Approved For Release 2003/04/18
: CIA-RDP96-00787R0002001 50009-7
novm
Four-state electronic random number
in this experiment.
An incorrect choree of targ
is
indicated.
Two
of the five
encouragement lights
at the top
of the machine are illuminated.
The
printer to the right
of the machine records data on
fan-fold paper tape.
Approved For Release 2003/04/18
: CIA-RDP96-00787R0002001 50009-7
Approved For Release 2003/04/18
: CIA-RDP96-00787R0002001 50009-7
Four-State E 1 o ctronic R andom Numb e r Generator
This
study provided an opportunity
to determine whether the
re-
mote
sensing capability could be extended
to the perception of
the
internal state of
a piece
of electronic equipment.
For this purpose,
an automated experiment designed around
a four-state electronic random
t
number generator was
initiated.
The solid-state machine has no moving
parts
and provides no sensory cue
to the user as
to its target genera-
tion.
In order
to determine unambiguously whether
a result was meaning-
.
''‘V
ful,
the following strategy was used.
First,
the randomness
of
the
machine was verified by over 10,000 pre-experiment trials
(details
given below).
Second,
the subjects interacted with the machine
to
generate
the data^ Third,
for any subject whose
score was significant,
the statistics
of
the machine during
the
successful ^perimiejli wera
tabulated to insure that the machine had not departed from randomness
in the period
in which a significant result was obtained.
Fourth,
a
subject generating
a good score was asked
to repeat
the entire experi-
ment after
a one-month lag period.
Finally,
the entire data analysis
was carried out by an independent statistics group
at
SRI.
The machine configuration provides
as
a target one of four art
slides chosen randomly
(p =
1/4)
by an electronic random generator.
The generator does not
indicate
its choice until the subject
indicates
his choice to the machine by pressing
a button
(see Figure
11).
(The
Approved For Release 2003/04/18
: CIA-RDP96-00787R0002001 50009-7
Approved For Release 2003/04/18
: CIA-RDP96-00787R0002001 50009-7
machine has four stable
internal
states.
A
1.0-MIIz square-wave
oscillator sends pulses
to an electronic
"scale-of-four" counter which
passes through each of
its four states 250,000
tifnes 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
f
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.
Approved For Release 2003/04/18
: CIA-RDP96-00787R0002001 50009-7
Approved For Release 2003/04/18
: CIA-RDP98-00787R0002001 50009-7
Under
the null hypothesis of random binomial choices with probability
1/4 and no learning,
the probability of observing ik successes
in n trials
is approximated by
the probability of
a normal distribution value,
*(*-!- i)/^
Pre-Experiment 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.
When 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 high-
Approved For Release 2003/04/18
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Approved For Release 2003/04/18
: CIA-RDP96-00787R0002001 50009-7
speed four-state electronic counter.
For
t}ie 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
considei'ed a danger signal.
Approved For Release 2003/04/18
: CIA-RDP96-00787R0002001 50009-7
Approved For Release 2003/04/18
: CIA-RDP96-00787R0002001 50009-7
We 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,
In troduction to
the Theory of Statistics
(McGraw Hill,
New York,
1950)
.
Approved For Release 2003/04/18
: CIA-RDP96-00787R0002001 50009-7