Effect Size Comparison for Gaussian and Rician Modelling within fMRI Data

It has been argued that due to the bias at low SNR, the Gaussian approach is unsuitable for modelling Rician fMRI data. As a result several estimators incorporating the Rician nature of the data have been proposed to measure the signal as accurately as possible. However, within fMRI the main objective is not to measure the signal, but rather to measure changes within the signal. As an increasing function of the signal, the mean can be used for this purpose as well. In this paper it is argued that, due to its lower variance, the sample average is a more suitable tool to detect changes in the amplitude than several conventional Rician parameter estimators at those SNR values common within fMRI measurements. While the interpretation is slightly different, this Rician mean-based approach is essentially equivalent to the Gaussian approach. Despite its bias, the Gaussian approach is therefore preferable within fMRI analysis.