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the remainder of the report.
Miscellaneous
The report contains
a section entitled
"Miscellaneous"
for the
purpose of displaying detailed data which wasn't directly required
by
the above more general
analysis.
Details such as
how many successful
choices
in the color red during the 50th
trial
were there,
or what was
the relationship of the number of passes
to the number of successes.
The terminology used
is
as
follows:
the term
"trial
refers
to the
string of machine states and corresponding choices from the time the
subject begins
until
he makes
25 non-passing choices.
A sample, is
a
machine state and/or subject choice
(including passes).
There are
(25 +
# passes/trial)
samples
in each trial.
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I.
Statistical
Analysis of the Machine Experimental
Data
SC
Forward-backward State Transition Analysis
In
a previous memorandum
(Memo ORD 2240-75,
12 June 1975
to
the question of randomness with the emphasis on state transitions
as an
indication
of non-randomness was addressed.
The data used
in
the investigation consisted
of pre-experiment trials.
The purpose of this
section
is to do
a similar
investigation using the actual
data which occurred during
S2
1 s
experiment.
Table
presents
all
possible transition frequencies.
All
transitions
should have equal
probability.
YELLOW
GREEN
BLUE
RED
YELLOW
204
199
199
216
GREEN
192
218
222
207
BLUE
211
206
228
222
RED
209
206
223
221
Restructuring
into
a
two-b>'-six table as
in Ref
produces:
Y/G
Y/B
Y/R
G/B
G/R
B/R
FORWARD
199
199
216
222
207
222
BACKWARD
192
211
209
206
206
223
The conclusion
based
on pre-experimental
data was that these state-pairs
show
a very strong relationship between forward
and
backward transition
frequencies
(coefficient of correlation =.93).
However,
computing
the coefficient
of correlation,
p S 2 actual
data
=
.58,
it becomes apparent that the
degree of dependence
is slightly reduced.
Therefore the dependence of
forward
to backward
states
can
no
longer
be considered
as
a
strong
indicator
of non-randomness.
>
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The data used
in the above discussion consisted of trials
from both
machine
and machine
2.
Since non-randomness, made apparent
by the state
transitions,
clearly existed
for pre-experimental
data,
the investigation of
the experimental
data continued
to
include
a search for this trend
in
the
individual
machines.
The transitions
(including identity)
are as
follows:
Machine
YELLOW
GREEN
BLUE
RED
YELLOW
GREEN
BLUE
RED
Machine
.
YELLOW
GREEN
BLUE
RED
YELLOW
108
120
111
124
GREEN
107
131
136
119
BLUE
126
124
138
135
RED
118
115
140
129
Computing
the two coefficients of correlation.
p machine
s2 data
=
.4934
and
p machine
s2 data
=
.4838
it
is obvious
that the forward apd backward transitions are even less dependent
than
in the combined case.
Thus ended
the search for non-randomness
through
state transition.
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As
a by-product the following table
is
produced
for general
information.
BOTH MACHINES
MACHINE
MACHINE
MEAN
SD
MEAN
SD
MEAN
SD
FORWARD
210.8
10.7
86.6
4.27
CNI
9.74
BACKWARD
207.8
9.00
86.2
.3.92
121
11.25
TOTAL DATA POINTS
3483
1446
2037
COEFF OF CO
.5843
.4934
,4838
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Experimental
Data
Randomness Analysis
3 l*
/ 7 0
C,
) £
The machine data used during the S2 experiment
has been combined, summarized
4/
and/or permuted
in an attempt
to establish evidence or randomness or non-
randomness.
If an obvious
indication of non-randomness would
have evolved
this
task would
be simplified because
it would have become
a closed form
problem
(i.e.,
the solution would
be
-
the data
has non-random characteristics)
.
.However, what-has
resulted
i s
that various
forms of the data
hav e bee n examined
with all
indicating that the data
is
random.
Tables,
plots and commentary are presented
in this
section to demonstrate
randomness and^in some cases just
to provide general
information concerning
the machines
data.
The distribution of the colors collectively and for each machine
is
as follows:
Yellow
Green
Blue
Red
Total
Mean
Machine
365
353
356
372
1446
361.5
Machine
475
505
538
519
2037
509.25
TOTAL
840
858
891
891
3483
870.75
Machine
was not used
in
as many trials
as machine
(44 trials
to
for machine
2),
thus
the difference
in totals.
The standard deviation of
binomial
distribution with n=3483 and p=l/4
is
25.56 which would
imply that
each separate number
is reasonably close
to the mean.
Accepting the distribution of the totals
consider the distribution of the
colors throughout the experiment.
