EEG and Brain Connectivity: A Tutorial - Bio-Medical Instruments, Inc.

where n is the number of observations and α i is the ith observation.
The length or magnitude of the mean vector is:
Eq. 23 -
2
r = x +
y
2
And the vector mean direction is:
Eq. 24 - Θ = arctan( x / y)
The magnitude of the mean vector gives an indication of the relative
dispersion or coherence of the observations. The range of r is 0.0 to 1.0. If
the phase angles or differences are clustered or clumped together in one
direction then r will approximate 1. If the phase differences are random over
the interval, then r will be small and approximate 0. The statistical
computation of the cross-spectral “atoms” provides a complete description
of the EEG phase locking, synchrony and phase angles (also phase resetting
if differences or derivatives as a function of time are used).
Eq. 25 -
Angular variance: s 2 = 2(1-r)
This is equivalent to variance in linear statistics.
Eq. 26 - Angular deviation: s = 2(1-r) 1/2
This is equivalent to standard deviation in linear statistics.