Intersection Crash Rate Screening — Counts vs Rates vs Critical Rate
A city has money to study one intersection. Four signalized intersections have three years of crash data. Ranking by crash count, by crash rate, and by the critical-rate test produces three different answers. This example shows why, and why the quiet intersection with only nine crashes is the one the statistics flag.
The data
| Study period | 3 years |
| Reference rate | Ra = 0.55 crashes per million entering vehicles (statewide average for four-leg signalized urban intersections) |
| Confidence | 95%, K = 1.645 |
| Intersection | Crashes (3 yr) | Total entering volume (veh/day) |
|---|---|---|
| Hwy 9 & Mill | 31 | 41,000 |
| Main & 1st | 26 | 32,000 |
| Elm & 5th | 14 | 15,000 |
| Main & Oak | 9 | 6,500 |
Crash rate tool: Intersection, 3 years, Ra 0.55, 95%; enter each site's crashes and volume.
Open the crash rate calculator →Million entering vehicles
Hwy 9 & Mill: m = 365 × 3 × 41,000/106 = 44.90 MEV → R = 31/44.90 = 0.691
Main & Oak: m = 7.12 MEV → R = 9/7.12 = 1.264
Rc = Ra + K√(Ra/m) + 1/(2m)
Main & Oak: 0.55 + 1.645√(0.55/7.12) + 1/14.2 = 0.55 + 0.457 + 0.070 = 1.078
The threshold for the small intersection is far higher, because nine crashes in three years could easily be bad luck at a site with 7 million entering vehicles.
Count, rate and critical rate disagree
| Intersection | N | m (MEV) | R | Expected at Ra | Excess | Rc | R/Rc |
|---|---|---|---|---|---|---|---|
| Hwy 9 & Mill | 31 | 44.90 | 0.691 | 24.7 | 6.3 | 0.743 | 0.93 |
| Main & 1st | 26 | 35.04 | 0.742 | 19.3 | 6.7 | 0.770 | 0.96 |
| Elm & 5th | 14 | 16.43 | 0.852 | 9.0 | 5.0 | 0.881 | 0.97 |
| Main & Oak | 9 | 7.12 | 1.264 | 3.9 | 5.1 | 1.078 | 1.17 |
By rate: Oak → Elm → Main & 1st → Hwy 9 (the exact reverse)
By critical rate: only Main & Oak exceeds Rc — the others are within normal random variation
What to fund
Main & Oak gets the safety study: its rate is significantly higher than similar intersections at 95% confidence. The other three sit at 93–97% of their thresholds, which is worth watching but not evidence of a problem. Before designing countermeasures, pull the crash reports: a cluster of one crash type (left-turn, rear-end, angle) at Main & Oak would point to a fix; a scatter of types would suggest regression to the mean.
Tools used in this example
Crash rate calculator and traffic flow for AADT and design volumes.
Frequently asked questions
Why not rank intersections by number of crashes?
Crash counts mostly track traffic volume. The busiest intersection here has the most crashes (31) but the lowest rate (0.69 per MEV), below the 0.55 + random-variation threshold for its exposure. Ranking by count sends money to busy sites that may be performing normally.
Why not just rank by crash rate?
Rates are noisy at low exposure. A small intersection can show a high rate from a handful of crashes. The critical rate adds a margin that is larger when exposure is small, so a site is flagged only when its rate is high enough not to be chance at the chosen confidence level.
What is excess crash frequency?
Observed crashes minus the number expected for a typical site with the same exposure (Ra × m). It ranks sites by how many crashes a treatment could plausibly remove. Here every site has 5 to 7 excess crashes over three years, which is why the HSM recommends Empirical Bayes methods to sort them more reliably.
What confidence level should be used?
Many agencies use 95% (K = 1.645). Lower confidence flags more sites and catches more true problems at the cost of more false alarms; higher confidence does the reverse.