Susan Blackmore and Tom Troscianko
Journal of Psychology (1985), 76, 459-468 Printed
in Great Britain
© 1985 The British Psychological Society
Possible reasons for belief in the
paranormal are discussed and two hypotheses suggested. The first -
that some belief in psi arises from misjudgements of probability -
predicts more errors in probability tasks among believers (sheep) than
disbelievers (goats). In two experiments subjects completed various
computer-controlled probability tasks. In the first sheep performed
worse than goats on most tasks and were significantly worse at
responding appropriately to changes in sample size. In Expt 2 sheep
were significantly worse at questions involving sampling.
The second hypothesis is that some belief in psi arises from an
illusion of control. Previous studies have shown a greater illusion of control among sheep in
psi tasks (even when no psi occurs). We predicted the same effect in
tasks not overtly involving psi. This was confirmed in Expt 3, using a
computer-controlled coin-tossing task. Half the trials allowed for
subject control of the coin and half did not. Sheep felt that they
were exercising greater control than goats (irrespective of actual
control) but estimated they had scored fewer hits. This could be
explained if sheep misjudged chance scoring level. This was tested and
sheep were found to underestimate chance scores. This 'chance baseline
shift' could underlie the illusion of control and the belief in psi.
No evidence of psi was found.
Why do people believe in the
paranormal? Surveys show that such belief is widespread and even
increasing (Truzzi, 1971). For example, Jones et al. (1977)
found that 58 per cent of a sample of students believed in half or
more of a list of paranormal phenomena and 27 per cent claimed to have
experienced a paranormal phenomenon. Indeed the most common reason
given for belief in the paranormal is one's own experience. In a
random postal survey Blackmore (1984) found that 25 per cent of
respondents claimed to have experienced telepathy, 36 per cent
professed belief in ESP (extrasensory perception) and of these 44 per
cent cited their own experience as the main reason. It appears that
the majority of believers are convinced that they have actually
experienced the paranormal. A further question therefore raised is why
people believe they have had paranormal experiences.
two main possibilities. One is that they have. The alternative is that
their belief is based on misinterpretation of normal
events as paranormal. Whether or not paranormal phenomena occur it is
useful to understand the processes which might give rise to belief in
psi even in its absence. The research reported here explores some of
commonly reported 'psychic' experiences include various forms of ESP (extrasensory perception) such as telepathy and
precognitive or prophetic dreams (Zusne & Jones, 1982). These have
in common that they depend on judgements of probability. For example,
I might dream that I am standing outside my house and a green and red
spotted car crashes into the fence. If the very next day I actually
see this happen, I may judge that this is so improbable that some
explanation other than 'just chance' is required. I may conclude that
the dream was paranormal. This involves the judgement that an
essentially unmeasurable probability is extremely low - too low to be
judgements are notoriously inaccurate. Kahneman & Tversky (1973)
have shown that a variety of heuristics, such as 'representativeness'
are used to judge probabilities and may give rise to serious errors.
People also show great confidence in their erroneous judgements, even
in the face of contrary evidence (Einhorn & Hogarth, 1978). Errors
in judgement of probability could give rise to belief in psi if, for
example, people underestimated the probability of a 'coincidence'. If
this is a factor in such belief we should expect believers in the
paranormal to make greater underestimations than non-believers. More
generally we could hypothesize that the judgements of believers should
be worse than those of disbelievers. Schmeidler (Schmeidler &
McConnell, 1958) coined the terms sheep and goats respectively for
believers and disbelievers in psi and we shall use these terms
throughout. Expts 1 and 2 compared probability judgements for sheep
and goats in a wide variety of tasks.
possible mechanism is selective forgetting, or errors in recall of
probabilities. In the example given above I might
forget all the dreams which did not come true and only remember those
which did. Or I might misremember my original predictions. Fischhoff
& Beyth (1975) asked subjects to estimate the likelihood of
certain events and then, unexpectedly, to recall their own predictions
and the actual outcomes. In retrospect subjects seldom perceived
having been surprised by the actual outcome. If this kind of process
contributes to belief in psi then we should expect sheep to be worse
at recalling their own predictions accurately. More generally we might
expect them to misremember events in a way which confirmed their
belief in psi. Experiment 3 incorporated measures of recall to test
powerful mechanism involves the 'illusion of control' (Langer, 1975).
