Cortical Functional Mapping by High-Resolution EEG - Quantitative EEG Analysis Methods and Clinical Applications - page 365

t -value equal to or higher than the value needed to have a statistical significance in a
single univariate test of p 0.00001.

Due to the excessive severity of the Bonferroni correction, the scientific commu-
nity has also shown interest in other methods that are less conservative in protecting
against type I errors. Examples are the procedures for controlling the false discovery
rate, described and discussed in several papers by Benjamini and coauthors [17, 18],
or the Holm-Bonferroni procedure [19]. An example will shed light on the last pro-
cedure, usually employed in some source localization algorithms for EEG or MEG
data.
Suppose that there are k hypotheses to be tested and the overall type 1 error rate

=

is . In our context, k could be equal to 3,000 (one t -test for each cortical dipole),

and the error rate is 5%. Execution of the multiple univariate tests results in a list of
3,000 p -values. The issue now is how to deal with such p -values by using the
Holm-Bonferroni procedure. This procedure starts by ordering the p -values and
comparing the smallest p -value to

α

/ k , the value of the Bonferroni correction to be
adopted for only one p- value. If that p -value is less than

α

/ k , then that hypothesis
can be rejected and the procedure started over again with the same

α

α . The procedure

tests the remaining k − 1 hypotheses by ordering the k − 1 remaining p -values and

comparing the smallest one to 1). This procedure is iterated until the hypothe-

sis with the smallest p -value cannot be rejected. At that point the procedure stops,
and all hypotheses that were not rejected at previous steps are accepted. This proce-
dure is obviously less severe than the simple application of the Bonferroni test on all
of the p -values with the threshold level

α /( k −

α / k .

13.5 Group Analysis: The Extraction of Common Features Within the
Population

In the previous paragraphs, we have considered the generation of a statistical repre-
sentation of the cortical areas that differ in spectral power in a particular subject
during the execution of a task A as compared to a task B . We also discussed a way to
validate the statistical results against the type I error due to the execution of multiple
univariate tests. Here, we move to the problem of generating a power spectra corti-
cal map representing the common statistical features for the analyzed population in
a particular frequency band. In this respect it is mandatory that the statistical corti-
cal activity estimated for each subject can be reported to a common cortical source
space. This could be performed by using the Tailaraich transformation, as usually
employed by scientists using fMRI.
After the statistically significant areas of cortical activation in all subjects have
been reported on a common cortical source space, it is possible to generate a group
representation of the results. We can again use color to indicate whether the activa-
tion of a single cortical voxel is significant in all of the population analyzed, or in all
but one analyzed, and so forth.
Figure 13.3 contrasts the areas of common statistically significant activity dur-
ing the execution of tasks A and B not by a single subject (as in Figure 13.2) but
rather by the entire population analyzed. The brain again is shown from different
perspectives, and the quantities mapped are the differences in spectral activation in