The Interval Property in Multiple Testing of Pairwise Differences

TL;DR

This paper highlights the importance of the interval property in multiple testing procedures and introduces residual-based stepwise methods that ensure this property across various statistical models.

Contribution

It identifies the absence of the interval property as a shortcoming in common procedures and proposes new residual-based methods that possess this property.

Findings

Standard procedures often lack the interval property.

Residual-based procedures have the interval property.

Proposed methods work across multiple models.

Abstract

The usual step-down and step-up multiple testing procedures most often lack an important intuitive, practical, and theoretical property called the interval property. In short, the interval property is simply that for an individual hypothesis, among the several to be tested, the acceptance sections of relevant statistics are intervals. Lack of the interval property is a serious shortcoming. This shortcoming is demonstrated for testing various pairwise comparisons in multinomial models, multivariate normal models and in nonparametric models. Residual based stepwise multiple testing procedures that do have the interval property are offered in all these cases.