This is especially relevant to PK (psychokinesis - the ability
to influence objects or events without the use of muscular action).
Under certain conditions people may feel that they are in control of
essentially chance events. If no normal mechanism is obvious the
illusory control may be attributed to psi. If this is the reason for
some belief in psi then sheep should show a greater illusion of
control than goats.
some previous research which bears on this. Langer (1975) found that
the illusion of control was greatest when subjects thought
that the task demanded some degree of skill. Langer & Roth (1975)
pinpointed the conditions which enhance this effect (such as early
success) and showed that there was a tendency for subjects to remember
a higher number of successes than there had in fact been. In an ESP
task Ayeroff & Abelson (1976) found that perceived success was
enhanced by subjects' involvement in the choice of test material and
by being given a warm-up session: factors which would be expected to
increase an illusion of control. Of course it is reasonable for a
believer to expect such factors to enhance ESP success. However, in
that study only subjective confidence in success was enhanced; actual
ESP scores were at chance levels. Ayeroff & Abelson concluded that
people behave in a chance situation as though it were a skill
situation, to the extent that skill-related cues are present. However,
it is important to note that for the believer in psi, an ESP task is a
skill situation. Therefore, it is perfectly natural for him to display
a greater illusion of control (and if psi exists possibly actual
relationship between belief in psi and illusion of control was tested
more directly by Jones et al. (1977) who found
that subjects who scored higher on a paranormal belief scale gave
higher estimates of their performance on a PK-type task than subjects
who scored lower on the belief scale. Also Benassi et al.
(1979) asked subjects to estimate their success during experiments on
PK. Even though scoring was at chance levels, believers (either
determined by instructional set or by rated belief) thought that they
were exerting greater control than disbelievers.
allow the conclusion that in a PK task sheep showed a greater illusion
of control than goats, even though no control (or PK) was
exerted. However, they do not demonstrate that sheep show, in
general, a greater disposition to an illusion of control. In tasks
which are overtly based on ESP or PK it is natural that sheep will
have higher expectations for their performance; they have a proposed
mechanism for success and presumably believe that the task is
essentially a skilled one (using the skill of psi). Goats perceive the
task as a chance task. As we have already seen (Langer, 1975), a
greater illusion of control appears when subjects think the task
More important to our hypothesis here
is whether the same relationship between belief and illusion of control will appear when
the task is not overtly one involving psi (and no psi occurs).
That is, the sheep and goats start with the same approach to the task.
This is tested in Expt 3.
Finally, there is a long tradition in
parapsychology of a relationship between belief in psi and performance on psi tasks - with
sheep performing better than goats. Pioneering workby Schmeidler (Schmeidler
& McConnell 1958), was followed by many replications and
extensions of the original findings (see Palmer, 1971, for a review).
More recently Layton & Turnbull (1975) manipulated both belief in
psi and evaluation and found that those exposed to a positive
evaluation scored higher on the ESP task. However, a replication did
not repeat this finding.
In Expt 3 reported here we were able to test for a difference
in ESP performance between
sheep and goats. We predicted that sheep would perceive their
performance as higher than goats, but that actual performance would
Experiment 1. Probability tests
were 50 schoolgirls aged between 14 and 18 years, from Colston Girls'
Procedure. A room was set aside in the school and the subjects came one at a time
to participate in the tests. One or other of the authors introduced
the subject to the experiment and offered any help if needed. However,
all the tests were run on an Apple II computer and were basically
self-explanatory. Each session took between 10 and 15 minutes.
There were four separate types of
task. First, subjects were told 'A hat contains a large number of pieces of paper with the digits 1, 2,
3, 4 and 5 on them in equal proportion. Please write a list of 20
numbers in the order that you think they might be drawn from this
hat'. In other words they were asked to generate a string of 20 random
numbers. The number of doubles (i.e. the same digit produced twice
consecutively) produced was counted where approximately four pairs are
expected by chance. People are generally poor at generating random
strings and generate fewer doubles than expected. We predicted that
sheep would perform worse than goats, that is they would produce
Second, subjects were presented with
12 examples of random mixtures of boys and girls invited to a party. In each case they were asked
to assess whether the choice of boys and girls was biased or unbiased,
using the semantic differential from 1 - certainly unbiased, to 5 -
certainly biased. Mean score was recorded. Sheep were expected to give
Third, subjects were presented with
eight examples of coin tossing and asked, as above, whether the coin was biased or not. For
example, 'I toss a coin 20 times and get "heads" 15 times.
