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I have a question about odds ratios vs. probabilities in terms of a contingency table (studying an exposure/disease). I know that once I have found an odds ratio, I can also find the probability by taking the odds ratio and dividing it by one plus the odds ratio.

However, I want to understand what exactly that probability represents ... is it a conditional probability? The probability of an individual having the disease given exposure?

whuber
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user272213
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    An _odds ratio_ is the ratio of two odds. Each individual _odds value_ in the ratio can be converted to a probability as you propose, but I don't think that the same transformation applied to an _odds ratio_ results in a probability value that has any easy interpretation. – EdM Jan 29 '20 at 17:34
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    [many Qs with answers about interpretation of odds and odds ratios](https://stats.stackexchange.com/search?q=interpr*+odds+odds-rat*+answers%3A1). Must be a dup in there. – kjetil b halvorsen Feb 17 '20 at 07:55
  • @kjetil Thank you. I have found that restricting searches with `answers:1` finds only *questions* and can omit the most relevant answers. Setting a small threshold on the score, as in `score:2`, eliminates relatively poor answers. Sometimes sorting by votes is useful, especially for basic, popular subjects. Thus, [this version of your search](https://stats.stackexchange.com/search?tab=votes&q=interpr*%20odds%20odds-rat*%20score%3a2) proved effective. – whuber Feb 17 '20 at 14:10

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