A two-choice, forced-choice method
is used in which a single trial consists
ever attained the higher level of per-
of the presentation of two light-sound
pairs. For the standard pair, a circular
spot of light and a 2000-hertz pure tone
begin simultaneously and terminate
simultaneously. For the variable pair,
quantum state, And in every case a
one-quantum function has been obtained in later sessions. A subject who
enters a two-quantum State typically
remains in that state for many sessions.
the signals begin simultaneously but the
light is terminated ¢ msec before the
sound, The rationale for using simultaneous terminations for the standard
is discussed elsewhere (5). On half the
trials, chosen at random, the standard
Switching to
is presented first; on the remaining
trials the variable occurs first. The subject responds by indicating whether the
offset of the light occurred before the
offset of the tone in the first pair or in
the second pair. When he indicates the
variable he is scored correct and the
proportion of correct responses is de-
termined for each of a number of
values of ¢. This proportion, P(c), as
a function of ¢, is the successiveness
discrimination function.
The shorter member of each pair of
signals has a duration of 2.0 seconds
and the empty interval between pairs
is also 2.0 seconds. An auditory signal
immediately following the subject’s
responsetells him whether the response
was correct, Trials are run at the rate
of one every 12 seconds. Usually only
one 20-minute session is conducted
each day for each subject. Equal numbers of the different values of ¢ are
randomly assignedtotrials.
Under some conditions the successiveness discrimination function can
be described adequately by a single
straight-line segment (6). A line fitted
to data intersects the level of chance
performance; that is, P(c) = 0.5, at
a value of t which is called x. The line
reaches P(c) = 1.0 at a value of ¢ of
(x + M) msec. The parameter M is
the minimum amount of time which
must be added to the interval between
the light and sound offsets to bring
P(c) from 0.5 to 1.0.
I have reported (3) an average value
of 54 msec for M from data obtained
by using highly practiced subjects
under conditions which were designed
to maximize performance. This value
was suggested as one estimate of the
duration of a quantum.
However, with several subjects I have
observed a strikingly different result
under certain conditions. Instead of a
“one-quantum”function they yield data
which, while still linear in form, span
about 100 msec. These “two-quantum”
functions have always been observed
early in practice, before the subject has
1338
formance
associated
the
with
the
one-
one-quantum
state
ordinarily requires some change in the
experimental procedure,
These observations suggested the pos-
sibility that there are two distinct states
such that when a subject is in state 1
his value of M is one quantum and
when he is in state 2 his M is two
quanta. Further, under some experimental conditions the probability of
being in state 2,
P2, may be close to
unity, while under other conditions the
probability of being in state 1 may be
close to unity.
If this conception is correct, then it
becomes apparent that the earlier
measurements of M were based on the
limited to the first quantum above x
and most subjects did not quite attain
a P(c) = 1.0 even for the greatest
value of ¢, Therefore, a new experiment
was done to test the adequacy of the
two-state model. The ten values of ¢
from 30 to 120 msec in 10-msec steps
were used and the interval between offsets for the standard was fixed at 20
msec. All of these intervals have a positive sign which indicates that the light
preceded the sound.
Twenty-three young, adult subjects
participated, 14 male and 9 female. We
eliminated four of them at the beginning because we were unable to cbtain
alpha in their electroencephalograms.
The remaining 19 were run through
One session per day and an electroen-
cephalogram was taken before and after
each session. Analysis of the electroencephalogram consisted of selecting
mean of two linear functions having the
monorhythmic single cycles of alpha
and measuring the period of each to
the nearest millisecond under a comparator. Twenty such samples were
measured in each record, giving forty
measurements per session. All of this
analysis was performed by assistants
who had no knowledge of the psychophysical analysis (7).
Obtained values of P(c)} are presented in Table 1 for 13 subjects. The
other six subjects are not analyzed
one case and two in the other. The
model failed to fit and five because they
assumption that a state 1 probability of
unity was actually achieved. To the extent that this condition was not met,
values of M7 would exceed the duration
of one quantum.
These considerations lead to a two-
state model of successiveness discrimi-
nation in which the successiveness discrimination function is the weighted
same x but spanning one quantum in
weighting factor is P2, the probability
of being in state 2. The function consists of the following four regions:
when:
(x—M) <t<x
P{c) equals:
0.50
xetc@tM) “GPa-osp,)
+ 0.5
oe
W+M)=t
(tf — x)P2
ai" +
< (x -+2M’)
(1 —0.5 P.)
t= (x + 2M’)
1.00
in which M’ is the quantum size in
milliseconds.
This two-state function rises from
P(c)
= 0.5 to P(c)
=
1.0 as two
linear segments, one connecting the
points (x, 0.5) and (x + M’, P) and
the other connecting (x + M’, P) and
(x + 2M’,
1.0). The intersection of
these segments occurs at P(c}) = P= 1
— 0.25 Po.
To apply this model requires obtaining data points over the range of
t between x and (x + 2M’). In the
earlier experiments this range was
further,
one
because
did not reach P(c)
the
two-state
> 0.90 even at
t = 120. An even wider rangeof values
of t should be used.
The combination of the three parameters of the two-state model which
yields the minimum squared-error fit
was determined for each of the subjects. For this solution, values of x
and M’ were found to the nearest millisecond and P was determined to the
nearest one hundredth, The results of
these computations are listed in Table
2 along with the modal (peak) alpha
interval.
,
The two-state function fits the data
satisfactorily, as Fig. 1 demonstrates.
This figure is a composite of all the
subjects with each one entered in rela-
tion to his own parameters as explained
in the caption of Fig. 1. The two segments of the function are both described adequately by the model, consistent with the deductions that there
are two segments and that they span
equal distances on the abscissa,
The quantities M4’ and alpha are very
similar. They have the same mean,
although the standard deviations suggest that M’ is somewhat more variable.
SCIENCE, VOL. 158