Simultaneous Confidence Interval
A simultaneous confidence interval is constructed so that all intervals in a family are jointly valid with overall confidence level $1-\alpha$.
In multiple comparisons, this means we can examine all pairwise treatment differences while controlling the family-wise error rate. A practical rule in STA305 is: if a simultaneous interval for $\mu_i - \mu_j$ does not contain $0$, then that pair is significantly different at the family level.