Copyright 1974, Journal of Parapsychology. Reproduced with permission.
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COMPARISON OF PK ACTION ON TWO DIFFERENT RANDOM NUMBER
GENERATORS
(Originally published in Journal of Parapsychology, Vol. 38, p. 47-55)
ABSTRACT: The objective of this series of tests was to compare the action
of PK on two electronic binary random generators- one simple and the other
complex- under psychologically equivalent conditions. In the testing room
the subject pressed a switch to initiate each trial and he was given
feedback by way of two different colored lamps as indicators of hits and
misses.
The simple generator produced a one-step binary output as the basis
for the subject to exert his PK on each trial. The complex generator,
on the other hand, based the binary output for each trial on the majority
decision of a rapid sequence of 100 binary events. The choice of which
generator was active on each trial was randomly made and neither the
experimenter nor the subject knew which generator was operating during a
given trial.
Significant results were obtained with both generators, and there
appeared to be no significant difference in the scoring between the two.
PK tests with dice, electronic equipment, and various other devices
appear to have produced scoring of comparable magnitude regardless of the
nature of the testing device. This raises the question of whether or not
the outcome of a PK test is independent of the structure of the randomizer
and the nature of the underlying random process.
The following study has been designed to test this question by comparing the
action of PK on two random generators of different degrees of complexity.
For this comparison the psychological test conditions were kept constant
because a psychological preference on the part of the subject for working
with one or the other generator could easily mask any effect due to the
physical differences between the generators. The experiment was carried
out during February and March, 1973, at the Institute for Parapsychology.
APPARATUS AND PROCEDURE
The apparatus was located in two rooms on different floors of the Institute.
The electronic equipment was on the lower floor; and the feedback apparatus
for the subject was on the floor above.
The Two Binary Random Number Generators
The simple generator (S) was identical to the one discussed in a previous
report (Schmidt, 1970). It generated sequences of binary random targets,
"heads" and "tails." The choice of target depended on a high-frequency
switch which oscillated between two positions and was halted at a time
determined by the random arrival of a radioactive strontium-90 decay
particle at a Geiger counter.
The complex generator (C) was built from a high-speed random number generator
(RNG) used in another, previous experiment (Schmidt, 1973). If the
high-speed generator was triggered, it produced a string of 100 binary
random numbers, designated as +1's and -1's, within three seconds. Each
individual binary number was generated by a process similar to the one used
in the simple generator. (The only difference was that for practical reasons
the random time element was not furnished by radioactive decay but by the
random output of an electronic noise generator. The high-frequency switch
was stopped when the noise amplitude passed a certain threshold.)
In the present experiment the individual random numbers in a string of 100
numbers provided by C were not recorded. The only information that was
recorded was the "majority vote," that is, whether more +1's or more -1's
occurred in the string. The majority-vote selection was made by an
evaluator box connected to the RNG. The box had two outputs, a "head"
output and a "tail" output, and, depending on whether more +1's or more -1's
occurred in a string, one or the other output emitted a signal. In the case
of a tie (50 +1's and 50 -1's) no signal was emitted. Thus the complex
generator made a binary decision (except in the rare case of a tie) by
taking the majority vote of 100 individual random events occurring during a
three-second time interval.
Previous to, and between, the PK tests with human subjects the randomness
of the generators was tested experimentally. For this purpose the equipment
was activated automatically at the rate of one trial every eight seconds
(similar to the typical operation rate in the PK tests) while the output
signals of the two generators were counted. In five such test runs of
approximately 16 hours each a total of 40,306 random numbers was produced
by each generator. Neither the total scores (average scoring rates 49.96%
and 49.8% with S and C, respectively) nor the chi-square values for the
sessions as units suggested any deviations from ideal randomness.
During the experiment the subject, in the upper room, was seated in an arm
chair looking at two feedback lamps, one of which lit up when he made a
hit, and the other when he made a miss. The lamps were mounted in two
sockets, one marked "head" and the other, "tail". These sockets were
attached to long cables so that the subject had the freedom to arrange the
lamps on a table in front of him or to attach them to hooks on the wall.
