The fallback procedure for evaluating a single family of hypotheses
The fallback procedure for evaluating a single family of hypotheses
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DOI：
10.1080/10543400500265660
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发表时间：
2005-01-01
影响因子：
1.1
通讯作者：
Dmitrienko, A
中科院分区：
文献类型：
--
作者：
Wiens, BL;Dmitrienko, A
在检验多个假设时，通常要考虑家庭误差率的控制。我们开发了一种称为“回退程序”的程序来控制多个主要假设测试时的家庭误差率。使用回退过程，在各种感兴趣的假设之间划分类型I错误率（alpha）。然而，与标准的Bonferroni调整不同，检验假设是按照先验确定的顺序进行的。只要假设被拒绝，I型错误率就可以累积起来，使得对后来假设的检验比在Bonferroni程序下更有力。与固定序列检验不同，回退检验允许考虑所有假设，即使一个或多个假设在过程的早期没有被拒绝，从而避免了对固定序列过程的共同关注。我们开发了回退过程的特性，包括通过将该过程描述为封闭测试过程来控制任意数量假设的家族错误率，以及通过alpha耗尽使测试更强大。我们将其与控制家族误差率的其他方法进行了比较，发现当对第一个假设的功率存在怀疑时，回退过程是固定序列过程的可行替代方案。这些结果扩展了先前开发的回退过程的属性（Wiens, 2003）。讨论了几个示例来说明回退过程的相对优点。
In testing multiple hypotheses, control of the familywise error rate is often considered. We develop a procedure called the "fallback procedure" to control the familywise error rate when multiple primary hypotheses are tested. With the fallback procedure, the Type I error rate (alpha) is partitioned among the various hypotheses of interest. Unlike the standard Bonferroni adjustment, however, testing hypotheses proceeds in an order determined a priori. As long as hypotheses are rejected, the Type I error rate can be accumulated, making tests of later hypotheses more powerful than under the Bonferroni procedure. Unlike the fixed sequence test, the fallback test allows consideration of all hypotheses even if one or more hypotheses are not rejected early in the process, thereby avoiding a common concern about the fixed sequence procedure. We develop properties of the fallback procedure, including control of the familywise error rate for an arbitrary number of hypotheses via illustrating the procedure as a closed testing procedure, as well as making the test more powerful via alpha exhaustion. We compare it to other procedures for controlling familywise error rates, finding that the fallback procedure is a viable alternative to the fixed sequence procedure when there is some doubt about the power for the first hypothesis. These results expand on the previously developed properties of the fallback procedure ( Wiens, 2003). Several examples are discussed to illustrate the relative advantages of the fallback procedure.