Step-up simultaneous tests for identifying active effects in orthogonal saturated designs

TL;DR

This paper introduces two step-up testing procedures for identifying active effects in orthogonal saturated designs, controlling the experimentwise error rate under effect sparsity assumptions.

Contribution

The paper proposes novel step-up simultaneous testing methods that effectively identify active effects while controlling error rates in orthogonal saturated designs.

Findings

Procedures control the experimentwise error rate at the specified alpha level

Methods are applicable under the assumption of effect sparsity

The procedures are proven to control error rates strongly

Abstract

A sequence of null hypotheses regarding the number of negligible effects (zero effects) in orthogonal saturated designs is formulated. Two step-up simultaneous testing procedures are proposed to identify active effects (nonzero effects) under the commonly used assumption of effect sparsity. It is shown that each procedure controls the experimentwise error rate at a given $\alpha$ level in the strong sense.