# Odds ratio interpretation

Does it make sense to say that the odds of some risk for a person in group A is $0.4$ times lower that that of someone in group B? Or would it be better to phrase it in "higher than" language?

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There is a difference between "0.4 times lower" (incorrect) and "0.4 times as high" (correct). E.g., if baseline odds are 0.5, then "0.4 times lower" = .5 - .4*.5 = .3, whereas "0.4 times as high" = .5*.4 = .2. –  rolando2 Nov 9 '11 at 12:42

Mathematically there really is no right answer. Whether you want to phrase this contrast as "0.4 times lower than" vs "2.5 times higher than" depends on the argument you are trying to build.

The argument is easier to build if you choose a more intuitive reference group and let that be the denominator. This may be chosen as:

• The more common group
• The group with fewer features (control group as opposed to the interventional group, non-diabetic group as opposed to diabetic group)
• Some natural rank ordering (thinner group as opposed to heavier group, younger group as opposed to older group)
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