Is my coin biased?'. Proportions of 'heads' were either 50 per cent or
75 per cent and the number of tosses was either 4, 12, 20 or 60. It
was predicted that goats would be more sensitive to the effect of
varying sample size.
Fourth, subjects were asked four
questions about sampling, including sampling with and without replacement. The questions and
possible answers are listed in Appendix I. It was predicted that goats
would more often give the correct answers.
Finally there were additional
questions concerning experience of precognitive dreams, communication using telepathy, belief
in ESP (Do you think that extrasensory perception is possible?), and
belief in their own 'psychic ability'. In each case a semantic
differential was used from 1 - extremely unlikely to 5 - certain. Age was also asked. Subjects were
thanked for their help and shown a printout of their scores if they wished.
Subjects' scores for the final four
questions were added together to give a total 'belief score'. Subjects
were then divided about the mean to give 19 sheep and 31 goats. The
results for each test are shown in Table 1.
prediction about random number production was not confirmed. As
produced fewer doubles than chance expectation (MCE = 4) and goats
produced more doubles (mean 2.3) than did sheep (1.6), but the
difference was not significant.
In the second
task subjects were given a score reflecting how well they
distinguished the random strings from the patterned ones. Again, as
predicted, goats achieved higher scores (mean 12.8) than sheep (mean
3.2) but the difference was not significant.
coin-tossing tests there were two types of example; for those with
equal numbers of heads and tails points were given if the rating decreased
with increasing number of tosses; for those with 75 per cent heads
points were given for increasing rating with sample size. The
total score was a percentage of the theoretical maximum (see Appendix
II). The subjects seemed quite unable to do this task correctly and
their responses to changing sample size were often in the wrong
direction, producing scores below zero. The mean score for all
subjects was less than zero. As predicted, the sheep (mean -22.4)
scored lower than the goats (mean –12.1). The difference is
significant (t = 2-0, P < 0.05). Only four out of the
19 sheep obtained scores above 0.
for the four sampling questions were added and compared for sheep (mean
4.6) and goats (mean 4.5) but no significant differences were found.
In summary, sheep were worse at responding appropriately to
increasing sample size. The
other differences were not significant but most were in the expected
direction. That is, goats seemed to be better than sheep at tasks
involving judgements about probabilities. It therefore seemed
worthwhile to carry out similar tests with a larger number of
Subjects. Subjects were 100 volunteer
students recruited through a poster in the Medical School of Bristol
University. The poster asked them to take part in a 10-minute computer
game. No further information was given.
The tasks were similar to those in Expt 1 with the following
differences. instead of using boys and girls at a party the students
were given series of 12 digits (0-5 inclusive) and asked whether the
numbers were randomly selected.
In the final
section the questions about psi were embedded among others asking for
an estimate of the likelihood (using the same five-point scale) of
certain unpredictable events such as an earthquake in Bristol or rain
next week. This was to avoid the possibility that subjects perceived a
connection between the belief questions and the probability tasks and
altered their answers accordingly.
On the basis of their answers to
the questions about psi the subjects were given total belief
scores and divided about the mean to give 48 sheep and 52
goats. The results are shown in Table 2.
There were no significant
differences between the two groups in the number of doubles generated in the random string, the score in the randomness - judging
task or in the coin-tossing task. Overall for the sampling
questions goats scored significantly higher than sheep, as
expected (; = 2-58, d.f. = 98, P < 0-05,
two-tailed). When the individual questions are taken
separately the goats always scored better than or equal to the
sheep. The difference on the 'birthday' question was
independently significant. As predicted, more
goats than sheep got this right (chi square = 5.0,
d.f. = 1, P < 0.05).
