Safety Evaluation of Multiple Strategies at Stop-Controlled Intersections

Chapter 4. Study Design

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 determined what changes in safety could be detected with available sample sizes.

Sample Size Estimation Overview

When planning a before–after safety evaluation study, it is vital to ensure that enough data are included such that the expected change in safety can be statistically detected. Even though in the planning stage the expected change in safety is unknown, it is still possible to make a rough estimate of how many sites would be required based on the best available information about the expected change in safety. Alternatively, one could estimate, for the number of available sites, the change in safety that could be statistically detected. For a detailed explanation of sample size considerations, as well as estimation methods, see chapter 9 of Hauer.⁽¹⁵⁾ The sample size analysis presented here is limited to 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, it was 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 empirical Bayesian (EB) methodology would likely require fewer sites. To facilitate the analysis, it was also assumed that the number of comparison sites was equal to the number of installation sites and the duration of the before and after periods were equal, which, again, was a conservative assumption.

Table 2 provides the crash rate assumptions. It shows the average number of crashes per year per intersection in the before period for each combination of crash type and intersection configuration. The locations of interest for this strategy were three- and four-legged, stop-controlled intersections. Intersection crash rates differ substantially depending on a number of factors (e.g., traffic control, traffic volume, geometric configuration, and area type). Therefore, the intersection crash rates assumed for these computations represented a general estimate based on the reference sites identified for this study. Rates A and B represent rural and urban, four-legged, stop-controlled intersections with two-lane major roads, respectively. Rates C and D represent rural and urban, stop-controlled intersections with four-lane major roads, respectively.

Crash rate = crashes/intersection/year.

Table 3 to table 6 provide estimates of the required number of before- and after-period intersection-years for total, fatal and injury, rear-end, and right-angle crashes, respectively, at four-legged stop-controlled intersections assuming both 90- and 95-percent confidence levels. Columns labeled “A-95%” and “A-90%” indicate Rate A (rural four-legged, stop-controlled with two-lane major roads) with 95- and 90-percent confidence levels, respectively. Similarly, columns labeled “B-95%,” “C-95%,” and “D-95%” indicate rates B, C, and D at the 95-percent confidence level. Columns labeled “B-90%,” “C-90%,” and “D-90%” indicate rates B, C, and D at the 90-percent confidence level. The minimum sample indicates the amount of data necessary to detect the safety effects with a desirable level of statistical significance. Larger safety effects require less data to achieve the same confidence level. These sample size calculations were based on specific assumptions regarding the number of crashes per intersection and years of available data. Intersection-years were the number of intersections where the strategy was implemented 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 three years since implementation, then there would be a total of 27 intersection-years of after period data available for the study. The number of intersection-years was estimated by first estimating the required number of intersection-related crashes and then dividing by the appropriate intersection crash rate.

Note: Assumes equal number of site-years for treatment and comparison sites and equal length of before and after periods.

Note: Assumes equal number of site-years for treatment and comparison sites and equal length of before and after periods.

Note: Assumes equal number of site-years for treatment and comparison sites and equal length of before and after periods.

Note: Assumes equal number of site-years for treatment and comparison sites and equal length of before and after periods.

Case 2 considers the data collected for both the before and after periods. The statistical accuracy attainable for a given sample size is described by the standard deviations of the estimated percent change in safety. From this, p-values are estimated for various sample sizes and expected changes in safety for a given crash history. A set of such calculations is shown in Table 7 through table 10. The calculations are based on the methodology in Hauer.⁽¹⁵⁾ The tables indicate the total intersection-years of data available in the before and after period.

*Results are to nearest 5-percent interval.

**Minimum percent reduction detectable for crash rate assumption. Crash rate assumption is based on actual crash rate for the before period from table 2.

*Results are to nearest 5-percent interval.

**Minimum percent reduction detectable for crash rate assumption. Crash rate assumption is based on actual crash rate for the before period from table 2.

*Results are to nearest 5-percent interval.

**Minimum percent reduction detectable for crash rate assumption. Crash rate assumption is based on actual crash rate for the before period from table 2.

*Results are to nearest 5-percent interval.

**Minimum percent reduction detectable for crash rate assumption. Crash rate assumption is based on actual crash rate for the before period from table 2.

Another strategy is to estimate the level of significance (i.e., the p-value) for which a minimum desired effect can be detected. For instance, assume the minimum desired level of effect is ten percent for total and target crashes. Based on the current knowledge of available data, table 11 indicates the p-value associated with a 10-percent change in crashes based on the before period data. These calculations use the crash rates from table 2. Given the existing sample size, it is likely this study can detect moderate treatment effects (e.g., a 10-percent change in total crashes) at the 10-percent level of significance.

Reference Group Overview

A reference group is required for the various intersection groups, including rural and urban, three- and four-legged, stop-controlled intersections with two- and four-lane major roads. Each reference group should consist of untreated sites adjacent to or in the vicinity of the treated sites. The untreated sites in each reference group should have geometric, traffic, and crash data for the same years as treated sites. Each reference group should be similar to its corresponding treatment group—particularly in terms of area type (e.g., urban or rural), geometric configuration (e.g., number of legs and number of through lanes), and annual average daily traffic (AADT)—except that these intersections were not treated during the study period. These sites are used in the calibration of safety performance functions (SPFs). Based on previous experience in similar analyses, the research team determined that at least 30 intersections for each intersection type in reference group would be desirable, as shown in table 12. Where it is impractical or infeasible to obtain the required sample size for one or more intersection groups, it is possible to combine groups and account for the differences through statistical modeling during the development of SPFs.

—Not applicable.