Step‐down multiple tests for comparing treatments with a control in unbalanced one‐way layouts

We show how a well‐known multiple step‐down significance testing procedure for comparing treatments with a control in balanced one‐way layouts can be applied in unbalanced layouts (unequal sample sizes for the treatments). The method we describe has the advantage that it provides p‐values, for each treatment versus control comparison, that take account of the multiple step‐down testing nature of the procedure. These joint p‐values can be used with any value of α, the fixed type I familywise error rate bound, that may be specified by the investigator. To determine the p‐values, it is necessary to compute a multivariate Student t integral, for which a computer program is available. This procedure is more powerful than the step‐down Bonferroni procedure of Holm¹ and the single‐step procedure of Dunnett.² An example from the pharmaceutical literature is used to illustrate the procedure.