# Controlling Familywise Error When Rejecting at Most One Null Hypothesis Each From a Sequence of Sub-Families of Null Hypotheses

## TL;DR

This paper introduces a new method for controlling the familywise error rate (FWER) in sequential hypothesis testing, allowing at most one rejection per subfamily, by adaptively adjusting significance levels based on previous rejections.

## Contribution

It proposes a novel procedure that adjusts critical values dynamically to control FWER when testing sequential subfamilies of hypotheses, improving upon existing methods.

## Key findings

- Effective control of FWER in sequential subfamily testing
- Adaptive adjustment of significance levels based on prior rejections
- Applicable to multiple testing scenarios with hierarchical structure

## Abstract

We present a procedure for controlling FWER when sequentially considering successive subfamilies of null hypotheses and rejecting at most one from each subfamily. Our procedure differs from previous procedures for controlling FWER by adjusting the critical values that are applied in subsequent rejection decisions by subtracting from the global significance level $\alpha$ quantities based on the p-values of rejected null hypotheses and the numbers of null hypotheses considered.