It is interesting to note that the
students did not generally do any better than the schoolgirls,
in spite of the fact that they were all older and were mostly
university students. It appears that several more years of education and selection for
university do not seem to improve ability at these types of
Subjects took part in a computer game in which they
tried to make a coin 'fall' as either 'heads' or 'tails', with
control exerted via a push-button. Half of the trials made
actual control possible and half did not. The latter could be
used to look for PK effects. Dependent measures were
the subject's perceived degree of control, the remembered
number of 'hits', an estimate of the subject's belief in psi,
and his or her age and sex. A further question was added
during the experiment (see below).
The main prediction was that sheep
would feel they had exerted greater control than goats,
whether or not they had done so. Other predictions were that
goats would be better able to distinguish between control and
chance conditions, and that sheep would remember a higher
'hit' score than goats. All predictions were made in advance
(Troscianko & Blackmore, 1983) and one-tailed tests were
used when the direction was predicted.
After observing the behaviour of
the first 47 subjects we also predicted that sheep are more likely than goats to misjudge the number of hits to be expected by
chance. A further question to test this was added for
One hundred volunteer subjects were recruited by advertising
in Bristol University's Medical School. Most were students and
staff. As an incentive a bottle of whisky (or similar) was
offered to the highest scorer. There were 67 males and 33
The task was a computer-simulated coin-tossing task. Each
session consisted of two short practice runs followed by four
experimental runs, each consisting of 20 trials. In each
trial, subjects were first given a target to aim for: 'heads'
or 'tails'. They then started the coin-tossing sequence by
pressing a push-button and the alternating faces were shown on
the screen. The subjects' task was to let go of the button at
the correct time so that the target face would be the last
There were (unknown to the
subjects) two types of trial. Two runs consisted entirely of
'control' trials in which real control was possible. The other two were 'chance'
trials in which no control was possible, as explained below.
The timing of stimuli was chosen,
after pilot trials, to make the task difficult but not
impossible. Heads and tails were shown for 200 ms each, with an inter-stimulus
interval of 40 ms. When the button was pressed the alternating
sequence started. When it was let go it stopped but with a
delay of n further faces, dependent on the type of
trial. In 'control' trials n was either 2 or 4 so that
the sequence always ended on the same face as the one showing
when the subject let go of the button. In 'chance' trials n
could be 1, 2, 3 or 4 (with equal probability). This prevented
any control being exerted by means of the push-button.
It has been suggested that PK can
only be exerted on truly random (i.e. indeterminate) events (e.g. Millar, 1978) and it can be argued that pseudo-random sequences
might be predictable by 'normal' means. The value ofn
(which would be affected by any putative PK) was therefore
determined from the state of an internal true random number
generator based on thermal noise. All other randomization
(such as order of runs, targets and first face shown) used the
computer's pseudo-random number generating function RND.
At the end of each run (of 20
trials) subjects were asked to indicate how much control they thought they had exerted over the outcomes of the coin tosses in that
run. A seven-point scale was used (from no control to total
control). At the end of the session (four runs) subjects were
asked to estimate (i.e. recall) how many hits they had scored
in each run. This question was not asked after each run
because once subjects knew they were to be asked they would
simply count the hits on subsequent runs. Next the following
questions were asked, again with a seven-point scale:
you believe in the existence of ESP (extrasensory perception)?
Do you believe in the existence of PK (psychokinesis,
i.e. the action of mind over matter)?
Do you believe that ESP/PK can be demonstrated in the
Subjects were then asked their age and sex. The last
53 subjects (i.e. 48-100 inclusive) were also asked
the following question:
Please estimate how many (out of 20)' hits' you would
score if you did the test with your eyes shut.
All subjects were given a printout of their scores
and asked not to communicate details of the experiment
to others until the end of the series. All data were stored on
disk for later analysis.
The mean sum of ratings for the three questions about belief in psi
was 12-67. This allowed division of the sample into 50 sheep
and 50 goats.
There were 67 male and 33 female
subjects. Of the females 16 were sheep and 17 goats; of
the males 34 were sheep and 33 goats. Since there was no
significant sex difference in beliefs all the data are
presented collapsed across sex.
The average age of sheep was 25.1
years and of goats 27.7. Average female age was 28.6 and
male 25.3. None of these differences is significant.