As a safeguard against generator bias for either side, the test procedure
was so arranged that in approximately half of each session the target was
the lamp in the "head" socket, and in the other half, the lamp in the
"tail" socket. Four different colored lamps were available, and the
subject was free to insert his favorite colored lamp into the target socket
and to change the colors of the lamps as often as he pleased. He was also
provided with a switch at the end of a cable long enough to reach his
chair. The subject pressed the switch to activate the test equipment for
each trial. His task was to try to make the target lamp light up each time.
When the subject triggered his hand switch, both generators were activated.
Only one was chosen, however, to be linked up to the feedback display for
that trial. This choice was made by a selector switch whose position was
determined by a prerecorded binary random number sequence stored in a tape
reader. After each trial the tape was advanced by one step, and the next
number on the tape (+1 or -1) determined the position of the selector switch.
In order to have sensorially identical test conditions for each trial, there
was a three-second delay in the trigger line to the simple generator so
that both generators would take the same length of time (approximately
three seconds) for producing a binary output after the subject had triggered
his switch. Neither the experimenter nor the subject knew which generator
was momentarily in action.
An ink pen-recorder on the lower floor registered the following data for
each trial:
a. Which generator was the active one, S or C.
b. The output of the active generator ("head" or "tail").
c. The output of S for the trials when S was not the active generator.
d. The target side.
Two electromechanical counters on the table in front of the subject in the
test room indicated the total cumulative score. The tape record showed
how the hits were distributed among the two generators. The recording (c)
of the output of S even when S was not the active generator (and the subject
was thus not motivated to obtain a particular output) was made with regard
to the possibility that a previous effort of a subject to obtain, say, a
"head" on one generator might "carry over" into the next trial even if that
generator were no longer the active one.
No systematic study was intended with regard to how the scoring rates might
depend on the subjects' attitudes or on other psychological factors. The
subjects were encouraged to relax and to visualize the target color in some
pleasant, possibly emotionally charged, context, and to start a trial (by
setting the switch) only when they felt as completely as possible "immersed"
in the target color. No attempt was made, however, to enforce this approach.
Thus, some subjects would even get tense and try to "enforce" the lighting of
the target lamp.
The subjects made their contribution to the test in one or in several
sessions. Each session was continued only as long as the subject was
optimistic and interested and felt able to concentrate well on the target
color. Sessions were frequently interrupted by coffee breaks, walks on a
porch, or by informal conversation. Much time was devoted to the discussion
of how one might best actively visualize the target color.
Objectives of the Experiment
The questions to be studied in the experiment were these:
1. Is there evidence of PK under both conditions; i.e., when the simple RNG
is active and when the complex RNG is active?
2. Is there an indication of a general scoring difference in the sense that,
for example, one of the generators is "easier" to influence by PK?
3. Do some subjects score significantly differently under the two conditions?
PILOT EXPERIMENT
After some encouraging exploratory studies a pilot test comprising
approximately 1,000 trials was made.
The subjects in the pilot test were members of the Institute and
others who had obtained promising PK scores in previous tests with
different equipment. These subjects were not pretested; the scores were
counted from the start. Only four subjects participated in the pilot.
One of them was the experimenter, subject H in Table 2.
Results
Table 1 shows the total score to be significant (CR = 3.0;
P = .002, two-tailed). The main contribution to this positive score
came from trials with the simple generator, which yielded a CR of 3.7
(P=.0002, two-tailed). The difference between the scoring on S and C
was suggestive (CR=2.2; P=.02, two-tailed). The trials on S
when it was inactive were at the chance level.
Table 2 gives the results for the individual subjects.
Table 1
OVERALL RESULTS OF PILOT EXPERIMENT
| Simple Generator Active | Complex Generator Active |
Total Active Trials | Trials with Simple Generator Inactive |
|---|
| No. of trials | 515 | 496 | 1,011 | 496 |
|---|
| Scoring rate | 58% | 51.2% | 54.7% | 50% |
|---|
| PQ | 26 | 0.5 | 8.9 | 0 |
|---|
| CR | 3.7** | 0.5 | 3.0* | 0 |
|---|
*P = .002 (two-tailed).
**P = .0002 (two-tailed).
Table 2
SCORES OF INDIVIDUAL SUBJECTS IN PILOT EXPERIMENT
| Subject | N_s | D_s | D_s* | N_c | D_c |
|---|
| H | 275 | 47 | -1 | 279 | -9 |
| B | 23 | 5 | -2 | 29 | -3 |
| C | 123 | 11 | 3 | 121 | 25 |
| P | 94 | 20 | 0 | 67 | -1 |
| Total | 515 | 83 | 0 | 496 | 12 |
Note-
N_s = Active trials with simple generator.
