Adjusted p-values for SGoF multiple test procedure

Area of Science:

• Statistics
• Statistical Methods

Background:

• Multiple comparison procedures are crucial for evaluating test statistics while accounting for multiplicity.
• The Sequential Goodness-of-Fit (SGoF) method is of significant interest for increasing statistical power in multiple testing scenarios.

Purpose of the Study:

• To introduce adjusted p-values for the SGoF multiple test procedure by allowing the test level to vary.
• To investigate the properties of these adjusted p-values and introduce a majorant version for enhanced hypothesis rejection.

Main Methods:

• The study defines adjusted p-values as the minimum level at which the SGoF procedure rejects a null hypothesis.
• It investigates properties such as being a subset of original p-values and introduces a majorant version and adjusted p-values for a conservative SGoF version.
• The handling of ties in p-values is also discussed.

Main Results:

• Adjusted p-values are shown to be a subset of original p-values, simplifying computation.
• The majorant version of the SGoF procedure demonstrates increased rejection of null hypotheses as the level increases.
• The study includes adjusted p-values for the conservative SGoF procedure and discusses tie handling.

Conclusions:

• The developed adjusted p-values extend the SGoF method, offering practical advantages for statistical power and hypothesis testing.
• The majorant and conservative versions, along with simplified computation, provide valuable tools for analyzing real-world data across various test sizes.