The question of significance level for a family of statements under two types of procedures of multiple comparisons is examined. It is shown how the simultaneous significance level for any contrasts of interest can be controlled with a known upper bound under both these types of procedures. In the case of one type of procedure which are based on t tests, the upper bound can be obtained by using either of two available probability inqualities. Under the other type of procedures which are exclusively used for post-ANOWA comparisons, an exact probability statement can be made which applies to all possible contrasts. If the significance levels for such a statement is α, then the simultaneous significance level for any subset of contrasts of interest is less than or equal to α Individual procedures belonging to the two groups are also briefly given especially as they are applied to the pairwise comparisons among the means.