Our main prediction was that sheep
would feel that they had exerted more control than goats,
in both the control and the chance conditions. Table 3 shows
the results obtained. These results confirm the main
hypothesis, that sheep give a higher estimate of control than
goats, in both types of run.
The information in Table 3 allows
the following other conclusions to be drawn:
(1) There is no evidence of PK in the chance runs;
the results are not significantly different from mean chance
expectation. (2) There is no evidence that sheep scored
differently from goats in the chance (or 'PK') runs; in fact
the goats obtained a slightly higher score. We have therefore
failed to replicate the 'sheep/goat effect'. (3) In the
control runs, both groups of subjects scored more hits than in
the chance runs (t = 8.11, P < 10-9) and estimated
that they were exerting more control (t = 5.37, P<
10-6). The chance and control conditions were
therefore clearly discriminable.
Our subsidiary predictions were (a) that goats would
be better able to distinguish between
chance and control trials, and (b) that sheep
would remember a higher number of 'hits'.
The first of these predictions was tested by taking
the ratio of ratings in the control conditions to the ratings in the chance condition. The
higher the ratio, the better the differentiation. The
prediction was not confirmed. Sheep obtained a score
of 1.24 and goats 1.25. The second subsidiary
prediction was not confirmed either. The results are
shown in Table 4.
the chance condition the results are in the opposite
direction to the one predicted and the difference
cannot therefore be significant on the planned
one-tailed test. In the control condition there is no
significant difference either.
Our final hypothesis was that sheep are more likely
to misjudge the number of hits to be expected
by chance (i.e. by performing a visual task without
visual information). This was tested, and confirmed,
for the final 53 subjects. As predicted the goats gave
more accurate estimates than the sheep. Where 10 is
the expected answer goats gave a mean estimate of 9.6
and sheep 7.9 (; = 2.1, d.f. = 98, P = 0.02).
Overall most subjects (33 out of 53) gave the answer
'10', but most of these were goats. Of 31 goats 23
said ' 10' but of 22 sheep only 10 did (chi squared =
4.53, d.f. = 1, P = 0.03). It seems clear that
sheep more strongly underestimate the number of hits
expected by chance. These results are shown in Table
hypothesis was confirmed: sheep felt that they were
exercising greater control over the outcomes of the
tests than did goats, even though there was no
difference in performance between the two groups. This
suggests that sheep are more prone to an illusion of
control in both psi and other tasks. Another
interpretation of this is to say that goats are more
cautious in their assessment of the control exercised.
Now consider the estimates of the
number of 'hits', as made at the end of each session. Our prediction, that sheep would remember more hits than goats, was
based on previous findings (Langer & Roth, 1975)
that an illusion of control is associated with a
higher remembered success rate. We found no such
effect: quite the reverse. This appears
counter-intuitive and therefore interesting. It
prompted us to ask why sheep - who consider themselves
to be exerting greater control than goats - say that
they have scored fewer hits? We shall propose an
answer which has other interesting implications.
In estimating how many hits they
had scored in each of the four runs the subjects had
to try to remember how well they had done throughout the experiment. At no
stage were they told how many hits they had obtained
in any run. They could of course count them as they
went along, but they did not expect to be asked this
question. The task was therefore difficult. When faced
with such a difficult task it is reasonable to suppose
that subjects might try to estimate how many hits they
would be expected to get by chance, and then add an
increment depending on how much they thought they
might have 'improved on chance'. The estimated value
would therefore depend crucially on the estimate of
chance scoring level. If this estimate were
systematically wrong for sheep it might explain our
paradoxical finding. It was this which prompted us to
add the final question – asking subjects how well
they thought they would do if they tried the
experiment with their eyes shut.
As we have seen sheep severely
underestimated the chance level of 10 while goats were
fairly accurate. Therefore the sheep might feel that a score of 9 out
of 10 represented a score better than chance; whereas
a goat would (correctly) classify it as below chance.
