Distributional Assumptions in Voxel-Based Morphometry

Abstract

In this paper we address the assumptions about the distribution of errors made by voxel-based morphometry. Voxel-based morphometry (VBM) uses the general linear model to construct parametric statistical tests. In order for these statistics to be valid, a small number of assumptions must hold. A key assumption is that the model's error terms are normally distributed. This is usually ensured through the Central Limit Theorem by smoothing the data. However, there is increasing interest in using minimal smoothing (in order to sensitize the analysis to regional differences at a small spatial scale). The validity of such analyses is investigated. In brief, our results indicate that nonnormality in the error terms can be an issue in VBM. However, in balanced designs, provided the data are smoothed with a 4-mm FWHM kernel, nonnormality is sufficiently attenuated to render the tests valid. Unbalanced designs appear to be less robust to violations of normality: a significant number of false positives arise at a smoothing of 4 and 8 mm when comparing a single subject to a group. This is despite the fact that conventional group comparisons appear to be robust, remaining valid even with no smoothing. The implications of the results for researchers using voxel-based morphometry are discussed.