The popluations
used
for
this
investigation
consisted of the first 25 samples of each
trial
(100 trials
total).
This
population
is acceptable since the distribution of
its
totals was reasonable
and since the performance of S2 was approximately the same
(success-29. 61%)
for this
subset.
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The following three approaches comprise the strategy used
to attack
the question of color distribution.
1.
__Eac,h
.,t.r.13-1..^abbreviated
to
25 samp les)
as analyzed separate interval
.
Obviously this will
indicate any bias within each trial.
2.
The data
{2500 samples)
is divided
into
intervals of f ive samples
each.
This will
indicate unusual
repetitions either within the
interval
or interval-by-interval
.
3.
The data
is reformatted
into
25 intervals
of 100 samples, where the
nth
interval
c onsi sts
of the
nt h j amp 1 e
in each
trial.
The results
of approach
is
shown
in
Figures
1.1. a,
1.1. b,
1.1. c,
and
1.1. d.
The binomial
distribution
for this strategy
(n=25 p=l/4)
is mean
6.25
i
'
"and
the variance
4.69.
The plots
indicate randomness throughout the 100
trials.
The results of approach
2 are similar
to approach
and are shown
in
the four tables
in
Figure 1.2.
The plots
indicated randomness
but are not
shown because of monotomy.
The binomial
distribution mean
is
1.25 and
the
variance
.94.
The
binomial
distribution mean and variance for approach
is
25 and 18.75
respectively
(Figure 1.3).
A plot of the data
(Figure
1.4)
for the
"RED"
case because of the concern
for the
higher variance and
ranges.
The 13th sample
seems
to
have an unusually high frequency of
"RED"
(44%).
However
in general
this investigation
has
not produced
a significant non-random characteristic.
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maximum
minimum
1 9
range
mean
24.92
variance
10.57666667
standard deviation
3.252178757
mean
deviat ion
2.6304
median
mode
Green Distribution
i
sample
size
maximum
!
minimum
1 5
range
|
mean
24.52
variance
24.59333333
standard deviation
4.959166597
mean deviation
3.9392
i
median
mode
Blue Distribution
sample
size
maximum
minimum
range
mean
24.84
variance
1 4.47333333
standard deviation
3.804383437
mean deviation
2.9664
median
mode
Red Distribution
sample
size
maximum
,
'
minimum
range
mean
25.72
variance
26.71
standard deviation
5.168171824
mean deviation
3. 3664
median
mode
Figure
1.3 Distribution of Machine Colors When Samples are Taken 100 at
a Time
(One
From
Each Trial)
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T1
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Number
of
Reds
45M
.
M
M
M
M
40M
M
M
M
M
35M
M
M
M
M
30M
M
M
M
M
25MO
M
M
M
M
20M
M
M
M
M
1 5M
o
o
o
a
o
oo
o
oo
o
,
o
o
o
o
m
m
m
m
m
m
Samp! e Number
Figure 1.4
Distribution of Machine
"Reds" when
the Samples are taken
100 at
a time
(one from each trial)
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Approach
has
been repeated for Machine
and Machine
2 separately to
check for abnormal i ti es
.
The binomial
distribution mean and variance are
as
follows:
Trials
Mean
Variance
Machine
8.25
Machine
10.5
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Machine
'Yellow
sample
size
-
.
maximum
minimum
range
mean
.
variance
7.75
standard deviation
2.783882181
mean deviation
2.224
median
mode
Machine
sample
size
maximum
'19
minimum
range
mean
1 3.52
variance
7.51
standard deviation
2‘. 740437921
mean deviation
2.176
median
mode
.
Green
sample
size
maximum
minimum
range
mean
'
10.68
variance
9.726666667
standard deviation
3.
1 18760438
mean deviation
2.3584
median
mode
....
M
sample size
maximum
minimum
range
mean
variance
standard deviation
mean deviation
median
mode
.
:
13.84
12.7233333?
3. 5669781
2.7808
sample
size
maximum
minimum
range
mean
variance
standard deviation
mean deviation
median
mode
10.32
7.726666667
2.779688232
2.3072
sample
size
maximum
minimum
range
mean
variance
standard deviation
mean deviation
median
mode
1 .6
f 0.5
3. 240370349
2.4
sample
size
maximum
minimum
range
mean
14.12
variance
8.943333333
standard deviation
2.990540642
mean deviation
. 984
median
mode
1 5
!
sample
size
maximum
minimum
range
mean
14.52
variance
10.01
standard deviation
v/
ff v
3.
