Random field theory-based p-values: a review of the SPM implementation

P-values and null-hypothesis significance testing are popular data-analytical tools in functional neuroimaging. Sparked by the analysis of resting-state fMRI data, there has recently been a resurgence of interest in the validity of some of the p-values evaluated with the widely used software SPM. The default parametric p-values reported in SPM are based on the application of results from random field theory to statistical parametric maps, a framework we refer to as RFP. While RFP was established almost two decades ago and has since been applied in a plethora of fMRI studies, there does not exist a unified documentation of the mathematical and computational underpinnings of RFP as implemented in current versions of SPM. Here, we provide such a documentation with the aim of contributing to contemporary efforts towards higher levels of computational transparency in functional neuroimaging.