Statistical measure · BEGINNER LESSON
OR
The odds ratio (OR) is a number that compares the odds of an event in an exposed group with the odds of the same event in a non-exposed group. It measures the strength of association between exposure and outcome, not the event’s absolute probability.
What OR is and what it measures
OR stands for odds ratio. It compares the odds of an event in one group with the odds in another group. Odds are the chance of an event happening divided by the chance of it not happening. OR is used to describe how strongly an exposure and an event are associated, especially in case-control studies and logistic regression models.
[1] Odds Ratio - StatPearls - NCBI Bookshelf [2] Bias of Odds Ratio Estimate in Fisher's Exact Test - PMC [3] Interpreting Risk and Impact Measures in Nursing Research
How it is calculated
With a 2 x 2 table, the OR can be written as (a/b) / (c/d), which is the same as ad/bc. Here, a, b, c, and d are the counts in the four cells of the table. If the event is rare, OR may be close to relative risk, but when the event is common OR can overstate the size of the effect.
[1] Odds Ratio - StatPearls - NCBI Bookshelf [2] Bias of Odds Ratio Estimate in Fisher's Exact Test - PMC [3] Interpreting Risk and Impact Measures in Nursing Research
How to interpret OR
An OR of 1 means the odds are the same in both groups. An OR greater than 1 means higher odds of the event in the exposed group, and an OR less than 1 means lower odds in the exposed group. This interpretation is about association, not direct probability.
[1] Odds Ratio - StatPearls - NCBI Bookshelf [3] Interpreting Risk and Impact Measures in Nursing Research
Uncertainty and limitations
A confidence interval gives a plausible range for the true population OR. If the interval includes 1, the result is not statistically significant in the usual sense because the true OR could be above or below 1. OR estimates from Fisher’s exact test can be biased, and zero cells can make the estimate or its bias undefined or infinite. Bootstrap methods may help estimate and correct bias, but zero cells remain a limitation.
[1] Odds Ratio - StatPearls - NCBI Bookshelf [2] Bias of Odds Ratio Estimate in Fisher's Exact Test - PMC
Where OR is used
OR is commonly reported in case-control studies and in logistic regression. It is often chosen when direct risks or incidences cannot be estimated. Because it can exaggerate effect size for common outcomes, careful interpretation is needed.
[1] Odds Ratio - StatPearls - NCBI Bookshelf [3] Interpreting Risk and Impact Measures in Nursing Research
SEE THE IDEA
How an odds ratio is built and read
Count the event and non-event in the exposed group.
Count the event and non-event in the comparison group.
Odds = event probability divided by non-event probability.
Divide exposed odds by non-exposed odds; compare the two groups.
Stepwise comparison from counts to odds to a ratio between groups.
OR compares two odds; it does not directly measure absolute risk.
TRY IT YOURSELF
Test your understanding
Choose an answer, then check the explanation.
PUT IT TOGETHER
Match each concept to its meaning
Drag a label onto its description, or select a label and then select a description. This also works with a keyboard.
4 pairs to match
Sources and further reading
This general lesson was generated from public source material. It explains a concept; it does not interpret a private paper or provide medical advice.