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

Parametric tests of linear models for images modeled as random fields are based like ordinary univariate tests on distributional assumptions. It is here shown that the effect of departures from assumptions in random field tests is more pronounced than in the univariate condition. Simulations are presented investigating in detail the influence of smoothing, unbalancedness and leverages on empirical thresholds. In certain conditions, significance tests may become invalid. As a case study, the existence and effect of departures from normality of gray matter probability maps, commonly used in voxel-based morphometry, is investigated, as well as the effect of different transformation strategies involving estimating the degree of transformation from the data by maximum likelihood. The best results are achieved with a voxel-by-voxel transformation, suggesting heterogeneity of distributional form across the volume for this kind of data.