Optimal Allocation,Precision, and Significance Tests

HORN (1979) queried the recommended ratio where p is the number of treated groups to be compared with a control and n and n₀ are the sizes of the treated samples and of the control. The rule was originally stated for maximizing the precision of estimates, and not for optimizing any aspect of significance tests. Although in applied statistics, significance tests are usually of far less importance, it is interesting (but scarcely surprising) that the same rule optimizes power and one or two related characteristics.