## Abstract

We consider the problem of simultaneously testing k ≥ 2 hypotheses on parameters θ_{1},...,θ(k) using test statistics t_{1},..., t(k) such that a specified familywise error rate a is achieved. Dunnett and Tambane (1992a) proposed a step-up multiple test procedure, in which testing starts with the hypothesis corresponding to the least significant test statistic and proceeds towards the most significant, stopping the first time a significant test result is obtained (and rejecting the hypotheses corresponding to that and any remaining test statistics). The parameter estimates used in the t statistics were assumed to be normally distributed with a common variance, which was a known multiple of an unknown σ^{2}, and known correlations which were equal. In the present article, we show how the procedure can be extended to include unequally correlated parameter estimates. Unequal correlations occur, for example, in experiments involving comparisons among treatment groups with unequal sample sizes. We also compare the step-up and step-down multiple testing approaches and discuss applications to some biopharmaceutical testing problems.

Original language | English (US) |
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Pages (from-to) | 217-227 |

Number of pages | 11 |

Journal | Biometrics |

Volume | 51 |

Issue number | 1 |

DOIs | |

State | Published - 1995 |

## Keywords

- Adjusted p values
- Biopharmaceutical testing
- Familywise error rate
- Multiple comparisons with a control
- Multivariate t distribution
- Simulation-based quantile estimation
- Simultaneous inference
- Stepwise tests
- Unbalanced designs

## ASJC Scopus subject areas

- Statistics and Probability
- Biochemistry, Genetics and Molecular Biology(all)
- Immunology and Microbiology(all)
- Agricultural and Biological Sciences(all)
- Applied Mathematics