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