## Abstract

A generalization of step-up and step-down multiple test procedures is proposed. This step-up-down procedure is useful when the objective is to reject a specified minimum number, q, out of a family of k hypotheses. If this basic objective is met at the first step, then it proceeds in a step-down manner to see if more than q hypotheses can be rejected. Otherwise it proceeds in a step-up manner to see if some number less than q hypotheses can be rejected. The usual step-down procedure is the special case where q = 1, and the usual step-up procedure is the special case where q = k. Analytical and numerical comparisons between the powers of the step-up-down procedures with different choices of q are made to see how these powers depend on the actual number of false hypotheses. Examples of application include comparing the efficacy of a treatment to a control for multiple endpoints and testing the sensitivity of a clinical trial for comparing the efficacy of a new treatment with a set of standard treatments.

Original language | English (US) |
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Pages (from-to) | 353-363 |

Number of pages | 11 |

Journal | Canadian Journal of Statistics |

Volume | 26 |

Issue number | 2 |

DOIs | |

State | Published - Jun 1998 |

## Keywords

- Biometric applications
- Familywise error rate
- Multiple comparisons
- Power
- Stepwise test procedures

## ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty