A recycling framework for the construction of Bonferroni-based multiple tests

Area of Science:

• Statistical methodology
• Hypothesis testing
• Biostatistics

Background:

• Controlling family-wise error rate (FWER) is crucial in multiple hypothesis testing.
• Traditional methods like Bonferroni correction can be conservative.
• Existing multiple testing procedures (MTPs) aim to improve power while controlling FWER.

Purpose of the Study:

• To describe novel Bonferroni-based multiple testing procedures (MTPs).
• To introduce a 'test mass' recycling strategy for alpha allocation.
• To provide a framework for tailoring MTPs for specific research needs.

Main Methods:

• Development of recycling MTPs based on splitting and reallocating nominal significance level (alpha).
• Utilizing raw p-values from individual hypothesis tests.
• Employing closed testing procedures, including serial and parallel gatekeeping, fallback, and Holm procedures.

Main Results:

• Demonstration of recycling MTPs as a class of closed testing procedures.
• Graphical displays and concise algebraic notation are provided for these MTPs.
• The recycling approach offers pedagogical benefits and flexibility in MTP design.

Conclusions:

• Recycling MTPs provide an efficient strategy for managing alpha in multiple testing scenarios.
• This framework facilitates the development of customized MTPs for diverse scientific applications.
• The described methods offer improved statistical power and conceptual clarity in hypothesis testing.