N_c = Active trials with complex generator.
D_s = Hits-misses for active trials on complex generator.
D_c = Hits-misses for active trials on simple generator.
D_s*= Hits-misses for nonactive trials of simple generator.
THE CONFIRMATORY EXPERIMENT
Since the pilot test gave significant evidence of PK, a confirmatory test
containing three sections each was planned and completed. In sections 1
and 2 the subjects were members of the Institute and others who had had good
PK scores in previous tests. In section 1 they knew that the experiment
aimed at a comparison between the two generators; in sections 2 and 3 no
mention was made of this comparison. Except in two cases, the subjects in
sections 2 and 3 were told only that the experiment was aimed at learning
somewhat more than just the existence of PK and that the experimenter was
interested in the effect of distance, the nature of the generator, and the
usefulness of vivid visualization in PK tests.
The subjects for section 3 were selected from random visitors to the
Institute on the basis of informal tests of about 10 trials with the
experimental equipment. The only difference was that in these selection
tests the simple and complex generators were not alternated. The simple
generator was used continuously. Subjects who showed a positive score and
expressed interest in this particular test were selected to take part.
The number of trials to be made in each section was preset at 1,000. (Table
4 shows that actually about 10% more trials were collected. These
additional trials were included in the evaluation, but the results are
practically unchanged if only the first 1,000 trials in each section are
considered.) The number of trials for each subject was specified to be
approximately 200 trials for each of the 5 subjects in section 1, 100 trials
for each of the 10 subjects in section 2, and 50 trials for each of the 20
subjects in section 3.
During all these tests the experimenter was in the same room with the
subject but he did not look at the target lamps.
Results
The overall scores in the confirmatory experiment with both types of
generators were positive and statistically significant. (See Table 3.)
The 1,695 trials when S was active gave a CR of 4.40 (P<
10^-5, one-tailed).
Table 3
OVERALL RESULTS OF CONFIRMATORY EXPERIMENT
| Simple Generator Active | Complex Generator Active |
Total Active Trials | Trials with Simple Generator Inactive |
|---|
| No. of trials | 1,695 | 1,609 | 3,304 |
1,609 |
|---|
| Scoring rate | 55.3% | 53.8% | 54.5% | 50.7% |
|---|
| PQ | 11.4 | 5.6 | 8.2 | 0.2 |
|---|
| CR | 4.40** | 3.0* | 5.2*** | 0.6 |
|---|
*P ~ 10^-3 (one-tailed).
**P < 10^-5 (one-tailed).
***P ~ 10^-7 (one-tailed).
Table 4
RESULTS FOR SECTIONS 1,2, AND 3 GIVEN SEPARATELY
| Section | Simple Generator Active |
Complex Generator Active | Total Active Trials |
Trials with Simple Generator Inactive |
|---|
| No. of trials | 1 | 572 | 547 | 1,119 | 547 |
|---|
| 2 | 552 | 523 | 1,075 | 523 |
|---|
| 3 | 571 | 539 | 1,110 | 539 |
|---|
| Scoring Rate | 1 | 55.8% | 53.8% | 54.8% | 52.1% |
|---|
| 2 | 55.8% | 53.9% | 54.9% | 50.7% |
|---|
| 3 | 54.3% | 53.6% | 54.0% | 49.9% |
|---|
| CR | 1 | 2.8 | 1.8 | 3.3 | 1.0 |
|---|
| 2 | 2.7 | 1.8 | 3.2 | 0.3 |
|---|
| 3 | 2.1 | 1.7 | 2.6 | 0.04 |
|---|
The 1,609 trials when C was active gave a CR of 3.0 (P ~ 10^-3,
one-tailed). The difference between C and S was not significant, although
the scores on S in all three sections were slightly higher than the scores
on C. (See Table 4, which gives the results of the individual sections.) The
scores on S, when it was inactive, were insignificant; i.e., there was no
evidence of a "carry-over" effect.
Table 5 gives the scores for the individual subjects in each of the 35
sessions. To discover whether or not some of these subjects might have
differentiated their scoring between the two generators, the 35 individual
CR_d values were calculated and gave
Sum(i=1...35) (CR_d^i)^2 = 30.5
which, with 35 degrees of freedom, was not significant. Two further
tests, the sign test and the
Wilcoxon test, also failed to indicate any
individual scoring differences between the two generators.
