# A Comparison of Methods for Identifying Location Effects in Unreplicated Fractional Factorials in the Presence of Dispersion Effects

## TL;DR

This study evaluates the robustness of four methods for identifying location effects in unreplicated fractional factorial designs, especially when heteroscedasticity caused by dispersion effects is present, revealing varying levels of reliability among them.

## Contribution

It provides a comparative analysis of existing methods' performance under heteroscedastic conditions caused by dispersion effects in fractional factorial designs.

## Key findings

- Box and Meyer, Lenth, and Berk-Picard methods generally perform well.
- Loughin-Noble method's error rate control deteriorates with larger dispersion effects.
- Simulation results highlight the importance of considering dispersion effects in analysis.

## Abstract

Most methods for identifying location effects in unreplicated fractional factorial designs assume homoscedasticity of the response values. However, dispersion effects in the underlying process may create heteroscedasticity in the response values. This heteroscedasticity may go undetected when identification of location effects is pursued. Indeed, methods for identifying dispersion effects typically require first modeling location effects. Therefore, it is imperative to understand how methods for identifying location effects function in the presence of undetected dispersion effects. We used simulation studies to examine the robustness of four different methods for identifying location effects---Box and Meyer (1986), Lenth (1989), Berk and Picard (1991), and Loughin and Noble (1997)---under models with one, two, or three dispersion effects of varying sizes. We found that the first three methods usually performed acceptably with respect to error rates and power, but the Loughin-Noble method lost control of the individual error rate when moderate-to-large dispersion effects were present.