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REPORT 
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Publication Number: FHWAHRT17077 Date: November 2017 
Publication Number: FHWAHRT17077 Date: November 2017 
The study design involved a sample size analysis and prescription of needed data elements. The sample size analysis assessed the size of sample required to statistically detect an expected change in safety and also determined what changes in safety could be detected with likely available sample sizes.
When planning a before–after safety evaluation study, it is vital to ensure that enough data are included such that it is statistically possible to detect the expected change in safety. While the expected change in safety is unknown in the planning stages, it is still possible to estimate the number of required sites (i.e., intersections) based on the best available information about the expected change in safety. Alternatively, one could estimate the change in safety that one could statistically detect for the number of available sites. Chapter 9 of Hauer provides a detailed explanation of sample size considerations and estimation methods.^{(5)} The sample size analysis presented in this section addresses two cases: (1) how large a sample would be required to statistically detect an expected change in safety and (2) what changes in safety could be detected with available sample sizes.
For case 1, the research team assumed that a conventional before–after study with comparison group design would be used because available sample size estimation methods were based on this assumption. The sample size estimates from this method would be conservative in that the EB methodology would likely require fewer sites. To facilitate the analysis, it was also assumed that the number of comparison intersections was equal to the number of treatment intersections and the durations of the before and after periods were equal, which was again a conservative assumption.
Table 1 provides the crash rate assumptions. Initially, the research team assumed that the locations of interest for this treatment would be fourlegged and threelegged signalized intersections. However, very few threelegged intersections were treated, and therefore, these intersections were dropped from the dataset. The research team used a central Florida study as the basis for assumptions on intersection crash rates.^{(6)} Intersection crash rates differ substantially depending on a number of factors (e.g., traffic volume, geometric configuration, and area type). Therefore, the intersection crash rates assumed represent the general lower and upper end of the crash frequency spectrum in Florida. Rate C represents the intersection crash rate for beforeperiod data for all intersections in Florida.
^{1}Data source: Kowdla.^{(6)}
^{2}Data source: project database.
Rate = Crashes/intersection/year.
— Indicates no available data.
Table 2 and table 3 provide estimates of the required number of before and afterperiod intersectionyears for crash rates A, B, and C to achieve statistical significance at 95 and 90‑percent confidence levels, respectively. The minimum sample indicated the level for which a study seemed worthwhile (i.e., it was feasible to detect with the specified level of confidence the largest effect that one might reasonably expect based on current knowledge about the strategy). The research team based these sample size calculations on specific assumptions regarding the number of crashes per intersection and years of available data. Intersectionyears is the number of intersections where the strategy was in effect multiplied by the number of years of data before or after implementation. For example, if a strategy was implemented at nine intersections and data were available for 3 years since implementation, then there was a total of 27 intersectionyears of afterperiod data available for the study.
Note: Assumes equal number of intersectionyears for treatment and comparison intersections and equal length of before and after periods.
Boldface indicates the sample size values recommended in this study.
— Indicates no data.
Note: Assumes equal number of intersectionyears for treatment and comparison intersections and equal length of before and after periods.
Boldface indicates the sample size values recommended in this study.
— Indicates no data.
The sample size values recommended for this study are highlighted in bold in table 2 and table 3 . These were recommended based on conservative estimates of the anticipated effects of the treatment. As noted, the sample size estimates provided were also conservative in that the stateoftheart EB methodology proposed for the evaluations would require fewer intersections than the less robust conventional before–after study with a comparison group. Estimates could be predicted with greater confidence or a smaller reduction in crashes would be detectable if there were more intersectionyears of data available in the after period. The same holds true if the actual data used for the analysis had a higher crash rate for the before period than was assumed.
Case 2 considered the data collected for both the before and after periods. RLILs were installed at 108 signalized intersections between 2004 and 2010. The before and after periods varied across intersections depending on the year of treatment installation. The total intersectionyears of data available was 365 for the before period for twolane major roadways and 599 for the after period. From this, one can estimate the minimum percent reduction detectable for the two confidence levels (i.e., 90 and 95 percent). The results of these calculations are shown in table 4 . The calculations are based on the methodology in Hauer.^{(5)}
^{1}Results were to nearest 5percent interval, and the crash rate assumption was based on actual crash rate for the before period.
For the available data, the minimum percentage changes in crash frequency that could be statistically detected at the 95 and 90percent significance levels were estimated using the beforeperiod crash rates (Rate C) in table 1 . The results indicate that the data should be sufficient for detecting the anticipated crash reduction effects highlighted in table 2 (i.e., 10‑percent reductions for all crash types except leftturn and disobeyed signal crashes, if such an effect were present). Using these results, the project team decided to proceed with the evaluation using the data available at the time.