This not only explains the
discrepant finding but also provides a possible
mechanism by which both the illusion of control and belief in psi could be
continuously reinforced. If a person consistently
underestimates the size of any pure chance effect,
then when chance outcomes occur he will seek an
additional explanation. This may be in terms of his
own control and so produce an illusion of control, or
may be interpreted as psi, so confirming his belief in
the paranormal. In this way errors in judgements of
probability might underlie both the illusion of
control and belief in psi. We have termed this
effect the 'chance baseline shift'.
We should emphasize that this
explanation is tentative and in need of further investigation.
It could, for example, be argued that our question
could have been misunderstood by the subjects. It
would also be helpful to repeat the experiment with
non-university subjects. However, our finding is
potentially interesting in that it suggests a possible
mechanism by which belief in psi could receive
constant reinforcement in the absence of any actual psi. In future experiments we
will investigate the putative chance baseline shift
more fully to establish under what conditions it is
likely to occur.
The three experiments reported here have
demonstrated some interesting differences in behaviour
between those who do and do not believe in psi. In the
first two experiments most of the differences, and all
the significant ones, were in the direction of the
goats performing better than sheep at tasks requiring
judgements of probability. This is in line with our
hypothesis that some belief in psi arises from
misjudgements of probability.
In the final experiment we found that sheep showed a
greater illusion of control than goats
even though the task was not overtly a psi task and no
psi occurred. This confirms our prediction from the
hypothesis that belief in psi may be fostered by an
illusion of control.
When asked to estimate how well they would perform at
this visual task if no visual information
were available the goats gave more accurate estimates
than the sheep – the sheep seriously underestimating
chance expectation. We suggest that this
'chance baseline shift' may strengthen belief in psi
even when no psi occurs.
We would like to thank Francois
Dupre for his assistance with programming and runningS. Blackmore was funded by the Perrott-Warrick
Studentship in Psychical Research.
Expt 3. He was on a visit funded by
Ecole Superieure d'lngenieurs en Electrotechnique et
Electronique, 89 Rue Falguiere,
75015 Paris, France.
T. Troscianko was funded by a grant from the Nuffield Foundation.
We would also like to thank the Headmistress and
pupils of Colston Girls' School, Bristol.
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Received 21 January 1985
Requests for reprints should be sent to
Susan Blackmore, Brain and Perception Laboratory,
Department of Anatomy, The Medical School,
University Walk, Bristol BS8 1TD, UK. Tom Troscianko is also at the above address.
Full text of questions, section 4, Expts 1 and 2
(a) 'A hat contains 10 red and 10 blue smarties. I
pull out 10 and 8 of them are red. Am I more likely to
get red or blue next time?' Possible answers given
were 'red', 'blue' or 'either equally likely'.
(b) 'A box contains buttons that are
either green or yellow, in unknown proportion. Out of
10 buttons taken out 8 were yellow. Which is more
likely to be pulled out next?' Possible answers were
'green', 'yellow' and 'either equally likely'.
(c) ' A coin is tossed to decide which football team
kicks off first. In the last four matches between
Mytholmroyd Athletic and Giggleswick United,
Mytholmroyd have kicked off first every time. Which is
more likely to kick off first at their next
encounter?' Possible answers were 'Mytholmroyd', 'Giggleswick'
and 'either equally likely'.
(d) ' How many people would you need
to have at a party to have 50:50 chance that two of
them will have the same birthday (not counting year)?
Possible answers were 22, 43 and 98.
It was predicted that goats would be more
likely to answer (a) blue, (b) yellow, (c)
either and (d)
Method of scoring 'coin-tossing' question
Assume that the sample size presented is n.
Then, for the case in which the proportion of 'heads'
is 75 per cent, a correct response would increase the
bias rating with increasing n. Thus, we
incremented the score by 1 if the subject actually
responded in this way, by zero if the subject gave the
same rating, and by - 1 if the subject decreased
the bias rating as n increased. Thus, the score
represents by how much a subject changes his or her
rating, irrespective of its absolute value. Similarly,
for the cases when the proportion of 'heads' was 50
per cent the score was incremented by 1 if the
subject's rating decreased as n increased, by
zero if it remained constant, and by — 1 if it
The overall effect of this scoring method was to
ensure that a high positive score would only be
obtained if the subject responded both to increasing n
and to the proportion of 'heads'. The score was
normalized so that the possible range was -100 to +
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