 240 in either the before or after period. The selection of a minimum sample of 240 accidents was arbitrary, i.e., to detect small safety effects, accident sample sizes needed may exceed 600 accidents in each the before and after period. This amount of data simply could not be collected within the scope of this study.
In addition, the comparison groups were not used to estimate the safety effects when the comparability tests indicated that the accident histories during the before and after periods at the experimental and comparison sites were not comparable. When the groups were not comparable, the before and after design, using the weighted average logic, was employed. 
The analysis plan included the following steps:
Details of the analysis procedure, along with an example of the paired comparison ratio method, are provided in appendix F.
As shown in table 9, accident rates decreased for both speed limit groups at the experimental sites after the speed limit changes were made. However, it is well known that safety is affected by other factors such as weather conditions, driver characteristics, increases in travel demand, etc. To account for the effects of these changes, a comparison group was used. For the group where speed limits were lowered, the accident rate at the comparison sites during the same time period decreased by 12 percent, while at the experimental sites, the decrease was only 2 percent. Conversely, the accident rate at the experimental sites where speed limits were raised decreased by 16 percent, while the accident rate at the comparison sites increased nearly 4 percent.
Contrary to public perception that accidents decrease when speed limits are lowered and increase when speed limits are raised, the accident rates in table 9 indicate that this perception may not be true. The data actually indicate that accident rates were reduced at sites where speed limits were raised and increased at sites where speed limits were lowered, assuming that the comparison site accident history reflects what actually would have occurred at the experimental sites. The validity of this assumption, as well as the results of the accident evaluation, are presented in the following paragraphs.
As previously mentioned, the statistical analyses were conducted for sites where speed limits were lowered, sites where speed limits were raised, and sites where the speed limits were posted at various levels relative to the 85th percentile speed. A summary of the results, by analysis method, is provided in table 10.
The EBEST analysis indicated that the average shrinkage in the data set where speed limits were lowered was 0.15. The average shrinkage in the data set where speed limits were raised was 0.10. Average shrinkage factors range from O (no regression-to-the-mean bias) to 1.0, indicating substantial bias. The shrinkage factors mentioned above indicate that regression-to-the-mean does not pose a major problem with the results given in table 10.
Table 9. Before and after accident rates for the study sites. ------------------------------------------------------------ Number of Accident Rate Percent Group Sites Before After Change ------------------------------------------------------------ Lower Limits Experimental 58 4.24 4.15 -2.1 Comparison 49 3.92 3.45 -12.0 ------------------------------------------------------------ Raise Limits Experimental 41 2.33 1.95 -16.3 Comparison 34 3.05 3.16 3.6 ------------------------------------------------------------The chi-square test of homogeneity listed in table 10 was used to determine if the treatment effects are consistent from site to site. As reflected in the p-values shown in table 10, it was concluded that the treatment effects are consistent for the sites included in each analysis group.
As shown in table 10, the results of the paired comparison ratio method indicate that accidents increased by 5.4 percent after speed limits were lowered at the experimental sites. This result is not statistically significant, as the level of confidence is 44 percent. (The level of confidence is obtained by subtracting the p-value from 1, and multiplying the result by 100, i.e., (1 - .56) x 100 = 44). In other words, in 44 times out of 100, chance alone would not have caused this difference. The cross-product method and the EBEST estimate produced the same conclusion.
The paired comparison ratio analysis indicates that a 6.7 percent reduction in accidents occurred at the sites where speed limits were raised. The level of confidence of this estimate is 59 percent. The 95 percent confidence limits for this estimate ranges from an accident reduction of 21 percent to an accident increase of 10 percent. The cross-product method and the EBEST estimate also indicated that an accident reduction occurred at the sites were speed limits were raised.
The analysis further indicates that injury accidents increased irrespective of whether the speed limits were raised or lowered. Because the number of accidents at the comparison sites was less than 240 in the before and after period, injury accident estimates were based on the before and after analysis which does not control for nonrandom factors that can affect the results. Consequently, the accident estimates for injury accidents should be treated with caution. This precaution is also applicable to the results for the other groups listed in table 10 where the safety effects were estimated with the before and after method.
To further examine the effects of altering posted speed limits on accidents, the experimental and comparison sites were subdivided into the following categories based on the posted speed limit and the speed data obtained during the study:
Before and after analyses were conducted for the sites where the speed limits were set within 5 mi/h (km/h) of the 85th percentile speed. The results indicate a 3.4 percent increase in accidents for this group. The level of confidence is 42 percent. Again, because the before and after design does not control for extraneous effects, this result may not be valid.
