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Enhancing Electrode Location Assessment in Cochlear Implantation via Computed Tomography Image Fusion

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Post Hoc comparisons in fixed-effect ANOVA: A sequential fusion approach with calibrated error control.

Yvonnick Noel¹

¹Department of Psychology, Rennes 2 University.

Psychological Methods

|July 13, 2026

Summary

This study introduces a novel sequential fusion procedure for post hoc analysis after ANOVA. This method offers a coherent, transitive partition of groups, improving upon traditional pairwise comparisons.

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Area of Science:

Statistics
Psychological Methods
Data Analysis

Background:

Traditional post hoc tests following Analysis of Variance (ANOVA), like Tukey's HSD and Holm-Bonferroni, control error rates but can yield nontransitive results.
Nontransitive patterns in pairwise comparisons lack interpretational coherence and do not form a clear partition of factor levels.

Purpose of the Study:

To propose and evaluate a novel sequential fusion procedure for post hoc analysis that guarantees a coherent, transitive partition of groups.
To compare the power and interpretational coherence of the fusion cascade method against established pairwise procedures.

Main Methods:

A sequential fusion algorithm iteratively merges groups with the most similar means, using likelihood-ratio tests for significance.
Family-wise error rate control is maintained through a calibrated sequence of critical values.
Extensive Monte Carlo simulations were conducted on balanced designs with varying numbers of groups and observations per group.

Main Results:

The fusion cascade procedure achieves comparable or superior statistical power to Tukey's HSD, Holm-Bonferroni, Benjamini-Hochberg, and Scheffé methods.
The method consistently produces a single, transitive partition of groups, ensuring interpretational coherence.
Simulation studies show the fusion cascade accurately identifies partitions under well-separated conditions, unlike pairwise methods which often produce nontransitive patterns.

Conclusions:

The sequential fusion procedure provides a statistically powerful and interpretable alternative for post hoc analysis following ANOVA.
This method ensures a coherent partition of factor levels, addressing limitations of traditional pairwise comparison techniques.
The approach is applicable to factorial designs by analyzing cell means, revealing interaction structures as partitions.