Application to biomedical signals - Practical Biomedical Signal Analysis Using MATLAB - page 118

through the skull and scalp to downwardly project scalp-recorded potentials, which
provides a computational estimate of the electrical potentials, that would be recorded
near the superficial cortical surface [Lee and Gevins, 1993].
Mapping is often performed for the sake of comparison, e.g., to detect changes
connected with medication, or to find out possible difference between groups. For
the comparison of one map with a group of maps the z statistics can be used. The
transformation: Z

X
σ X of a map derived from an individual subject ( X ) is calcu-
lated for each pixel of a map of an individual subject in comparison to the mean
( X ) and standard deviation σ X for a group of maps. The t -statistics can be used to
differentiate between maps, but to use this statistics, the normal distribution of the
group data has to be assumed. In many cases the distribution can be transformed to
an approximately normal one by Box-Cox transformation [Box and Cox, 1964]. A
special case of this transformation is subjecting the data to logarithmic transform of
the type: y

X −

=

which is often used to normalize the values of absolute power
spectra. The second assumption of t -test is the homoscedasticity (the assumption that
the variances in both compared groups are equal). In cases where the variances can
be different, one should use the Welch's t test [Welch, 1947]. For comparison of val-
ues that cannot be transformed to normal distribution, non-parametric tests should be
used. The problem of choice of the appropriate test is discussed in section 1.5.2. To
make statistical inference on the maps pixel by pixel one has to take into account the
multiple comparison problem. This problem and its possible solutions are discussed
in Sect. 1.5.3.

= log ( x )

4.1.6.2.2 Measuring of dependence between EEG signals Interdependence be-
tween two EEG signals can be found by a cross-correlation function or its analogue
in the frequency domain—coherence. Cross-correlation can be used for comparison
of EEGs from homologous derivations on the scalp. A certain degree of difference
between these EEGs may be connected with functional differences between brain
hemispheres, but a low value of cross-correlation may also indicate a pathology.
In EEG studies, not correlations but rather coherences are usually estimated, since
they provide the information about the rhythm synchronization between channels.
Conventionally, ordinary coherences calculated pair-wise between two signals have
been used for EEG as well as for ERP studies. However, for the ensemble of chan-
nels taken from different derivations the relationship between two signals may result
from the common driving from another site. This is often a case for EEG, the sig-
nals recorded from the scalp are strongly interdependent. Therefore the patterns of
bivariate coherences are usually complicated and not consistent. To obtain a com-
plete pattern of coherence structure of multichannel EEG the estimation not only of
ordinary, but also of partial and multiple coherences is recommended [Franaszczuk
et al., 1985].
In Figure 4.8 ordinary (bivariate), partial, and multiple coherences are shown for
sleep EEG stage 2 [Kaminski et al., 1997]. Multiple coherences have high ampli-
tudes for all derivations and whole frequency range which means that the system
is strongly interconnected. Ordinary coherences decrease monotonically with a dis-