Before and after analyses were also conducted for the sites where the speed limit was posted more than 5 mi/h (8 km/h) below the 85th percentile speed and the new limit was also set more than 5 mi/h (8 km/h) below the 85th percentile. The results indicate a 2.8 percent reduction in accidents; however, the level of confidence is only 29 percent.
Although many transportation engineers and the public consider speed limits to be associated with safety, there have been very few studies of the effect of changing speed limits on accidents on nonlimited access highways. Kessler found that when speed limits were raised at 30 locations in Illinois. the 85th Percentile speeds were not changed I however, accidents decreased from 62 to 40.  Wenger examined accident experience at 25 locations in St. Paul, Minnesota and found that raising speed limits from 30 to 35 or 40 mi/h (48 to 56 or 64 km/h) adversely affected accidents. Dudek and Ullman recently examined the impacts of posting speed limits below the 85th percentile speed at 6 locations in Texas and found no conclusive effect on either travel speeds or accidents. 
One problem with the previous research is the small number of sites used to estimate the safety effects. The number of sites and the number of accidents was too small to determine if speed zoning had an effect on accidents, consequently the findings were generally described as not statistically significant.
The study with the largest accident sa
mple size conducted to date was recently completed by Parker in Michigan. The study included experimental sites where speed limits were changed and corresponding comparison sites 8efore and after accident data were collected for 68 nonlimited access highway sections and 86 comparison sections. The analysis revealed that accidents at the 47 experimental sections were speed limits were lowered were reduced by 1.75 percent, however, the level of confidence in the estimate was only 42 percent. Accidents at the 21 sites where speed limits were raised decreased by 3.05 percent with a level of confidence of 53 percent. In addition, further analysis revealed that when speed limits were posted within 5 mi/h (8 km/h) of the 85th percentile speed, accidents decreased by 3.45 percent. The level of confidence of this estimate was 73 percent. Accidents were not reduced at sites where the speed limits were set more than 5 mi/h (8 km/h) below the 85th percentile speed. The Michigan results are similar to the findings reported in this study:
In summary, the results of this analysis, and the findings of other investigators indicate that lowering speed limits on nonlimited access roadways does not reduce accidents nor does raising speed limits increase accidents. Contrary to popular belief, the results indicate that lowering speed limits well below the 85th percentile speed does not decrease accidents.
These results should not be construed to imply that posted speed limits do not have some beneficial safety effect. Clearly, setting speed limits lower than the 85th percentile of traffic did not reduce accidents, thus, reducing the speed limit alone is not an effective safety measure for an accident problem or hazardous location. As reported by others, however, maximum speed limits may improve safety when they are set at the upper end of the minimum accident risk band to encourage motorists to drive within the minimum accident risk band.[1,6,10] As noted earlier in this report, speed limits at the study sites were generally set below the average speed of traffic, and accordingly, may not be assisting motorists in selecting a safe and reasonable speed.
Table 11. Multivehicle and single vehicle accidents. ----------------------------------------------------------------------------- Speed Multiple Vehicle Single Vehicle Limit Before After Diff Before After Diff Change No. Pct. No. Pct. Pct. No. Pct. No. Pct. Pct. ----------------------------------------------------------------------------- -15 & -20 149 67.42 74 72.5S 5.13 72 32.58 28 27.45 -5.13 -10 503 68.44 270 74.38 5.94 232 31.56 93 25.62 -5.94 - 5 205 74.01 177 83.10 9.09 72 25.99 36 16.90 -9.09 + 5 548 69.28 393 74.86 5.58 243 30.72 132 25.14 -5.58 +10 & +15 275 77.90 115 79.31 1.41 78 22.10 30 20.69 -1.41 ----------------------------------------------------------------------------- 1 mi/h = 1.61 km/h
As can be seen by examining figures 31 through 33, the results do not provide a clear indication of a direct relationship between changes in accidents and changes in the 3 speed parameters examined. It is important to note, however, that, as the figures clearly show, the changes in the speed distribution are quite small, perhaps too small to greatly affect major changes in accidents.
A separate analysis was also conducted to determine if a relationship exists between the ratio of after-to-before 85th percentile speeds and the ratio of after-to-before accidents. For example, if the after-to-before speed ratio is greater than 1.0, then, there has been an increase in the 85th percentile speed. One might expect that an increase in speed could increase the accident ratio. Similarly, when the speed ratio is less than 1.0, one might expect a decrease in the accident ratio. Shown in figures 34 and 35, respectively, is a plot of the accident-speed ratios. The plots do not show a clear relationship between the accident-speed ratios. Again, this may be due to the small changes in speeds found at the experimental sites.
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