I know in studies where relative risk or odds ratio is calculated, if confidence interval overlaps 1, then the P-value is not significant. Is similar relation true for following situations as well?
Consider 2 sets of values with means m1 and m2. I think, if 95% confidence intervals of m1 and m2 are not overlapping, then the p-value for an unpaired t-test comparing them will yield P<0.05, indicating that they are not from same population. Is this true?
Or does one need only to check if m2 lies outside the 95% confidence intervals of m1 (or m1 lies outside 95% confidence intervals of m2), then the p-value of unpaired t-test between 2 sets will yield P<0.05?
Thanks for your insight.
Edit: A corollary of above (as discussed in the comments) is that if notches of 2 boxplots do not overlap, there must be a significant difference between the them.