# How to interpret OR (odds ratio) decimals? Are they percentages? [duplicate]

How to interpret OR (odds ratio) decimals? Are they percentages?

OR with probabilities $p_1,p_2$ for two events is

$$\frac{\frac{p_1}{1-p_1}}{\frac{p_2}{1-p_2}}$$

Like if one gets an OR of, say, $2.25$, then does this mean that the nominator event is 225% more likely than the denominator event? What does "odds" mean?

• It might help to give you a concrete answer if you said what the events and groups are. As it stands all we can say is that the odds of something in one group are 2.25 times the odds of the something in some other group. – mdewey Nov 27 '16 at 12:05
• @mdewey Well in this case I get 2.25 if I take the odds ratio of the chance of getting skin cancer when taking beta carotene ($p_1$) and not taking ($p_2$). – mavavilj Nov 27 '16 at 12:37
• So whatever the odds were of getting skin cancer in the beta carotene group (ie the ratio of those who did to those who did not) it was 2.25 times the odds in the group not getting it. – mdewey Nov 27 '16 at 13:31
• @mdewey But is odds the same as "2.25 more likely to"? – mavavilj Nov 27 '16 at 13:43
• If you measure likeliness in terms of odds then yes, if you measure likeliness in terms of risk then no you need the risk ratio unless you are interested in absolute risk in which case you need the risk difference. – mdewey Nov 27 '16 at 13:47