Predominance of seven and the apparent spontaneity of numerical choices

Abstract

When asked to report the 1st digit that comes to mind, a predominant number (28.4%) of 558 persons on the Yale campus chose 7. Three further experiments sought to establish whether this predominance was due to an automatic activation process or to a deliberate choice. The 1st experiment with 237 undergraduates showed that the response pattern changed markedly (with 17.3% choosing 7) when the request was for a number between 6 and 15. The 2nd experiment showed that if 7 was mentioned by the E as an example of a response, its frequency dropped significantly (to 16.6%). The 3rd experiment showed that if a number in the 20s was requested the choice pattern remained unchanged (27 was chosen by 27.7%), but if a number in the 70s was requested, 77 was chosen only by 15.5%. All these results are consistent with the idea that Ss choose the response such that it will appear to comply with the request for a spontaneous response. (PsycINFO Database Record (c) 2012 APA, all rights reserved)

Full text

Journal
of
Experimental Psychology:
Human
Perception
and
Performance
1976,
Vol.
2, No. 2,
291-294
The
Predominance
of
Seven
and the
Apparent
Spontaneity
of
Numerical
Choices
Michael
Kubovy
and
Joseph
Psotka
Yale
University
When asked
to
report
the first
digit
that comes
to
mind,
a
predominant
number
(28.4%)
of the
respondents choose
7.
Three
further experiments
sought
to
establish whether this predominance
is due to an
automatic
acti-
vation
process
or to a
deliberate choice.
The first
experiment shows that
the
response pattern changes markedly (with 17.3% choosing
7)
when
the re-
quest
is for a
number between
6 and 15. The
second experiment shows
that
if
7 is
mentioned
by the
experimenter
as an
example
of a
response,
its
fre-
quency
drops significantly
(to
16.6%).
The
third experiment shows that
if
a
number
in the 20s is
requested,
the
choice pattern remains unchanged
(27
is
chosen
by
27.7%),
but if a
number
in the 70s is
requested,
77 is
chosen
only
by
15.5%.
All
these results
are
consistent with
the
idea
that
subjects
choose
the
response such that
it
will
appear
to
comply with
the
request
for
a
spontaneous response.
Seven
Yale
University
undergraduates
asked
558
people
to
give
the first
number
between
0 and 9
that
came
to
mind.
Figure
1
shows
the
proportion
of
respondents
choosing
each
digit
from
0 to 9,
together
with
similar
data
from
several
previous
ex-
periments
(Heywood, 1972; Simon,
1971;
Simon
&
Primavera,
1972). Although
these
data
were
collected under
a
variety
of
different
conditions
in a
variety
of
places
(Heywood
obtained
his
data
in
England),
they
all
show
a
striking
prominence
in the
choice
of the
digit
7.
Dietz
(1933)
reported
a
preference
for 7
among
500
people choos-
ing
a
number from
0 to 99 in yet
another
country,
the
Netherlands.
In
fact,
the
phenomenon
is so
reliable
that
it is
reported
as
commonplace
by
Fodor
(1947)
and is
used
as the
basis
for
parlor
tricks
(Gardner,
1973)
and
mindreading
acts.
In
addition,
A
partial report
on
this investigation
was
pre-
sented
at the
45th
annual meeting
of the
Eastern
Psychological
Association,
Philadelphia, April
18,
1974.
Alice
F.
Healy
did
much
to
improve
the
clarity
of
this
paper with
her
comments
on
various
drafts.
Joseph
Psotka
is now at the
Department
of
Psychology,
University
of
Waterloo, Canada
N2L
3G1.
Requests
for
reprints should
be
sent
to
Michael
Kubovy, Department
of
Psychology, Yale Uni-
versity,
New
Haven, Connecticut 06520.
the
number
7 has a
long
history
of
super-
stition
behind
it.1
One
psychologist
(Heywood,
1972) com-
mented
that
"the
existence
of
such
un-
motivated
preferences
remains
a bit of ex-
perimental
debris
that
tidy
psychological
theories
have
yet to
sweep
up" (p.
358).
The
purpose
of the
present
paper
is to
show
that
this
stable
and
pandemic
phe-
nomenon
of
heptaphilia
is far
from being
unmotivated.
The first
experiment
in
this
series
is
designed
to
establish
a
baseline
to
which
we
will
compare
later
results.
EXPERIMENT
1
Method
Seven
students2
from
an
introductory
statistics
section
taught
by one of the
authors
(M.
Kubovy)
stopped
558
passersby
on the
Yale campus
and
said,
"Please
give
me the first
number that comes
to
mind between
0 and
9."
1
Even
so
eminent
a
psychologist
as
George
A.
Miller
has
quite candidly admitted
his
attraction
to 7
(1956,
p.
96).
2
We are
grateful
to the
following
students
for
their diligent
data
collection:
Lon M.
Berkeley,
Debbie
L.
Davis, Cheryl
A.
Lewis,
Peter
E.
Marshall,
Jonathan
T.
Walker, Greg
J.
Wiber,
and
Walter
R.
Winning.
291

