Simultaneous confidence intervals for the interpretation of primary and secondary effects in factorial designs without a pre-test on interaction

TL;DR

This paper introduces a method for constructing simultaneous confidence intervals in factorial designs that avoids pre-tests for interaction, enabling clearer interpretation of primary and secondary effects.

Contribution

It proposes a new inference procedure for factorial designs that does not rely on pre-tests for interaction, improving interpretability of effects.

Findings

Provides a simultaneous inference procedure for factorial effects.

Avoids the need for pre-test interaction checks.

Enhances clarity in interpreting primary and secondary effects.

Abstract

The analysis of low dimensional factorial designs with possible interactions is a relevant issue. Instead of the common pre-tests for interaction, a simultaneous inference procedure of the primary factor at the respective level of the secondary factor as well as pooled over all its levels is proposed.