J 63853404
mean deviation
2.6624
median
1 3
mode
M
Figure
1 .6Mtr9K?fW
;«6RSi
|ee?|4j0^3/04/18
: CIA-RDP96-00787R000200150011-4
and
Macl,1n0
a
Trial
Tn T v' i
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Best Strategy
Based on the above analysis what
is
the best strategy
to pursue?
No
good strategy
is available based on
the randomness of the data.
The best
possible strategy based
on the above transition matrices
is:
.
If
the subject can't distinguish between machine then press
blue
when blue appears,
else pass.
2.
If the subject can distinguish them on Machine
T,
press yellow
when yellow occurs,
and on Machine
2 press
blue when red occurs.
For
all
its worth,
of the existing data
the following success would
result
-
26%,
26%,
and
27%.
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Analysis of S2
Data Responses
The attempt here
is
to discover
a reason for S2's success
at responding.
The investigation was unable
to give
a definitive reason for
his
success.
Although no strategies were uncovered there was
in one case
a
indication
that
the subject was
learning.
Two major approaches
have been
taken
in this
investigation.
They are
as follows:
1.
Strategy of S2
- Was there any trends
in the way he guessed?
Did
he respond based on the previous
state of the machine?
V
2.
Hit analysis
-
Did the subjects'
hits
(correct choices)
increase
within
a, run;
did
it increase from run
to run
( i
. e .
,
was
he
learning?)
Strategy of S2
For general
information and future reference the first figure
(Figure
2.1)
presented
is
the actual
choices,.
On e item of curiosity from this
is that
when
he..passes,
he tends
to do
it
in
stri ngs.
This characteristic of course
wasn't pursued because of
its
insignificance to
this report;
however, observations
like that are pointed out throughout the report
as
possible importance
to
those
in the field.
Total
Color Choices
The distribution of S2's color choice totals are shown
below.
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J
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03 07
i
i
i
_*
i 013
777777777737 037 037 7
120713
Ficjure
2.1 Subjects Color Choices
for
First
Fifty Trials
(0-yellow,
1-green,
2-blue,
3-red,
7-pass)
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Hit Analysis
This
section
is significantly more important than the randomization
analysis of the machine data.
The reason
is
that
if he
is
not learning from
the machine or
he
is
not taking advantage of biases
then the discovery of
such non-randomness
is of little value
to
the overall
analysis.
Learning from Trial
to Trial
The question of whether the subject learned from trial
to
trial
can
best
be answered
by examining the following three
plots..
The first
is
the
number of hits
vs.
the
trial
number,
the second
is
a frequency distribution
of the number of trials
vs.
number of hits,
the third
is
the accumulated
probability
vs.
the trial
number.
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Number
of
Hits
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15M
M
M
m
o
on
M
1 ON
D
r-i
do
o
o
o
o
no
oo
o
o
o
M
D
D
O
OOODOD
000
MO
D
00 0
D
0 ODD
D
MO DO
D
000 000
5M0
D
DO
M
M
MOOD
M
OM
M
M
M
M
M
M
M
M
M
M
£0
100
Trial
Number
Figure 2.2
Plot of number of hits/trial
Frequency
of
Hits
per
Trial
£5M
M
M
M
M
SOM
M
M
M
M
15M
M
M
M
M
1 OM
M
M
M
M
5M
M
M
M
M
OM
M
M
M
M
MO 000 OMO 000 OMO
£0
Figure 2.3
Frequency plot of Number of Hits
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cn
p
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Cumulative
Probability
of
Success
0.30M
M
M
M
M
0 O
0 00
0.2 9M
OOO
'00-00
0 000000 0000
0000000
M
000
0 00
0000
(
M
M
M
0.28M0
M
M
MOO
M
0.27M
M'
M
M
M
0.26M
M
M
M
M
0.25MMO
M
M
.
M
0.24M00
M
M
M
M
M
M
M
M
M
Trial
Number
Figure
2.4
Cumulative Success
Ratio of Subject
(both machines
used)
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000
M
1 00
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Accumulative
Probability
M
M
M
M
0.31M
M
M
M
M
0.30M
M
M
M
M
0.29M
M
M
M
M
0.28M0
M!
M
M
:
M
i
0.27M
S
M
M
M
M
0.26M
M
M
M
M
0.25M
M
M
M
0.24M
00M
M
M
M
M
M
M
M
M
O
M
Trial
Number
Figure 2.5
Accumulative Probability of Success on Machine
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Accumulative
0.30M
M
M
M
M
0.29M
M
M
M
M
0.28MC?
M
Mi
Mi
M
j
0.27M)
M‘
M
M
t
M
0.26M
'•
M
o
;
!l
0 b " j\
,C )(5
o
od
b
o
*
i
i
b
M
i
M
i
M
0.25M
!
m
;
M
I
M
i
M
:
0.24M Od M
'
M
i
.
