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

Stat Med. 1991 Jun;10(6):939-47. doi: 10.1002/sim.4780100614.


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 alpha, the fixed type I family wise 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 Holm and the single-step procedure of Dunnett. An example from the pharmaceutical literature is used to illustrate the procedure.

Publication types

  • Comparative Study
  • Research Support, Non-U.S. Gov't

MeSH terms

  • Animals
  • Cardiomyopathy, Hypertrophic / drug therapy
  • Cardiomyopathy, Hypertrophic / physiopathology
  • Factor Analysis, Statistical
  • Multivariate Analysis
  • Rats
  • Research Design
  • Statistics as Topic*
  • Therapeutics*
  • Thyroid Hormones / physiology


  • Thyroid Hormones