# What is an Odds-Ratio?

An odds ratio (OR) is a statistic that quantifies the strength of the association between two events, A and B.

Odds-Ratio is not the same as relative risk (RR). Relative risk is calculated on the whole population.

However, in clinical studies, an odds-ratio is generally preferred because data for the entire population is not available.

# How to calculate an Odds-Ratio?

To calculate an OR, you need 2 variables with 2 modalities for each variable. It could be 2 Yes-no variables or 2 List variables with 2 possible values.

For example, it could be Smoker (Yes-no) vs Gender (List with 2 possible values).

- In the "Statistics" menu, click on "Test variables"
- Pick the first variable (for example "Smoker")
- Pick the second variable (for example "Gender")
- Open the panel "Find an association between ..."
- The odds-ratio and its confidence interval are displayed in the "What to write in results" box

*The calculated OR is 0.026 with a confidence interval ranging from 0.0035 to 0.2*

# The OR is not calculated

There are 2 main reasons why an OR would not be calculated:

- One of the cells of the contingency table is equal to 0
- A List variable with more than 2 values

## One of the cells of the contingency table is equal to 0

The contingency table is a table generated from the distribution of the 2 variables. It represents the frequency of each possible combination of each variable. In the example below, it counts how many patients are both "Women" and "Diabetics" (n=1), both "Women" and "Non-diabetics" (n=117), etc...

The Odds-Ratio can not be calculated if at least one of the cells of the table is equal to 0.

## A List variable with more than 2 values

An OR can only be calculated if the contingency table has 4 cells. If one of your variable has more than 2 possible values (modalities), then an OR will not be computed.

However, you can group some values together to obtain only 2 values. For example, if you have a variable "Smoker" with 3 modalities "Never smoker", "Former smoker" and "Active smoker", you could group together "Never smoker" and "Former smoker". See the following link for more information: How to group values (modalities) of a List variable?

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