The Number of Non‐zero, Post Hoc Contrasts From Anova and Error‐rate. I

When F m in anova is significant, Scheffé's procedure provides no limit to the number of contrasts which can be declared significant. The new procedure described here provides a limit ( r ) to the number of significant contrasts which can be asserted. If assertions are made for v 1 contrasts, which include r declarations of significance, the expectation of r/v 1 will be a linearly decreasing function of v 1 if traditional critical F values are used. A table is provided of new critical F values which set this expectation at a constant (0.05 or 0.01). The new critical F values are recommended for use whenever contrasts are sought, post hoc , for significance.