£
[f
M
M
y
M
0000
/
doooo
od
di
p
oo o
d
l jh
!
o
Px0
M
V
M
M
M
M
Trial
Number
Note:
V
-
Points
at which
he switches machines
Figure 2.6
Accumulative Probability of Success
on Machine
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The first plot
(Figure
2.2) demonstrates the randomness
of the number
of hits while the second plot
(Figure 2.3) demonstrates the frequency
distribution takes on
a
"normal"
appearance.
The accumulative probability plots,
at
first glance, indicates
that the subject was
in
a
learning mode for the
first five trials.
A closer examination of the data
indicates
that this Can
occur naturally
as
part of the statistical
distribution.
The first three number of hits points are
7,
5,
and
6 considering
the
first 75 points
as the population with probability of success
=
.2936
(the
final
probability)
then the expected value
is
(using binomial
distribution)
and
the variance
is
15.55
(S.D=3.9).
As
a normal
deviation
from the
n&ean
(i.e., -using normal
distribution approximation P(x<18)=.T3.
Although
the observed learning can
be rationalized
as
a
natural
statistical
deviation
it warranted further
investigation.
The plots
of
the accumulative
probability of success for machine
and machine
2 are presented
in
Figure 2.5
and
Figure
2.6.
The plot for machine
(Figure 2,5)
is
a
typical
sinesodial
decreasing amplitude convergent curve.
The plot for mac hine
2 however,
is
;
very suspicious
in terms
of learning.
The major
peaks
of the curve
(at
approximately
trial
TO,
23,
40 and
56)
are increasing which implies
his
probability of success
is continuing
to
increase
instead of converging on
one point.
Another
interesting
point^i-s—t-hat the points
at which
he switches
onto machine
2 are
,
9,
and
36.
Also of concern
is
the sharp upward
turn during
the
last
8 samples.
• The hits
totals
for this
period,
starting
at sample 49
is
10,
10,
11,
6,
8,
7,
and
for
a
total
of
hits out of
a possible 200 for
a probability
of success
of
.36.
Once again using the binomial
distribution and using
the
probability of success of
.29
(the
cumulative probability up
to the 49th
point)
the expected mean
is
58 and the standard deviation
6.42.
Using
the
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cl U 1 o'
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1 0 1 12 01 1 3 0 1 3 o
:
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: CIA-RDP96-00787R0002001 5001 1-4
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Addraved* For Release 2003/04/18
: CIAtRDR96j-00787R0
100200150Q1 1-4
Tlglirel.j
CoTor states
ot macmne Z during
the experiment
(0 yellow,
green,
2 blue,
3 red)
Approved For Release 2003/04/18
: CIA-RDP96-00787R0002001 5001 1-4
50M
M
M
M
M
40M
M
M
M
M
30M
'
M
Number
M
of
M
Passes
M
20M
M
.
M
M.
M
1 0M
M
M
M
M
OMOOOOOOOO
M
M
000
0 0
0 o
000
'
000
M
M
M
'
M
oo
Trial
Number
Figure 3.4
Total
number of passes
summed over
a
trial
Approved For Release 2003/04/18
: CIA-RDP96-00787R0002001 5001 1-4
)
M
100
Number
of
Passes
0 0
o
35M
M
ApprovecfoFor Release 2003/04/18
: CIA-RDP96-00787R0002001 5001 1-4
MO
M
30M
M
O
M
M
M
25M
MO
M
M
M
O
20M
M
M
' M
M
1 5M
M
M
M
M
I OMO
M
M
M
M
5M
M
M
M
MO
OM
M
M
000
M
M
Samp! e Num^gp
0 0
0 00
oo
000
M
M
000000000
Figure 3.5
Total
number of passes summed over sample number
Approved For Release 2003/04/18
: CIA-RDP96-00787R0002001 5001 1-4
Approved For Release 2003/04/18
: CIA-RDP96-00787R0002001 5001 1-4
C.
Number of passes
and
the number of hits
vs.
the trail
number
on one plot.
