  Multiscale entropy (MSE) has been a prevalent algorithm to quantify the
complexity of fluctuations in the local mean value of biomedical time series.
Recent developments in the field have tried to improve the MSE by reducing its
variability in large scale factors. On the other hand, there has been recent
interest in using other statistical moments than the mean, i.e. variance, in
the coarse-graining step of the MSE. Building on these trends, here we
introduce the so-called refined composite multiscale fuzzy entropy based on the
standard deviation (RCMFE{\sigma}) to quantify the dynamical properties of
spread over multiple time scales. We demonstrate the dependency of the
RCMFE{\sigma}, in comparison with other multiscale approaches, on several
straightforward signal processing concepts using a set of synthetic signals. We
also investigate the complementarity of using the standard deviation instead of
the mean in the coarse-graining process using magnetoencephalograms in
Alzheimer disease and publicly available electroencephalograms recorded from
focal and non-focal areas in epilepsy. Our results indicate that RCMFE{\sigma}
offers complementary information to that revealed by classical coarse-graining
approaches and that it has superior performance to distinguish different types
of physiological activity.
