A questionnaire in the Daily Telegraph in Britain on March 16 1994 listed
ten statements (e.g. I have a cat, I have a scar on my left knee) and
respondents were asked whether each was true for them. They then
estimated the number likely to be true for others and the distribution
of probabilities for given numbers of statements being true.
"Probability misjudgement" theories of the origin of belief
in the paranormal predict that people should underestimate the number
of statements true for others, and that believers (sheep) should
underestimate more than non-believers (goats).
6238 replies were received. 59% were sheep and 52% were male. There was a
large sex difference, 70% of females were sheep but only 48% of males.
On average 2.4 statements were true for each person. Sheep claimed
that more statements were true for them than non-believers did. This
suggests a possible means by which sheep come to believe in psychic
The mean estimate of number true for others was 3.6. Sheep gave
higher estimates but the difference between the number true for self
and the estimate for others was the same for sheep and non-believers.
Sheep were no worse than non-believers at estimating the distribution
of the number of true statements. The probability misjudgement
theories are not confirmed.
Belief in the paranormal is widespread (Clarke, 1991;Gallup and Newport,
1991). The most common reason given is personal experience (Blackmore,
1984; Palmer, 1979) and strength of paranormal belief is positively
correlated with number of subjective paranormal experiences (Glicksohn,
1990). This correlation might be explained in at least three different
ways. (1) Some people have genuine paranormal experiences (2) People
who believe in the paranormal for other reasons are more likely to
interpret normal events as paranormal (3) People who misjudge the
probability of coincidences are more likely to misinterpret normal
events as paranormal and this encourages their belief.
The third possibility has been proposed by Blackmore and Troscianko (1985)
and by Brugger, Landis and Regard (1990). "Probability
misjudgement" theories predict that believers should show worse
probability judgements and greater underestimates of chance
coincidences than non-believers.
Attempts to test these theories have used computer controlled probability
judgement tasks (Blackmore and Troscianko, 1985), repetition avoidance
in generating random numbers ((Blackmore, Galaud and Walker, 1994;
Brugger et al, 1990, Brugger et al, 1994), ESP tasks (Broughton, 1991)
and variations on the “birthday paradox” (Matthews and Blackmore,
1995). However, the results have been mixed and do not provide strong
support for the "probability misjudgement" theories.
One of the problems is that all these experiments use laboratory tasks
which may bear little relationship to real life situations. The study
reported here investigated the appreciation of coincidences in a way
more relevant to people's personal experiences.
A common type of coincidence occurs in the course of psychic and Tarot
readings, and astrology. The reader tells the client various facts
about him or herself and the client judges that far more were true
than could have been guessed by chance.
The "probability misjudgement" theory suggests that clients
underestimate the chance that something that is true for them is also
true for others (and hence can easily be guessed by the psychic) and
underestimate the chance of several guesses simultaneously being true.
If this is the reason for their belief, believers should underestimate
more than non-believers.
The study reported here had four aims: first, to find out the prevalence
of belief in the paranormal and any sex differences in belief, for a
very large, though not random, sample; second, to find out how
frequently a number of simple statements are true for that sample;
third, to obtain people's estimates of how many statements are likely
to be true for other people; and fourth, to compare believers and
non-believers in their judgments. The hypotheses were that people
would generally underestimate the number of statements that were true
for others, and that believers would underestimate more than
Procedure. The study was chosen to be carried out as part of
British Science and Technology Week in March 1994 by publication in
the Daily Telegraph newspaper. There are two editions of this paper,
North and South, and a slightly different questionnaire was printed in
each on March 16 1994.
The Questionnaire. The questionnaire consisted of a list of ten
statements of the kind that might be produced by psychics, such as
"There is someone called Jack in my family", or that might
be important in psychic experiences, such as "Last night I
dreamed of someone I haven't seen for many years" (see appendix).
Respondents had to say whether each statement was true or false for
Next they were asked "Suppose you stopped the first person you met in
the street and asked him or her about the same ten statements. How
many times would you expect him or her to say True?". Then they
were asked to imagine the same person in the street and estimate how
likely it was that a given number of statements would be true for that
person, using a five-point scale from extremely likely to extremely
unlikely. To cover as much of the range as possible without making the
task too onerous, those in the North were asked to estimate for none,
three and seven statements and those in the South for one, five and
nine statements. The resulting distribution could then be compared
with a theoretical distribution.
Finally respondents were asked their age and sex and whether or not they
believed in extrasensory perception (e.g. telepathy or clairvoyance).