Investigation of the hits/passes relationship
was dropped when the coefficient of correlation between the
two was computed
at -.114
Approved For Release 2003/04/18
: CIA-RDP96-00787R0002001 5001 1-4
Approved For Release 2003/04/18
: CIA-RDP96-00787R0002001 5001 1-4
Pass
and
Hit
Total
50M
M
M
M
M
40M
M
M
M
M
30M
M
M
M
M
20M
M
M
M
M
1 OM
000
p
p
P
P
P
PO
PPP
p
p
p
p
PP
MPP
PP
P
PP
P
PP
PP
MPPP
P
P
PP
P
P
0 0
P
P
PP
P
PPPOP'
P
o
POPP POPPPPP POO
PPPPP
OPO
PPPP
PPP
P
P 0
P
PP
P
M
M
P
P
P
OM 00000000
M
M
OOP
000
P
OPP
o
M
M
M
M
M
1 00
Trial
Number
-
passes
per trial
P
-
hits
per
trial
Figure 3.6
Plot of number of hits
per
trial
and number of passes
per
trial
Approved For Release 2003/04/18
: CIA-RDP96-00787R0002001 5001 1-4
Approved For Release 2003/04/18
: CIA-RDP96-00787R0002001 5001 1-4
IV.
Tables of state transitions which reflect the influence of the subject
on the machine.
For color choices
of the subject the table shows
the number
of colors
the machine
has on
the next sample.
For example on the first table,
when
the
subject picked yellow,
on the next sample 197
times
the machine
state was yellow.
MACHINE STATES ON
FOLLOWING SAMPLE
Yellow
Green
Blue
Red
Yellow
Green
Machine
Blue
Red
120
105
112
Pass
Yellow
109
1 24
128
141
Green
Machine
Blue
Red
121
125
136
102
Pass
146
162
161
168
Yellow
197
201
215
236
Green
.
113
Both
Machines
Blue
Red
241
230
235
214
Pass
230
245
259
249
Figure 3.7
State Transitions
from Subject Choice to Future Machine State
Approved For Release 2003/04/18
: CIA-RDP96-00787R0002001 5001 1-4
Test
Description
Scoring
AAAOAA-1
4 -4.
.
-
-
.
-
. -
.
-
?
Approved ror Kelease zuuorUH-iio
. uiA-Kur iio-uu r o / ^00(g£)01. 001^4
s3
s4
S5
s6
Halstead Category
Test
Nonverbal test requiring abstraction of conceptual relation-
ships.
Score:
Total errors.
Tactual Performance
Test
Requires placement
of
10 geometrically shaped blocks
in
their correct locations on a formboard while blindfolded.
Separate RT,
LT,
and bimanual trials.
Score:
Total
time
(min.).
16,4
11.8
7.7
7.7
11.4
6.9
Speech Perception
Test
Discrimination of non-word speech sounds.
Score:
Total errors.
Seashore Rhythm Test
Discrimination of nonverbal rhythms.
Score:
Number correct.
Finger Tapping Test
Measure of
finger oscillation rate for 10-sec.
period,
both
RT and LT hand trials.
Score:
No.
taps/10
sec.
RT/LT
RT/LT
RT/LT
RT/LT
RT/LT
RT/LT
53/50
53/49
48/47
54/53
47/47
48/43
Trail Making Test
(Part A)
Requires connecting numbered circles
in order from 1
to
25.
Paper and pencil task.
Score:
Total times
(sec)
Trail Making Test
(Part
B)
Requires connecting alphabetic and numbered circles by
alternating
1->A*2->B,
etc.
Score:
Total
time
(sec)
Knox Cube Test
Measure of attention span and immediate visual memory.
Score:
Number correct.
Raven Progressive
Matrices
Nonverbal intelligence
test
involving spatial matrices.
Score:
Number
correct.
Verbal Concept
Attainment Test
Requires abstraction of verbal conceptual relationships.
Score:
Number
correct.
Buschke Memory Test
Requires learning a 20-word list
in
a maximum of
12 trials with
repetition of words omitted after each trial.
Score:
Max.
no.
words correctly remembered;
List:
no. words consistently remembered
Total
:
14/20
17/20
18/20
19/20
20/20
20/20
List
:
8/20
14/20
11/20
16/20
15/20
16/20
(8 trials) (7
trials^
Grooved Pegboard Test
Requires insertion of
25 pegs
in their holes
in a pegboard.
Both
RT and LT hand trials.
Score:
Total time
(sec).
' RT/LT
RT/LT
RT/LT
RT/LT
RT/LT
RT/LT
76/74
69/70
58/67
59/67 W
48/50
7 2/70
r-:
_
Spatial Relations
Subtest
of
the PMA
Requires mental rotation and identification of fibres
rotated
in
2 dimensions.
Score:
no.
correct
-
no<.
errors.
-
-
-
Gottschaldt Hidden
Figures Test
Requires tracing outline of simple figure hidden wjLthin
lines of more complexAf>J3gey§d
:
, £3ArBE>P.96-00787R odb2tf01 500^4-
~
v.good
outst.
outst.