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machine
has four sfaole
internal
states,
A
.
0-mFIz square-wave
oscillator sends pulses
to an electronic "scale-of -four' counter which
passes
through each of
its four states 250,000
tihies
per second.
The
state
of
the counter
is determined by the length
of
time
the oscillator
has
run,
that
is,
the
time between subject choices.)
As soon as
the
subject
indicates his
choice,
the
target slide
is illuminated
to provide
visual and auditory
(bell
if correct)
feedback as
to
the correctness
/
or incorrectness
of his choice.
Until that
time,
both subject
and
experimenter remain ignorant of
the machine’s choice,
so
the experiment
is
of
the double-blind
type.
Five
legends
at
the
top
of the machine
face
are
illuminated one
at
a time with increasing correct choices
(6,
8,
10,
...)
to provide additional reinforcement.
The machine choice,
subject
choice,
cumulative
trial number,
and cumulative hit number are
recorded automatically on
a printer.
Following trial number
25,
the
machine must be reset manually by depressing
a RESET button.
A methodological feature
of
the machine
is
that
the
choice
of
a
target
is not
forced.
That
is,
a subject may press
a PASS button when
he wishes
not
to guess,
in which case
the machine indicates what
its
choice was.
-The machine
thus
scores neither
a hit
nor
a
trial
and
then
goes
on
to make
its next
selection.
Thus, the subject
does not have
to
guess
at
targets when he does
not
feel
that
he has
an
idea
as
to which
to choose.
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Approved For Release 2000/08/07
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Undci-
the null hypothesis
of random binomial
choices with probability
1/4
and no learning,
the probability of observing ^k successes
in n trials
is approximated by
the probability
of
a normal distribution value,
*
(
k
- 1 - i)/73"715
Pre-Experime nt Randomness Tests
The design objective was
to build
a four-state machine, with each
state equally
likely
to occur on each
trial,
independent
of
the
past
sequence
of
states.
If
the machine meets
this objective,
it should not
be possible
to devise
a rule for future play that significantly differs
from chance.
A simple example
of
such
a rule would be
to select
the
machine
state observed
in the preceding trial;
if
this
strategy were
to produce scores significantly above
chance
(25 percent hits), we
would reject
the hypothesis
of randomness
of
the machine under
test.
Before experimentation machines purchased from Aquarius Electronics,
Albion,
California,
were extensively
tested for randomness.
Data were
analyzed on
a CDC-6400 computer,
and the machine finally selected for
•
use met established criteria for randomness.
In developing randomness
tests,
we
are guided in part by
a knowledge
of
the machine
logic.
V/hen one
of
the four choice keys or
the pass key
is depressed,
the current machine state
is displayed;
then
a brief
time
after’ release
of
the
key,
a new machine
state
is established
(but
not
shown
to
the
subject)
by sampling the instantaneous state
of
a
liigh-
Approved For Release 2000/08/07
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Approved For Release 2000/08/07
: CIA-RDP96-00787R000700090011-6
speed four-state electronic counter.
For
the machine
to be
random,
the times of dwell
of
the counter
in each
of
the four states must be
precisely equal;
otherwise,
the distribution of outcomes
will
be biased
The first randomness
test
is
thus based on tallying
the number of
occurrences
of each of
the four states.
This
test should detect
a
stable bias,
yet may miss
a drifting bias.
To test for
this second
possibility we also tally the distribution of outcomes
in each group
of
100
trials,-
then compute
a likelihood ratio test
statistic
(see
below)
for each group.
Under the null hypothesis
of equal likelihood
of
the four states,
these statistic values
are distributed approxi-
mately
as chi-square with three degrees
of freedom and
their sum for
m groups distributed approximately as chi-square with three m degrees
of freedom.
This
test ,may also detect stable bias,
but
is not as
powerful for this purpose
as
the first
test.
Variable bias
of
still
a shorter period,
if substantial,
can be tested for by
tallying
the
frequency with which the previous machine
state
is
repeated;
an overall
repeat ratio
("all")
significantly above
0.25
is
indicative of such bias
If
for any reason the machine were
to fail
to sample
the counter
\
to establish
a new state,
the
previous machine state would be
repeated.
To
test
for this possibility,
we tally
the number of repeats following
the depression
of
each
key.
A repeat ratio significantly greater
than
0.25 should be considered
a danger signal.
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Wc also tally
the
initial machine
states following reset and
the
i
transitions between
states.
In each case,
the number of occurrences
of
each
of
the four possible outcomes
should be approximately equal.
When
repeats are deleted from
the sequence
of
trials
("nondiagonal transi-
tions
),
the four states
should also be approximately equal
in frequency.
In testing
the null hypothesis
of
four equally likely outcomes
of
a
trial,
a likelihood ratio
test
is used.
The statistic
i=l
under
the null hypothesis
is distributed approximately
as chi-square
with three degrees
of freedom,
with rejection for large values
of
this
statistic
. *
The computer program used
in testing randomness
includes
a subroutine
for computing
the probability of
a chi-square value
as
large or larger than that observed.
In testing
the null hypothesis that
the probability of
a. repeat
is
0.25,
the binomial probability
of obtaining
the observed number K
or more repeats
in N trials
is computed.
For K greater than
1000,
a
normal distribution approximation
is
computed,
assuming
the statistic
to be approximately normal with mean zero and standard deviation one.
^Alexander Mood,
Introduction
to
the Theo ry of Statistics
(McGraw Hill,
New York,
1950).
-
—
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The
typical
tost pattern used was six passes followed by 25
choices
of one
color,
repeating
this
for each of
the four colors.
In
this way
each of
the five
keys other
than reset were given approximately equal
use.
Typically,
2000 to 6000 trials were made
in each sitting.
In
the
absence
of
any unusual results
in
the randomness
tests,
a minimum of
10,000 trials were made before using
a machine with experimental
subjects
With 10,000 trials,
the expected fraction of repeats
is
0.25 with
a
standard deviation
of 3/200
= O.OOS66.
A computer listing of the results of randomness
tests
is included
in Table
1.
No significant departures from randomness
were, observed.
Subject Data
Data was collected from subjects
SI through
S6
.
Each subject was
asked
to complete
100 25-trial
runs
(i.e.,'a total
of 2500
trials each).
The results
are tabulated
in Table
2.
.(One subject,
S3,
declined
to
complete
the 2500-trial
run,
indicating
a
lack of
rapport with the
machine
and,
hence,
a
lack of motivation for the
task.)
For
the
six
subjects,
only one
(S2)
scored significantly above
chance.
For the
2500 trials 'that
subject
averaged 29.36 hits/100 trials
rather
than the
expected 25/100,
a result whose
a. priori probability under
the null
-7
hypothesis
is
p
= 3x10
.
His
scores
are plotted
in Figure
12.
The statistics
of
the machine during the successful
run of subject
S2 were tabulated for
the entire 3488 machine transitions
(2500 choices,
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