A total of 6238 usable replies was received. Overall 51.7% of the sample
was male, and 59% of respondents were believers in the existence of
ESP. There were more people in the older age groups, as follows: under
25, 4%; 25-34, 6.5%; 35-44, 12%; 45-54, 22%; 55-64,24%; 65 and over,
The percentage of people for whom each statement was true was as follows
for statements 1 to 10:- 21.3, 33.5, 9.7, 24.1, 16.4, 26.9, 26.4,
28.3, 28.7, 27.1, respectively. To give examples, almost 30% claimed
that their back was giving them trouble, that they are one of three
children, that they own a tape or CD of Handel's Water Music, or that
they have a cat. 34% said they had a scar on the left knee. The mean
number of statements claimed to be true was 2.42 and the mean
estimated number true for other people was 3.57, which is
significantly higher (t=60.47, 6237 df, p<.0001). In other words
people have overestimated the number that would be true for others.
Respondents were divided into believers and non-believers on the basis of
their answer to the ESP question. The number of true statements was
higher for believers (2.56) than non-believers (2.23). These
differences are shown in Figure 1. They are significant for questions
2 (chi2 = 74.0), 3 (chi2 = 22.7), 4 (chi2 = 8.7), 6 (chi2 =33.5) and 9
(chi2 = 33.1) (all 1df).
The estimates of the number true for others were also higher for believers
(3.73) than non-believers (3.35) but the amount of over-estimation did
not differ between believers and non-believers. In other words, there
are significant differences between believers and non-believers in the
number of statements claimed to be true for self and in the number
estimated to be true for others but not in the difference between
Probability estimates for the South and North versions of the
questionnaire were combined to give the results shown in Table 1.
Results were compared for believers and non-believers but they do not
3.9 1.6 2.6
3.6 4.4 4.8
4.0 1.5 2.6
3.3 4.2 4.7
Three Five Seven Nine
Number of statements true
Table 1. Estimated likelihood of a given number of statements being
true for a random person.
There was a large sex difference in belief. Among females 70% were
believers but among males only 48% were (chi2 = 296, 1 df,
p<.000001). The percentage of believers does not change much with
age, although it is lowest in the youngest group (chi2 = 15.3, 5 df,
p<.01). The percentage of believers in males and females also does
not change much with age. This is shown in Figure 2. A series of chi
squared analyses (from youngest to oldest with 1df) shows that the sex
differences are highly significant in all age groups except the
youngest (chi2=2.3, ns; chi2=33.2, p=<.0001; chi2=33.5,
p=<.0001; chi2=52.2, p=<.0001; chi2=75.8, p=<.0001;
The probability misjudgement theories are not supported by these data.
They predicted that people would underestimate the number of
statements that were true for others, and that believers would
underestimate more than non-believers. This was not found. Indeed
people’s probability estimates were generally good and did not
differ between believers and non-believers. This null finding in so
large a sample suggests that misjudgements of probability are not
likely to be an important factor in the determination of paranormal
The figures for the number of individual statements true are surprisingly
high. You might easily be impressed if a medium or psychic correctly
told you the name of a specific piece of music you owned. However,
nearly 30% owned the music chosen here. 27% of respondents had been to
France in the past year (another common psychics' gambit) and 21% had
a Jack in their family. Clients are often impressed by accurate names
given, even when these are fairly common names. This figure suggests
that a correct name might quite easily be obtained with relatively
Also of interest is that 10% had dreamed the previous night of someone
they had not seen for many years. Statisticians have sometimes tried
to work out the odds of a coincidence between a dream and a real event
and have had to make many assumptions or "guesstimates" to
do so (Blackmore, 1990). This figure provides a fair estimate for one
side of the equation.
The major, and unexpected, finding was that believers reported far more of
the statements true than non-believers. Conceivably this could be due
to actual differences in lifestyle or family between believers and
non-believers. For example believers may be more likely to have cats
or even to injure themselves. Several of the questions were made
deliberately vague to make them more closely comparable to the kinds
of statements made by psychics. A possible explanation for the large
difference is that believers used more inclusive categories when
answering the questions. However, the vaguest questions were not
obviously the ones with the largest difference. For example, the
largest difference between believers and non-believers was in the
statement “I have a scar on my left knee”. Although there is
clearly some leeway possible in what counts as a scar, this does not
appear to be as flexible as a statement like “There is someone
called Jack in my family” for which there was no difference. Clearly
further research would be needed to establish the origin of these
large differences between believers and non-believers.
