Controlling IER and EER in replicated regular two-level factorial experiments

TL;DR

This paper introduces new Monte Carlo and exact-variance methods for effectively controlling error rates in replicated regular two-level factorial experiments, improving the identification of active effects on mean and variance.

Contribution

The paper proposes novel Monte Carlo and exact-variance techniques that better control IER and EER in factorial experiments, addressing limitations of existing hypothesis testing methods.

Findings

Methods control IER and EER effectively in simulations

Real data demonstrates improved performance over traditional methods

Enhanced accuracy in identifying active effects on mean and variance

Abstract

Replicated regular two-level factorial experiments are very useful for industry. The goal of these experiments is to identify active effects that affect the mean and variance of the response. Hypothesis testing procedures are widely used for this purpose. However, the existing methods give results that are either too anticonservative or conservative in controlling the individual and experimentwise error rates (IER and EER). In this paper, we propose {a Monte Carlo method} and an exact-variance method to identify active effects for the mean and variance, respectively, of the response. Simulation studies show that our methods control the IER and EER extremely well. Real data are used to illustrate the performance of the methods.