Table 1. Two-state experiment. Proportion of carrect responses for each value of the interval (4) between offsets of the variable. N is the number of trials upon which each proportion
in the row ts based.
Variable interval t (msec)
Subject
30
40
50
60
70
80
90
100
110
120
JE
MK
RW
PR
KH
VK
SK
JA
200
240
220
90
140
240
160
180
0.55
56
58
58
55
56
56
62
055
64
62
68
56
66
61
67
0.60
75
69
71
69
60
72
74
067
.80
81
76
74
73
84
.90
40.72
93
87
87
83
81
88
1
O83
96
92
88
SL
88
93
94
0.89
.96
96
9)
91
94
98
98
0.97
98
.96
98
97
.96
28
9
0.96
99
1.00
0.98
27
99
~=1.00
~=0,.97
0.98
99
.99
..97
96
99
99
99
JK
DU
TN
JM
230
128
320
224
53
52
53
52
58
54
57
56
59
66
61
55
68
.66
70
70
75
76
74
74
84
.84
76
83
84
87
84
90
35
93
89
93
0.93
93
92
96
97
98
.96
99
JS
150
3
.66
76
82
89
o4
96
98
1.00
.99
frequently occurring interval between zerocrossings based upon the indicated sample
size.
correlation between the quantum size
and alpha is significant, the rank-order
coefficient being 0.74. If ane uses posi-
Sub.
ject
tion with respect to the median of
alpha to predict position with respect
x
(msec)
JE
MK
23
24
RW
24
PR
KH
VK
SK
JA
JS
JK
DU
™
JIM
20
27
20
25
20
23
33
34
26
36
M’
(msec)
67
95
40
49
.88
93
14
94
89
88
83
85
a
94
53
56
41
49
42
41
47
47
51
60
OL
49
Mean == 48.1
Standard deviation —
5.9
40
Peak
alpha
Alpha
ple
size
(3),
the
to the median of the quantum size and
44
57
800
960
combines the resuits of the two studies,
50
50
43
49
50
42
48
46
50
51
360
560
960
640
720
600
920
320
800
560
rectly.
In interpreting the degree of asso-
44
[9 of the 21 subjects are classified cor-
880
ciation between these two quantities
one should consider the errors of
measurement. I[ cannot estimate the
reliability of Af° at the present time;
however, the reliability of alpha is
something short of perfect. If one com-
48.0
4.0
pares peak alpha obtained in the beforesession records with that obtained at
the ends of the sessions, the means are
47.7 in both cases and the rank-order
correlation is 0.86 for the same 13
7
subjects (8).
Sr
-
The values of P which were obtained
imply a range of Ps. extending from
a“
x
ia
ar
7
7h
-
GE
7
aL
S x
—
xem!
xeeM'
tT (VARIABLE INTERVAL)
Fig. 1.
Composite
two-state
successive-
ness discrimination function for
13 sub-
jects. The line is the theoretical function
with P = 0.86, the obtained average value.
For each data point for each subject, ¢
was converted into (¢ — x)/M’, and P(c),
the value of P(c) predicted by theory,
was calculated all from the individual's
own parameters. Then the error of prediction [P(c) — P(c)] was calculated. These
errors were grouped together in intervals
of 0.2 on the (f — x)/M’ scale and averages were taken of them and of their cor-
responding values of (f — x)/M’ within
each group. These averages determine the
coordinates of the points in this figure.
we
8 DECEMBER 1967
channel after the first signal occurs but
before the second. If attention can
switch only at the end of a time quan-
tum, and since thefirst signal is equally
likely to occur at any time during a
quantum, then the successiveness discrimination function should be linear
and it should span one quantum. This
accounts for the state 1 function. The
tion of this view. One could speculate
Their ranges are similar, 40 to 60 for
M’ and 4°! to 57 for alpha.
As in the earlier study
that attention switch from the channel
containing the first signal to the other
two-state model requires some elabora-
Table 2. Parameters of the two-state model
computed from the data of Table 1. M and x
are to the nearest millisecond, P to the nearest
0.01; P= 1—0.25 P:. Peak alpha is the most
dependentsignals as successive requires
0.20 to 1.0. No subject exhibited pure
state | performance under the condi-
tions of this experiment. The variables
which influence the percentage of trials
on which a subject is in state 1° rather
than state 2 have yet to be identified.
One possibility, for which I have some
evidence, is that the range of values of
f is itself such a variable. When the
range is narrow, making the task a
more difficult one, as in the earlier experiments, the probability of being in
state | is higher than it is when the
task is relatively easy. Another effective
factor may be whether or not the subject is informed of the correctness of
his decisions.
My interpretation of successiveness
discrimination has recently been pre-
sented elsewhere (3). Briefly, the suggestion is that discriminating two in-
that state 2 occurs when an additional
quantum of time is inserted in the
visual information pathway prior to the
display area or when the switching of
attention can occur only in every second quantum
(for example, only at
positive-going zero crossings) (9). Either
of these assumptions brings the twostate hypothesis into the theory but
there seems to be no basis for a choice
between them at this time.
ALFRED B, KRISTOFFERSON
Department of Psychology,
McMaster University,
Hamilton, Ontario, Canada
References and Notes
1.C. T. White, Psychol. Monog. 77, whole
No. 575 (1963).
2. W. W. Surwillo, Electroencephalog. Clin.
Neurophysiol. 15, 105 (1963); ibid. 16, 510
(1964); R. E. Dustman and E. C. Beck, ibid.
18, 433 (1965): L. K. Morrell, NMeuropsychologia 4, 41 (1966).
3. A. B. Kristofferson. Acta Psychol, 27, 93
(1967).
4.M. W. Schmidt and A. B. Kristofferson,
Science 139, 112 (1963).
5. A. B. Kristofferson, National Aeronautics and
Space
Administration,
CR-194
(Clearing
House for Federal Scientific and Technical
Information, Springfield, Va., 1965).
, National Aeronautics and Space Administration, CR-454 (Clearing House for
Federal Scientific and Technical Information,
Springfield, Va., 1966}.
7. Since these data were analyzed we have
begun
computing
electroencephalographic
power spectra with autocorrelation functions.
Comparisons between this computer analysis
and the visual analysis used in this report
indicates that they agree very well in determining peak frequencies and individual
differences in peak frequency.
8. Nine of the original subjects are female. Three
of these were excluded by the electroencephalogram screening and three failed to give
adequate psychophysical data in the time that
was available. The remaining three (MK, JA,
and JM in Table 2) are the ones for whom
the discrepancies between M’ and alpha are
the largest.
9. Statements of this kind do not imply a
causal role for the electrical changes which
constitute the electroencephalogram. In fact,
there is evidence that contradicts such a
view. For example, G. K. Smith and H.
Langsam of this department have experiments under way which show that the spontaneous spike activity in single cortical neurons is unaffected by voltage clamping of the
cells’ environment.
10. This research is supported by grant No.
NGR-52-059-001 from NASA and by grant
No. APB-112 from the National Research
Council of Canada, The technical assistance
of C. Greifeneder and F. Theodor is gratefully acknowledged.
10 October 1967
1339