Biomedical Engineering Reference
In-Depth Information
while the subject is “at rest”; however, there may be significant changes in the sub-
ject's level of arousal between the time when the subject is at rest and when the
experiment is performed. Long intervals between the experiment and the baseline
condition may yield statistical results that are due to differences in conditions not
related to the functional task; such differences may also occur immediately before or
after an experiment.
Multiple trials of a functional task are recorded in order to achieve stable
time-frequency estimates of EEG signal energy associated with the task and the ref-
erence interval, as mentioned above. The minimum number of trials that should be
used is difficult to define, but 25 is a good place to start, and for many tasks a greater
number of trials is desirable. The length of the reference interval is an important con-
sideration and should be taken into account when designing the experimental task
itself. Longer intervals will generally yield more stable estimates of “baseline condi-
tions.” It is important for the reference interval to capture not only the variability of
energy across different frequencies but also its variability across time. However, if
the reference interval is too long and the intertrial interval is too short, the reference
interval may be contaminated by residual activation or deactivation from preceding
trials.
Statistical analyses may be performed on time-frequency estimates of EEG sig-
nal energy using a variety of approaches. To use parametric methods such as
t
-tests,
ANOVAs, or regression analyses, it is necessary for the energy estimates to approxi-
mate a normal distribution, and for this purpose the natural logarithm has been
commonly used [38, 39]. The stability of power estimates, and thus the power of sta-
tistical tests, can be enhanced by decimating the time-frequency space, that is, reduc-
ing the time or frequency resolution of the estimates.
An important and frequently overlooked problem for time-frequency analyses
of event-related EEG signal changes is that of accounting for multiple comparisons.
In a typical event-related task, the poststimulus interval of interest may be 1 to 2 sec-
onds, and the frequency spectrum of interest may extend from 1 to 200 Hz or
beyond. The energy in each of the two-dimensional time-frequency “pixels” in this
time-frequency plane is being tested for a significant difference from baseline, and if
the time and frequency resolution are maximized, there will be an enormous number
of statistical tests, or comparisons (e.g., 1,000 time divisions
×
200 frequency divi-
sions
200,000 comparisons). However, if the threshold for statistical significance
is the customary
p
-value of 0.05, the chance that a nonsignificant difference will be
significant is 1 in 20, and for 200,000 comparisons we can expect that at least
10,000 time-frequency pixels will be deemed different from baseline when they are
not.
The easiest but most conservative method to correct for multiple comparisons is
the Bonferroni correction, which simply divides the
p
-value by the number of com-
parisons (e.g., corrected
p
-value
=
0.00000025). It may be surpris-
ing that such an extreme threshold for statistical significance can be exceeded, but it
is routinely surpassed in many pixels of a typical time-frequency analysis of iEEG
ERD/ERS responses. Nevertheless, the Bonferroni correction is probably inappro-
priately conservative in the application at hand because it assumes that each statisti-
cal comparison is independent of all others, and event-related energy changes in
adjacent pixels are not independent of each other. Instead, these energy changes are
=
0.05/200,000
=
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