Modelling the data and not the images in FMRI

The standard approach to the analysis of functional magnetic resonance imaging (FMRI) data applies various preprocessing steps to the original FMRI. These preprocessings lead to a general underestimation of residual variance in the downstream analysis. This negatively impacts the type I error of statistical tests and increases the risk for reporting false positive results. A genuine approach to the statistical analysis of FMRI data of brain scans is derived from first principles that is deeply rooted in statistical test theory. The method combines all preprocessing steps of the standard approach into one single modelling step, enabling valid statistical tests to be constructed. On population level, BOLD effects are modelled by random effects meta regression models. This acknowledges that subjects are random entities, and it acknowledges that the accuracy of the BOLD signal is estimated with various certainty in an FMRI. The concept of a reference scalar field is introduced that enables individual effect sizes to be related to each other with respect to a common unit. In particular, multicentre studies will gain interpretability and power by its use.