Odds Ratio and Relative Risk

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Calculate

Example: in a study, 40 of 100 smokers and 10 of 100 non-smokers developed bronchitis. How much does smoking raise the odds and the risk of bronchitis? Change the values to work out your own case.

2 × 2 table Row 1: exposed with and without the outcome (a, b). Row 2: unexposed with and without the outcome (c, d). Rows separated by a semicolon. Confidence (%)

Step by step

What each term means

Odds Ratio (OR): How many times higher the odds of the outcome are in the exposed group. Odds are the ratio of those with the outcome to those without: a/b among the exposed and c/d among the unexposed. OR = 1 means no association.
Main Diagonal (a · d): Exposed with the outcome (a) times unexposed without it (d): the two cells that “agree” with the association.
Other Diagonal (b · c): Exposed without the outcome (b) times unexposed with it (c). Dividing a · d by b · c is the same as dividing the odds of the exposed, a/b, by those of the unexposed, c/d.