Table 5
RESULTS FOR INDIVIDUAL SUBJECTS IN THE CONFIRMATORY TEST
Section 1
| Subject | N_s | D_s | D_s* | N_c | D_c |
|---|
| 1 | 112 | 0 | 11 | 104 | 12 |
| 2 | 112 | 8 | -3 | 115 | 13 |
| 3 | 107 | 19 | +4 | 111 | -11 |
| 4 | 138 | 16 | -9 | 125 | 7 |
| 5 | 103 | 23 | 20 | 92 | 20 |
| Total | 572 | 66 | 23 | 547 | 41 |
Section 2
| 6 | 73 | 5 | 0 | 55 | 3 |
| 7 | 39 | 11 | 4 | 54 | -2 |
| 8 | 51 | 1 | 1 | 45 | 17 |
| 9 | 69 | 13 | -5 | 61 | 9 |
| 10 | 52 | -2 | -2 | 59 | -5 |
| 11 | 50 | 8 | 2 | 53 | 15 |
| 12 | 61 | 9 | -5 | 40 | 2 |
| 13 | 50 | 14 | 4 | 47 | 11 |
| 14 | 54 | 4 | -5 | 60 | -14 |
| 15 | 53 | 1 | 13 | 49 | 5 |
| Total | 552 | 64 | 7 | 523 | 41 |
Section 3
| 16 | 24 | 4 | 5 | 24 | 2 |
| 17 | 32 | 0 | 2 | 30 | -4 |
| 18 | 65 | 5 | -6 | 59 | 7 |
| 19 | 34 | 8 | 2 | 27 | 5 |
| 20 | 23 | 3 | -5 | 21 | -1 |
| 21 | 23 | -1 | -4 | 27 | 5 |
| 22 | 25 | -3 | 0 | 18 | 4 |
| 23 | 26 | 2 | -4 | 26 | 2 |
| 24 | 23 | 3 | 7 | 27 | -3 |
| 25 | 10 | 0 | 6 | 17 | 5 |
| 26 | 27 | 5 | -10 | 23 | 5 |
| 27 | 15 | 4 | 5 | 22 | -2 |
| 28 | 28 | -6 | 2 | 22 | 4 |
| 29 | 19 | 3 | 0 | 15 | 5 |
| 30 | 36 | 10 | -3 | 25 | -3 |
| 31 | 17 | 5 | 0 | 19 | 3 |
| 32 | 38 | 10 | 8 | 43 | 5 |
| 33 | 50 | 10 | -3 | 56 | -4 |
| 34 | 21 | -7 | -4 | 19 | 7 |
| 35 | 32 | -6 | 1 | 19 | -3 |
| Total | 571 | 49 | -1 | 539 | 39 |
| Grand Total | 1,695 | 1,697 | 121 | 1,609 | 29 |
DISCUSSION
The experiments compared the PK action on two binary random generators of
different structures. During the experiments the two generators were
automatically interchanged so that neither subject nor experimenter knew
which generator was momentarily in action.
Under these conditions PK effects on both generators were observed, but
there was no significant difference between the two scoring rates.
Whereas the sensory conditions for working with the two generators were
identical, one cannot completely rule out the possibility that either the
experimenter or the subject could have parapsychically known which generator
was momentarily the active one or that the experimenter could have applied
some goal-oriented PK so as to obtain some particular result when he later
compared the two scoring rates. Thus the psychological equivalence of the
two testing conditions would not rule out a parapsychological experimenter
effect. Assuming tentatively that such psi-induced differences between the
two conditions are small, the findings may stimulate a further study of the
following "equivalence hypothesis":
If we have two systems which generate random signals, and if these signals
are, in the absence of PK, statistically equivalent (i.e.,
indistinguishable), PK affects the two systems to the same degree provided
we use sensorially equivalent conditions.
REFERENCES
SCHMIDT, H. A PK test with electronic equipment.
Journal of Parapsychology, 1970, 34, 175-81.
SCHMIDT, H. PK tests with a high-speed random number generator.
Journal of Parapsychology, 1973, 37, 105-18.
Institute for Parapsychology
College Station
Durham, N.C. 27708
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