  Historically, applications of RFT in fMRI have relied on assumptions of
smoothness, stationarity and Gaussianity. The first two assumptions have been
addressed in Part 1 of this article series. Here we address the severe
non-Gaussianity of (real) fMRI data to greatly improve the performance of
voxelwise RFT in fMRI group analysis. In particular, we introduce a
transformation which accelerates the convergence of the Central Limit Theorem
allowing us to rely on limiting Gaussianity of the test-statistic. We shall
show that, when the GKF is combined with the Gaussianization transformation, we
are able to accurately estimate the EEC of the excursion set of the transformed
test-statistic even when the data is non-Gaussian. This allows us to drop the
key assumptions of RFT inference and enables us to provide a fast approach
which correctly controls the voxelwise false positive rate in fMRI. We employ a
big data \cite{Eklund2016} style validation in which we process resting state
data from 7000 subjects from the UK BioBank with fake task designs. We resample
from this data to create realistic noise and use this to demonstrate that the
error rate is correctly controlled.
