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

This computation is repeated for each frequency component to yield the
complete coherence spectrum, a typical plot of coherence is frequency on
the horizontal axis (abscissa) and coherence on the vertical axis (ordinate).
Coherence is sometimes defined and computed as the positive square-root
and this is referred to as “coherency”.
12- Some Statistical Properties of Coherence
How large should coherence values be before they can be considered
reliable? The answer is it depends on the true coherence relationship and the
degrees of freedom used in the averaging computation in equation 13. In
general the degrees of freedom increase as a square root of N (i.e., the
amount of smoothing) and the more the degrees of freedom the better (i.e.,
averaging across frequency and/or across repetitions or “smoothing”). The
trade off is between frequency resolution and reliability, the longer the
interval of time over which averaging occurs or the larger the number of
repetitions then the greater are the degrees of freedom. Short time intervals
of low frequencies by their nature have low degrees of freedom. For this
reason the NeuroGuide uses the default of a 1 minute sample, e.g., the theta
frequency band 4 – 7 Hz NeuroGuide EEG coherence for a 1 minute sample
= 7 (0.5 Hz bins) + 117 FFTs = 124 x 2 = 248 degrees of freedom. To test
the statistical properties of coherence select shorter segments of simulated
EEG and systematically change the signal-to-noise ratio in the NeuroGuide
demo signal generator at www.appliedneuroscience.com. After launching
the NeuroGuide demo click Open > Signal Generation.
13- How large should coherence be before it can be regarded as
significantly larger than zero?
Low degrees of freedom always involve “Inflation” of the true signalto-noise
relationship between two channels when a Pearson product
correlation coefficient is computed. EEG coherence is no exception and
this explains why coherence is highly inflated when the degrees of freedom
are low and the bandwidth is small. For example, figure 8 shows the
inflation of coherence (y-axis) when a signal in one channel (4 Hz – 19 Hz
sine wave) is compared to random noise in a second channel with increasing
degrees of freedom (x-axis) and different bandwidths. The ideal is
coherence = 0.