If I have an odds ratio of 1.2 say between group A and group B but a confidence interval of (0.99,1.5) which only just about contains 1. Can I make the conclusion that there is no association between group A and group B?
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1$\begingroup$ This really comes down to the issue in the post Why do statisticians say a non-significant result means “you can't reject the null” as opposed to accepting the null hypothesis? You can't know for sure that the odds ratio in the population as a whole is "really" one; even in your sample you did not find an odds ratio of one. But if that was a 95% confidence interval, then you did not find significant evidence (at the $\alpha=0.05$ level) to reject the null hypothesis that the population odds ratio is one. $\endgroup$– SilverfishDec 12, 2015 at 16:46
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$\begingroup$ In other words, you do not have strong evidence that the true odds ratio isn't one ... but that doesn't mean you know the true odds ratio is one, either. $\endgroup$– SilverfishDec 12, 2015 at 16:49
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1$\begingroup$ Briefly: you may conclude that you have not been able to detect an association (at your desired level of confidence). $\endgroup$– whuber ♦Dec 12, 2015 at 17:11
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$\begingroup$ @Silverfish , yes I would never feel comfortable writing "accepting the null"! Certainly been drilled out of me since high school, I was just wondering how much the actual closeness of the confidence interval matter. $\endgroup$– therunningmanDec 12, 2015 at 17:17
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$\begingroup$ In terms of how much the "closeness" matters: if you did a 95% confidence interval and it only just included one, then the p-value would be only just above 0.05. (So if you'd tested at e.g. $\alpha = 0.1$ then the result might have been significant, i.e. the 90% confidence interval may not have included one.) $\endgroup$– SilverfishDec 12, 2015 at 17:20
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