292
MICHAEL
KUBOVY
AND
JOSEPH PSOTKA
FIGURE
1.
Frequency
distribution
for
Experiment
1,
with
data
from
similar
experiments.
Results
Since
these
results
were designed
to
establish
a
baseline, they
are
presented
with
the
results
from
previous
experiments
cited
in the
introduction
and are
shown
in
Figure
1.
Thirteen clusters, ranging
in
size
from
14 to
328,
were averaged
: 2
(males
and
females)
from
Simon
(1971),
2
(males
and
females)
from
Simon
and
Primavera
(1972),
1
from
Heywood
(1972),
and 8
from
Kubovy's
seven
students
(one
of
whom
reported
separate
data
for
males
and
females).
In 11 of the 13
clusters,
7 was the
modal choice, with
an
estimated percentage
of
28.36%.
The
standard error
of the
per-
centage
of 7 was
calculated
assuming ran-
dom
unequal cluster sampling (Kish, 1965,
pp.
187-188);
it was
found
to be
1.93%.
The
square-root design
effect
(the factor
by
which
we
would underestimate
the
standard
error
had we
pooled
our
clusters
and
considered them
as one
simple random
sample
of the
same
number
of
elements,
n =
1,770)
was
found
to be
1.915.
In
Experiments
2-4 we
shall assume
a
design
effect
of
3.666
(Vdel
-
1.915).
That
is,
we
shall augment
the
standard errors
of
our
estimated proportions
by a
factor
of
1.915
in
order
to
take into account
the
effects
of
clustering.
EXPERIMENT
2
There
are two
ways
to
conceptualize
the
predominance
of 7 in the
results
of
Experi-
ment
1.
On the one
hand,
7
could
be an
automatic
association activated
by the
request.
If
such were
the
case,
the
fre-
quency
of the
response would
be
resistant
to
subtle suggestion
and
context
effects.
On
the
other
hand, this choice could
be the
outcome
of a
decision process
which
is
under
conscious control.
In
such
a
case,
7
might
predominate because
it
appears
to be
the
most
"appropriate"
response
to the
request
for a
spontaneous choice.
It
follows
that
the
frequency
of the
response would
change
in
contexts
where
7 is not a
spon-
taneous-looking
response.
The
following
experiment
was
designed
to
demonstrate
that
the
frequency
of 7 is
context
sensitive.
We
simply
chose
the set
of
numbers
from
6 to 15 as the set of
responses.
Method
The
experiment
was
conducted
on 237
under-
graduates
in two
Yale
psychology
classes:
30
students
in
introductory
statistics (not
the
section
taught
by
Kubovy)
and 207
students
in
introductory
psychology.3
The
students
were
asked
to
write
down
"the
first
number
that
comes
to
mind
between
6 and
15."
Results
and
Discussion
The
choice
frequency
distribution
is
shown
in
Figure
2. The
pattern
of re-
sults
is
strikingly
different
from
that
of
Experiment
1.
There
are
three notable features
to
these
data.
First,
7 is not
preferred over
8 and 9.
Second,
single
digits
are
overwhelmingly
preferred
over two-digit responses. Third,
numbers which
have
a
special
connotation
(7,
11, 12, 13) are not
chosen more
often
3
Special
thanks
go to H.
L.
Roediger
of
Purdue
University,
to
Jeff
Carlson,
Mary
Weigand,
and
Edward
Thompson
of
Southern
Connecticut
State
College,
to
Anne
Peplau
of the
University
of
California,
Los
Angeles,
and to
Robert
P.
Abelson,
Barry
P.
Cook,
James
E.
Cutting,
Alice
F.
Healy,
and
Robert
Rescorla
at
Yale
University,
for
their
collaboration
in
Experiments
2-4,
and in
studies
preliminary
to
them.

