# Appendix C. Risk Ratio

The risk ratio compares the severity of crashes associated with a particular factor to the severity of all other crashes (e.g., the percentage of angle crashes that result in a serious injury or fatality divided by the percentage among all other crashes, excluding angle crashes). Crash types or factors with a risk ratio greater than 1 are overrepresented with respect to severe crashes. Formally, the risk ratio is defined by the following equation.

Figure C.1 Equation. Risk Ratio

Where:

A = the number of severe crashes of a particular type or emphasis area;

B = the total number of nonsevere crashes of the same type as in A;

C = the number of severe crashes, excluding those of the same type as in A; and

D = the total number of nonsevere crashes, excluding those of the same type as in A.

To illustrate this concept further, a few examples are provided below. Conventionally, data used to compute the risk ratio (variables A, B, C, and D) are arranged in a 2×2 matrix, where the first row corresponds to the numerator values in the formula above, and the second row corresponds to the denominator values.

Severe Crash | Not a Severe Crash | Total Crashes | |
---|---|---|---|

Rural Area | 523 (A) | 5,768 (B) | 6,291 (A+B) |

Not a Rural Area (Urban Area) | 700 (C) | 24,396 (D) | 25,096 (C+D) |

Source: Sample data, Cambridge Systematics, Inc., 2015.

Given this data, the formula to calculate the risk ratio is as follows:

Figure C.2 Equation. Severe Crash Risk Ratio for Rural Areas

Based on this calculation, crashes in rural areas are around three times more likely to result in a fatality or serious injury than those in urban areas.

A similar example for DUI crashes is provided here:

Severe Crash | Not a Severe Crash | Total Crashes | |
---|---|---|---|

DUI | 201 (A) | 1,589 (B) | 1,790 (A+B) |

Not a DUI | 1,022 (C) | 28,575 (D) | 29,597 (C+D) |

Source: Sample data, Cambridge Systematics, Inc., 2015.

Figure C.3 Equation. Severe Crash Risk Ratio for DUI Crashes

A risk ratio can also be developed for a combination of factors. An example for DUI crashes in rural areas is shown here:

Severe Crash | Not a Severe Crash | Total Crashes | |
---|---|---|---|

Rural DUI Crash | 93 (A) | 597 (B) | 690 (A+B) |

Not a Rural DUI Crash | 1,130 (C) | 29,567 (D) | 30,697 (C+D) |

Source: Sample data, Cambridge Systematics, Inc., 2015.

Figure C.4 Equation. Severe Crash Risk Ratio for DUI Crashes in Rural Areas

As an outcome of this step, the transportation planner would understand the categories of crashes by type, severity, contributing factor, or geography that may be a focus for planning and programming or that should be a consideration in nonsafety-specific projects.