# What is the odds ratio formula?

## Odds ratio

*from English: odds - odds, chances and ratio - ratio**Synonyms: odds ratio, risk ratio, opportunity ratio, cross product ratio, odds ratio*

### 1 definition

The **Odds ratio**, short **OR**, or that **Odds ratio** is a measure from statistics that says something about the strength of a relationship between two characteristics. Two "odds" are compared with one another. The odds ratio relates to odds and not to probabilities such as relative risk (RR).

### 2 calculation

The data obtained can be presented in a crosstab:

Number of people with risk factor | Number of people without a risk factor | |
---|---|---|

ill | x | y |

not sick | v | w |

The odds ratio is then calculated as follows:

- (x / v) / (y / w)
- or (x / y) / (v / w)
- or x * w / y * v.

It can have values between 0 and ∞.

### 3 interpretation

A value greater than 1 means that the odds of the first group are greater, a value less than 1 means that the odds of the first group are smaller. A value of 1 means an equal odds ratio.

### 4 application

The odds ratio is often used in epidemiology to express how closely a suspected risk factor is related to a specific disease. One compares people with a potential risk factor for a disease with people who have this risk factor *Not* exhibit. The odds ratio then expresses how much greater the chance in the group with a risk factor is to get sick - compared to the chance in the group without a risk factor.

In the context of case-control studies, the odds ratio is often used to assess the ratio of sick and healthy people after exposure to a potentially harmful agent. In principle, however, the odds ratio can be used for all study designs (e.g. also for cross-sectional studies).

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