PREDOMINANCE
OF
SEVEN
AND
APPARENT
SPONTANEITY
293
than other responses having
the
same
number
of
digits
(8 and 9, 10 and
14).
Seven
was
chosen
by
17.3%
(standard
error:
1.85%,
assuming random unequal
cluster sampling)
of the
subjects, 11.05%
less
than
the
baseline, which
is a
statistically
significant
difference,
z —
2.74,
p =
.0035
(after
multiplying
the
standard error,
1.85,
by
1.915).
This
context sensitivity
of the
numerical
response does
not
preclude
its
being auto-
matically
activated.
It
does however reduce
the
plausibility
of
such
a
mechanism.
EXPERIMENT
3
If
7 is not
automatically activated
by
the
request, then perhaps
it
predominates
because
it
appears
to be an
"appropriate"
response.
The
present experiment reduces
the
apparent
spontaneity
of 7 by
suggesting
to the
subjects
that
it is on the
experi-
menter's mind
and
could
be a
"typical"
response.
Method
The
experiment
was
conducted
on 319
under-
graduates
in
three Yale psychology classes.
The
students were asked
to
write down "the
first
number
that
comes
to
mind
between
0 and 9,
avoiding
frac-
tions,
and
using
only
whole
numbers like
7."
140
LD
2!
Ul
ED
X
CJ
i—
I_LJ
LJ
CC
£10
30
20
N
=
237
7
8
10 11
N
12
13
m
15
LD
Z
CO
o
LJ
h-
Z
LJ
LJ
or
LiJ
Q_
3Q
20
10
N
= 319
FIGURE
2.
Frequency
distribution
for
Experiment
2.
FIGURE
3.
Frequency
distribution
for
Experiment
3.
Results
The
choice frequency distribution
is
shown
in
Figure
3. As
expected,
the
fre-
quency
of 7 is
dramatically
reduced:
It is
chosen
by
only
16.61%
(standard
error:
2.18%)
of the
students.
Thus
there
is an
11.75% drop
in the
choice
of 7,
which
is a
statistically
significant
difference;
z
—
2.55,
p
=
.0054
(after multiplying
the
standard
error, 2.18,
by
1.915).
EXPERIMENT
4
A
second method
for
reducing
the ap-
parent
spontaneity
of 7 is
employed
in
this
experiment;
it is
designed
to
make
the
choice
of 7
appear obvious
and
easily
explicable. Since spontaneity implies
free-
dom
from
obvious causality,
we
expect
respondents
who
seek
to
appear
to
comply
with
the
request
for the first
response that
comes
to
mind
to
shun
a
trite response.
Method,
Two
groups
of
subjects were studied.
The first,
consisting
of a
class
of 166
undergraduates
in an
introductory
psychology section,
was
asked
to
give
a
number between
20 and 29. The
other, consisting
of
139
students enrolled
in
another section
of the
same
class,
was
asked
to
give
a
number between
70
and 79.

