So, I know that if we get a p<= 0.05 (95% CI), I know that the null hypothesis can be rejected. Now my question is how do I do that with CI?

Eg. in the table below A17S group has a CI of (27.835-31.865) whereas the A17T group has a CI of (31.36-34.972).

I know I am a bit wrong when thinking that only CI's that do not overlap are significant. Indeed the same data when performing a t-test gives me significance (p=0.02).

So my question is this:

If I have two confidence intervals, how do I decide that the difference is statistically significant at say 95% CI?

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The relation between overlapping confidence intervals and p-values is a bit tricky. Under some reasonable conditions, if two 95% confidence intervals don't overlap then the p-value for testing a difference between the means is about 0.005; non-overlapping 90% intervals give about p = 0.02. This page provides a general discussion of the issues.

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