The study is unique in providing such a large sample for looking at belief
in ESP and sex differences in belief. Previous studies have varied
widely in any sex differences found. Generally females show more
belief than males but there has been much argument over whether this
difference is genuine or still exists. Irwin (1985) has reviewed
studies of sex differences and argued that sex should not be
considered a primary correlate of belief in the paranormal. However,
in this large sample we have found the usual sex difference with
females being far more likely to be believers. It might be suggested
that the sex difference is predominantly in older people and is
disappearing as time goes by. Figure 5 suggests that this is not true,
except for the possible exception of the youngest group. Possibly sex
differences are finally diminishing in the under 25s. Since Irwin used
students aged about 20 this may explain why he found no sex
differences. In future it would be interesting to look further at
these changes with age.
Belief in the paranormal itself may also be diminishing but not to any
great extent. For example twenty years ago Evans surveyed readers of
New Scientist and found that 67% thought that ESP was likely or
certain to exist, compared with the 59% found here.
As far as these figures are concerned it must be born in mind that the
sample was not random. It consisted of a self-selected sample of
Telegraph readers. The Daily Telegraph is a serious newspaper with a
conservative outlook and its readers tend to be intelligent and aged
around 40 years or over. These figures cannot be generalised to the
whole population but they nevertheless give a useful indication.
More important, and less prone to this potential bias, are the differences
between believers and non-believers. Most interesting is that the
number of statements claimed to be true is much higher for believers
than non-believers. Conceivably this could be due to actual
differences in lifestyle or family between believers and
non-believers. Alternatively it could be that believers interpret the
questions more broadly and are more likely, for example, to include
distant relatives as family. The ANOVAs show that there is a main
effect of belief so this difference cannot be attributed to sex
differences. This would mean that, in visiting a psychic or
interpreting a Tarot or astrology reading, believers would be more
likely to find statements that they judged to be true of themselves.
In this way their belief in these psychic practices would be
increased. Not surprisingly there is the same sheep-goat difference
for the number of statements true for others. It is important to note
that these are the only significant differences between believers and
Comparing how many statements were actually true for each person and how
many statements respondents thought would be true for others, it was
expected that the former would be higher than the latter but this was
not so. In fact people thought that more of the statements would be
true for other people than were true for themselves. Possibly this
could involve a "false consensus effect", that is, people
tend to assume that others are more similar to themselves than they in
fact are (Marks & Miller, 1987). Another possibility is that they
guessed the purpose of the survey and therefore tried to push the
results in their prefered direction. This, however, would suggest that
believers would give a higher number for others than themselves and
non-believers lower. This was not found.
The probability misjudgement hypothesis suggests that believers should
generally be worse at estimating probabilities than non-believers. We
might therefore expect a greater difference for believers than
non-believers between the number of statements true for self and the
estimate for others. However, this was not found and the difference
scores are remarkably similar for believers and non-believers. This is
evidence against the idea that misjudgements of probability underlie
The estimates people gave of the likelihood of any given number of
statements being true for the person they met in the street were
generally quite accurate given the true mean number correct is 2.4.
The distributions of actual number correct and estimated likelihood
cannot directly be compared, but the shapes of the distributions are
What then can we conclude about the "probability misjudgement"
This is by far the largest study ever conducted on this topic. Although
the sample is not random it contains a wide distribution of ages and
roughly equal sex distribution. The task was piloted on students until
a version was found that was easy and quick to complete. There is no
evidence that people failed to understand the questions and the very
good estimates of probability they gave suggest that the task was able
to tap probability judgements rather accurately. Given all this I
suggest that the lack of the expected sheep-goat effect is very
telling. It appears that the biggest difference between believers and
non-believers is not in their probability estimates but in their
tendency to claim that statements are true of themselves and of
The results of this large scale survey do not provide evidence to support
the probability misjudgement hypothesis. They do, however, suggest
that believers are more likely than non-believers to claim that a
statement is true of themselves. As found in previous research, belief
in the paranormal is widespread and far higher among females than
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Acknowledgements: I wish to thank Paul Northcott for his help with the
The ten statements.
is someone called Jack in my family
2. I have
a scar on my left knee
night I dreamed of someone I haven't seen for many years
travel regularly in a white car
5. I once
broke my arm
6. My back
is giving me pain at the moment
7. I am
one of three children
8. I own a
CD or tape of Handel's Water Music
9. I have
10. I have been to
France in the past year
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