Biomedical Engineering Reference
In-Depth Information
Although the above presented method is computationally intensive, at present it
causes no problems in most of the standard applications. However, corrections for
multiple comparisons imply very low effective critical values of probabilities needed
to reject the null hypothesis. For the analysis presented in [Durka et al., 2004] critical
values of the order of 10 4 were routinely obtained. If we set p
10 4 in (4.32), we
=
10 6
obtain a minimum N rep
=
resampling repetitions to achieve 10% relative error
(
,
)
for the values p
.
In [Durka et al., 2004] either parametric or resampled statistical tests were applied
to energies in each resel separately. However, the very notion of the test's confidence
level reflects the possibility of falsely rejecting the null hypothesis. For example, a
confidence level of 5% means that it may happen in approximately one in 20 cases. If
we evaluate many such tests we are very likely to obtain many such false rejections.
This issue is known in statistics as the issue of multiple comparisons, and there are
several ways to deal with it properly.
To get a valid overall map of statistically significant changes we suggest the ap-
proach chosen in [Durka et al., 2004] that is a procedure assessing the false discovery
rate (FDR, proposed in [Benjamini and Hochberg, 1995]). The FDR is the ratio of
the number of falsely rejected null hypotheses ( m 0 ) to the number of all rejected null
hypotheses ( m ). In our case, if we control the FDR at a level q
i
j
05, we know
that among resels declared as revealing a significant change of energy, at most 5% of
them are declared so falsely. [Benjamini and Yekutieli, 2001] proves that the follow-
ing procedure controls the FDR at the level q under positive regression dependency,
which can be assumed for the time-frequency energy density maps:
=
0
.
1. Order the achieved significance levels p i , approximated in the previous section
for each of the resels separately, in an ascending series: p 1
p 2
≤···≤
p m
2. Find
p i
m q
i
k
=
max
i
(4.33)
3. p k is the effective significance level, so reject all hypotheses for which p
p k .
are marked significant if the null hypothesis H i , j
0
Resels r
(
i
,
j
)
can be rejected using
the significance level p k for the probabilities p
of the null hypothesis (4.27).
An example of ERD/ERS time-frequency maps together with the assessment of their
significance obtained with the above described procedure is illustrated in Figure 4.20.
(
i
,
j
)
4.1.7.3.4 ERD/ERS in the study of iEEG The ERD/ERS methodology was
also applied to iEEG signals. The most advanced method providing the highest and
most adaptive time-frequency resolution—matching pursuit was used, e.g., by [Zy-
gierewicz et al., 2005] for evaluation of ERD/ERS responses from cortex during hand
movement and for iEEG analysis during speech perception [Ray et al., 2003].
The ERD/ERS methodology applied to the iEEG made it possible to study high
gamma responses (HGR), which are difficult to record in standard EEG. They were
 
Search WWH ::




Custom Search