# Extracting Weight of Evidence from p-Value via Bayesian Approach to Activation Likelihood Estimation Meta-Analysis

## TL;DR

This paper introduces a Bayesian method to convert p-values into evidence strength measures for neuroimaging meta-analyses, improving interpretation of results.

## Contribution

A novel Bayesian approach to transform p-values into Bayes factor bounds for neuroimaging meta-analysis.

## Key findings

- Statistically significant effects in neuroimaging vary widely in evidential strength when assessed with Bayes factors.
- Bayes factor bounds range from 46 to 410 for traditionally significant effects in finger-tapping experiments.
- The method reveals hidden heterogeneity in evidence strength that standard thresholds obscure.

## Abstract

Background: p-values are ubiquitous in scientific research, yet they fundamentally fail to quantify the strength of evidence for or against competing hypotheses. This limitation is particularly problematic in neuroimaging meta-analyses, where researchers need to assess how strongly the available data support specific and spatially consistent patterns of brain activation across studies. Methods: In this work, we present a practical approach that transforms p-values into their corresponding upper bounds on the Bayes factor, which quantify the maximum plausible evidence in favor of the alternative hypothesis given the observed data. The method is illustrated within the framework of Activation Likelihood Estimation, the most widely used coordinate-based meta-analytic technique in neuroimaging and applied to a reference dataset comprising 73 finger-tapping experiments. Results: The results show that effects traditionally classified as statistically significant using the canonical Activation Likelihood Estimation framework actually span a wide range of evidential strengths, with Bayes factor bounds varying approximately from 46 to 410. This finding reveals substantial heterogeneity in weight of evidence that is concealed by conventional threshold-based inference. Conclusion: By enabling the construction of voxel-wise maps of evidential strength while remaining fully compatible with existing analysis pipelines, the proposed approach helps to avoid common misinterpretations of p-values and improves the interpretability and reliability of neuroimaging meta-analytic conclusions. It therefore provides a conservative, Bayesian-inspired complement to standard significance maps.