An asymmetric relation between CIs (confidence intervals) and statistical significance constantly trips up students (and others). A quick-and-dirty summary follows (a fuller discussion, with helpful examples, is found on the Stata Blog here).
In short: if the individual CIs do not overlap, then the difference is statistically significant. However, the reverse is not necessarily true. That is, CIs for individual parameters can overlap even if their difference is statistically significant. What is also true is that if the difference is statistically significant, the CI for the difference will exclude zero.
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