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# Evaluations of Low Cost Safety Improvements Pooled Fund Study

PPT version for Printing

## Analytical Basics

### Overview

• Analytical basics of observational before–after studies:
• Why empirical Bayes (EB)?
• Empirical Bayes Approach – Fundamentals
• Study design
• Interpretation of results

### Why Empirical Bayes?

• Problem with conventional (simple) before–after studies basics of observational before–after studies:
• Difficulty of "controlling" for changes in safety due to factors other than the treatment
• Regression to mean
• Traffic volume changes

### Why Empirical Bayes?: Accounting for other changes

• Regression to the mean:
Actual data for untreated intersections
Number of intersections Accidents/year/ intersection in 1974–76 Accidents/intersection in 1977 Percent Change
256 0 0.25 Large increase
218 0.33 0.55 67
54 2.00 1.56 –22
29 2.67 1.62 –39
• Traffic volume:
• Research shows that crashes are not proportional to AADT
• Therefore to account for traffic volume changes
• Cannot simply compare crashes per unit of traffic volume (see next slide)
• Must use a safety performance function (SPF) that specifies the (non–linear) relationship between crashes and traffic volume
• Need a method that accounts for regression to the mean and non–linear effects of traffic volume changes
• Empirical Bayes method does this

### Empirical Bayes Approach –– Fundamentals

• Compares the crash counts in the "after" period to an estimate of what would have occurred in the absence of the treatment (B).
• B is a weighted average of the counts in the "before period" and the number of crashes expected to occur at similar sites (P).
• P is estimated from a safety performance function (SPF) that links crashes to traffic volumes and site characteristics.
• The SPF is calibrated from crash, volume and geometric data from reference sites "similar" to the treatment sites.

### Study Design

• Sample sizes for treatment sites based on:
• Crashes/site/year
• Expected percent change in crashes in each category
• Desired level of significant (confidence)
• Minimum sample size
• Desired Sample size

### Interpretation of Results –– Example

• Percent reduction = 20 percent with standard error = 11 percent
• Result is not significant at the 5 percent level (95 percent confidence level) since 20/11 (=1.82) is not larger than 1.96
• Or 95 percent confidence interval of +/– 1.96 standard errors is between –1.6 and 41.6 and includes zero
• Result is significant at the 10 percent level since 20/11 (=1.82) is larger than 1.64 or since +/– 1.64 standard deviations DOES NOT include zero
• 20/11 = 1.82 standard deviations – – >> significant result at the 7 percent level (93 percent confidence level)

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