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In the current experiment, viewers 002, 009, and 372 were asked to press a button whenever
they “perceived” an RS. The total number of stimuli during a session of 10 runs was not known in
advance because of the randomization procedure. The null hypothesis is that the probability of a
time interval having a stimulus is the same for those intervals with a button press as for those without
a button press.
In other words, the presence or absence of a stimulus
is independent of the
presence or absence of a button press. We tested this null hypothesis to determine if a viewer is
cognitively aware of the RS.
In Table 2, the fractional hitting rate
is p
= A/(A+B), and the fractional missing rate
is
pz = C/(C+D). The total number of 1-second intervals is N = (A+B+C+D), and the total stimulus
rate
is po =
(A+C)/N
.
Table 2
Data Schema for Interval Conditions
Stimulus
Yes
No
Response
Yes
A
B
No
C
D
Then the following statistic
is approximately normally distributed with a mean of 0 and a
variance of
1 under the null hypothesis:
z =
(P l -Pi)
JpoV
/>o)((A+a) + (c!o>
)
Table 3 shows N, p0 , Pu Pz,
z, p-value, and the effect size,
r,
for the three sessions for
which button-press data were collected. As in the earlier SRI study, there is no indication that the
viewers were cognitively aware of the RS.
Table 3
Button Pressing Results
Viewer
N
Po
Pi
P2
z
P
r
1210
0.198
0.164
0.951
0.163
1280
0.068
0.094
-0.978
0.836
l
372
1089
0.157
0.119
0.160
-0.996
0.840
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IV DISCUSSION AND CONCLUSIONS
We have found statistical evidence that the relative phase shift from -0.5 to 0.5 seconds of
an RS are not characteristic of the data at large (Zs = 1.99, p
0.024, effect size = 0.599). The
combined statistic for the PS indicates that the relative phase shift from -0.5 to 0.5 seconds of a PS
are also not characteristic of the data atlarge (Z» = 2.92, p
0.002, effect size = 0.924). Averaged
across
all viewers, the magnitude of the
results, as indicated by their effect sizes of 0.599 and
0.924, respectively,
is considered robust by accepted behavioral criteria defined by Cohen. 9 *
A.
Root-Mean-Square Phase
Searching for a change of phase as a result of an RS is a natural extension of results quoted in
the literature.
For example, Rebert and Turner6 report an example of photic driving
(i.e., an
extreme example of phase locking) at 16 Hz.
In their work, a subject was exposed to a 16-Hz
visual DS randomly balanced with no stimulus during 4-second epochs. The average power spectra
showed approximately 10-Hz alpha activity during the no-light epochs, and a strong 16-Hz and no
10-Hz peak during the 16-Hz epochs.
One interpretation of their result
is that the alpha rhythm was blocked, and the CNS
“locked” on to the flashing stimulus.
Eason, Oden, White and White, 10 report a phase-shift
phenomenon when a rare stimulus, which
is random relative to the internal alpha
activity,
is
presented as a DS:
“...when a stimulus flash is presented, the resulting primary evoked response acts as a
trigger stimulus which temporarily synchronized a certain percentage of the neural
elements
normally
under
the
influence
of
an
internal
pacemaker.
...
Desynchronization of the elements participating in the evoked response would occur
as the elements are brought back under the influence of an internal pacemaker or are
affected by neurons not involved in the response.”
In other words, the internal alpha is momentarily interrupted by an external stimulus, and, in the
absence of continuing external stimuli, returns back to its original frequency, but at a random phase
relative to
its pre-stimulus state.
To understand what would be expected
in our experiment for the
distribution of RMS
phases during the Monte Carlo simulations, we examine a hypothetical case.
Suppose that the
*
Values of 0.1, 0.3, and 0.5 correspond to small, medium, and large effects, respectively.
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viewer’s alpha activity was a continuous wave at a single frequency. A phase change is computed
between 500 ms before and 500 ms after each Monte Carlo “stimulus.”
Therefore, regardless of
the entry point, the relative phase change would be zero, and the RMS phase over many such
“stimuli” would also be zero.
Real alpha activity, however, is not continuous,
Rather, it appears in bursts lasting from 100
to 5000 ms.
Random Monte Carlo "stimuli” would sometimes occur within such bursts and
sometimes
near
the
edges.
Thus,
we
would
expect
a
nonzero RMS
phase
over many
such “stimuli," but the individual relative phases would not be uniformly distributed.
Depending
upon the viewers’ alpha characteristics, the distributions would be enhanced near zero RMS phase.
If we assume that Eason, et al., are correct, and that a phase shift is expected as a result of
an RS, then the expected distribution of RMS phases is uniformly distributed on
[-tt, it].
In this
case, the phase change
is related to the relative timing between the external stimulus and the
internal alpha—a completely random relationship.
Thus, the variance of the RMS phases in the
experimental condition should be larger than those computed during the Monte Carlo runs. Figure
is a schematic representation of these models.
Figure
16.
Idealized Distributions for Relative Phase Shifts
As a
first step in testing these models, we computed the expected variance for the RMS
phase, given that the individual phases are uniformly distributed on
[tt, it]
.
Using a Taylor Series
expansion for RMS phase, the variance
is given by: 11 *
*
We thank Professor Jessica M. Utts,
Statistics Department, University of California, Davis,
California, for suggesting this approach.
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