How to interpret the odds ratio when it is less than 1? is that ratio needed to be inverted? and if yes, then how to interpret it? can you plzz explain it through an example.

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    $\begingroup$ In what context are you using odds ratios ? Give a bit more to work on $\endgroup$ – Riff Jul 1 '16 at 8:58

Odds ratio is used to compare how associated are two properties. Since we don't know what kind of properties are you comparing, I'll just suppose that you are comparing presence of a risk factor and presence of a disease (e.g. smoking and lung cancer). In fact, odds ratio was invented to do so.

The (slightly simplified) interpretation of odds ratio goes as follows:

  • If odds ratio equals 1, then the two properties aren't associated. That is, your risk factor doesn't affect prevalence of your disease.
  • If odds ratio is bigger than 1, then the two properties are associated, and the risk factor favours presence of the disease. The greatest the odds ratio, the more the risk factor favours the disease.
  • If odds ratio is lower than 1, then there is a negative association. That is, your risk factor is counteracting the disease and people seems more likely to get the disease when your risk factor is not present than when it is present.

If odds ratio is lower than 1, one quite logical action could be start thinking that the real factor risk is the opposite of your supposed factor risk. In the smoking and lung cancer example, getting an odds ratio below 1 could be seen as evidence that NOT smoking causes lung cancer. Therefore, it could be a good idea to take "not smoking" as risk factor and compute the odds ratio again - you will get the inverse of the odds ratio you have now.

To finish, I would like to give a couple of comments about the simplification I made in this answer:

  • Beware of significance and sample size. If you take a sample of your population and compute odds ratio, it is a random variable. If your sample is large, the odds ratio you will get will be close to the real value, but if association between risk factor and disease is weak and your sample is small, you can get a value below 1 just as a random effect.
  • Keep in mind that correlation doesn't imply causality. For sake of simplicity I mixed both things a lot in this answer, but the fact that risk factor and disease are associated means that usually the same people have both, but it doesn't necessarily mean that the risk factor "causes" the disease.
  • $\begingroup$ Thank you for answering my question. It was explained very well. Thank you once again. $\endgroup$ – Rahul Gupta Sep 9 '16 at 5:40

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