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Multimodal Cross-Device and Marker-Free Co-Registration of Preclinical Imaging Modalities

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Non-normality and transformations of random fields, with an application to voxel-based morphometry.

Roberto Viviani¹, Petra Beschoner, Katja Ehrhard

¹Department of Psychiatry III, University of Ulm, Leimgrubenweg 12, 89075 Ulm, Germany. roberto.viviani@uni-ulm.de <roberto.viviani@uni-ulm.de>

|January 16, 2007

Summary

Parametric statistical tests for random field images are sensitive to distributional assumption violations, more so than univariate tests. Simulations reveal smoothing and unbalanced data can invalidate significance tests, especially for neuroimaging data.

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Area of Science:

Neuroimaging analysis
Statistical modeling
Random field theory

Background:

Parametric tests for linear models in random fields rely on distributional assumptions, similar to univariate tests.
Departures from these assumptions can have a more significant impact in random field tests compared to univariate analyses.

Purpose of the Study:

To investigate the influence of assumption violations on statistical tests in random field models.
To examine the impact of smoothing, unbalancedness, and leverages on empirical thresholds in these tests.
To assess departures from normality in gray matter probability maps for voxel-based morphometry and evaluate transformation strategies.

Main Methods:

Simulations were conducted to study the effects of smoothing, unbalancedness, and leverages on empirical thresholds.
A case study focused on gray matter probability maps from voxel-based morphometry.
Maximum likelihood estimation was used to determine optimal data transformation strategies.

Main Results:

Departures from distributional assumptions in random field tests are more pronounced than in univariate settings.
In specific scenarios, significance tests may become invalid due to assumption violations.
Voxel-by-voxel transformation yielded the best results, indicating distributional heterogeneity in gray matter data.

Conclusions:

Statistical inference in random field models is highly sensitive to distributional assumptions.
Voxel-based morphometry data, specifically gray matter probability maps, often exhibit non-normality.
Adaptive, voxel-wise data transformation is recommended for robust statistical analysis in neuroimaging.