294
MICHAEL
KUBOVY
AND
JOSEPH
PSOTKA
0123456789
FIGURE
4.
Frequency distribution
for
responses
in
the 20s and 70s for
Experiment
4.
Results
The
results
are
shown
in
Figure
4.
Twenty-seven
was
selected
by
27.7%
(standard
error:
6.65%)
of the
respondents
who
were asked
to
choose
in the
20s,
whereas
77 was
selected only
by
15.5%
(standard
error:
6.08%)
of the
respondents
who
were
asked
to
choose
in the
70s.
Thus,
27
was
chosen
.7%
less
often
in'the
20s
than
7 was
chosen among
the
single
digits;
this
difference
is not
significant with
the
design
effect
factor
(2
=
.10)
or
without
it
(z
=
.17).
On the
other
hand,
77 was
chosen 12.86% less
often
in the 70s
than
7
among
the
single digits, which
is a
statistically significant
difference,
2 =
2.01,
p
=
.022.
The
difference
between
the two
groups (12.20%)
is
statistically significant
if
a
standard
comparison
of
proportions
is
performed,
z =
2.60,
p
=
.0047.
GENERAL
DISCUSSION
The
four
experiments support
the
notion
that
the
predominance
of 7 is due to a
choice.
The
data
are
also compatible with
the
idea
that
the
choice
in
tasks
of
this
sort
is
motivated
by the
desire
to
appear
to
comply
with
the
request
of the
experi-
menter, even when there
is no
utilitarian
reason
to do so. The
experimenter's
request
is
essentially
a
request
for a
spontaneous
response,
and the
subject
is
placed
in a
paradoxical
situation—only
if he
does
not
try to
comply
can he
comply.
But
then
his
response might
not
appear
to be in
com-
pliance
because
of its
commonness
or
obviousness.
So, if he
wishes
to
appear
to
comply,
the
subject must
carefully
select
his
response
and
thus
fail
to
comply.
We
believe
that
this
is
what subjects
do.
Why
does
7
appear spontaneous
?
Perhaps
7
is
unique among
the
numbers
from
0 to 9
because
it has no
multiples among
these
numbers,
and yet it is
itself
not a
multiple
of
any of
these numbers.
The
numbers
fall
into
groups:
2, 4, 6, 8
form
one
group;
3, 6, 9
form
another. Only
0,
1,
5, 7
remain.
One
can
rule
out 0 and 1 for
being
endpoints,
and
perhaps
5 for
being
a
traditional mid-
point. This leaves
us
with
7 in the
unique
position
of
being,
as it
were,
the
"oddest"
digit.
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Dietz,
P. A.
Over
onderbewuste
voorkeur.
Neder-
landsche
tijdschrift
voor
psychologie,
1933,
1,
145-162.
Fodor,
N. The
psychology
of
numbers. Journal
of
Clinical
Psychopathology,
1947,
8,
S2S-S56; 628-
654;
841-847.
Gardner,
M.
An
astounding self-test
of
clairvoyance
by Dr.
Matrix.
Scientific
American, 1973, 229,
98-101.
Heywood,
S. The
popular
number
seven
or
number
preference.
Perceptual
and
Motor
Skills, 1972,
34,
357-358.
Kish,
L.
Survey sampling.
New
York:
Wiley, 1965.
Miller,
G. A. The
magical
number seven
plus
or
minus
two: Some limits
on our
capacity
for
processing
information.
Psychological
Review,
1956,
63,
81-97.
Simon,
W. E.
Number
and
color responses
of
some
college
students:
Preliminary evidence
for a
"blue
seven phenomenon."
Perceptual
and
Motor
Skills,
1971,
33,
373-374.
Simon,
W.
E.,
&
Primavera,
L. H.
Investigation
of
the
"blue seven phenomenon"
in
elementary
and
junior
high school
children.
Psychological
Reports,
1972,
31,
128-130.
(Received
August
11,
1975)