Approved For Release 2003/04/18
: CIA-RDP96-00787R0002001 5001 1-4
sample
size
maximum
minimum
range
mean
variance
standard deviation
mean deviation
median
mode
100
a \ 239494949
2*059003387
*s3
•
1 .6314
Number
of
Yellow
per
Trial
15M
M
M
M
M
0 0
10M
M
M
M 0
0(5
0 00
MO
0 0 000
000
5MO
00 0
0000
M
0000 0
M
M
M
OM
M
M
M
M
M
M
0 0
0 00
M
M
00 000
0 0
M
M
1 00
Trial
Number
Figure
1.1. a
Distribution of Machine Yellows Over Trials
Approved For Release 2003/04/18
: CIA-RDP96-00787R0002001 5001 1-4
Approved For Release 2003/04/18
: CIA-RDP96-00787R0002001 5001 1-4
sample
size
maximum
minimum
range
mean
variance
standard deviation
mean deviation
median
mode
100
6.13
5. 35 16
I 6
I 62
2.419011 402
1.9404
Number
of
Green
per
Trial
i
1 5M
M
M
M
M
10M
MO
M 0
M
MO
0 0
5M
0 OOOO
M O
M
M
M
0M
M
M
M
0 0
0 M
M
M
0 0
0,000
0 0 0
000
0 0
M
'
M
M
M
100
Trial
Number
Figure 1.1. b
Distribution of Machine Greens Over Trials
Approved For Release 2003/04/18
: CIA-RDP96-00787R0002001 5001 1-4
Approved For Release 2003/04/18
: CIA-RDP96-00787R0002001 5001 1-4
sample
size
:
maximum
minimum
range
mean
variance
standard deviation
mean deviation
median
mode
! 100
6.21
5.218080808
2.284311 889
1.8194
Number
of
Blue
Per
Trial
I 5M
M
M
M
M
()
I0M
()
M
M
M
0 0 00
M 0
000
5M
0000
M0
M
MO
M
OM
M
M
o
0 0 000000
o
0000
a
M
M
M
M
o
o
00 0
000
000
000
M
M
M
M
100
Trial
Number
Approveffl^gLetare 200^^1 Bu:tStArWPg$tftPW#0^Q|Q'b5001 1 -4
Approved For Release 2003/04/18
: CIA-RDP96-00787R0002001 5001 1-4
sample
size
maximum
minimum
range
mean
variance
standard deviation
mean deviation
median
mode
100
6.43
4.631414141
2. 152072058
1.7158
Number
of
Red
Per
Trial
15M
M
M
M
MO
I0M
M
O
M
000
MO
0000
M
0000
5M
M
0 0
M
0 0
M
0o
0 o o
o
0 00
0 0
0 00 00
00 00
0 o
M
OM
M
M
M
M
M
M
M
M
o
o
M
M
1 00
Trial
Number
/
•
Appr§Wpd Ron Release 2003/04/18
: CIA-RDP96-00787R0002001 5001 1-4
HwpFen.saT
ulstnbutTon of Machine Reds Over Trials
Approved flarrifeeteks® 0(fO3jffiH7lb&
: CIA-RDP96-00787R0002001 5001 1-4
sample
size
maximum,
minimum
range
mean
variance
standard deviation
mean deviation
500
1.246
0.9594028056
0.9794910952
0.784848
median
I
mode
Distribution of Green
sample
size
maximum
minimum
range
mean
variance
standard deviation
mean deviation
median
mode
500
.
1 .226
0.996917835/
0. 9984577285
0.804512
Distribution of Blue
dstat
grp? <3*
sample
size
maximum
minimum
range
mean
variance
standard deviation
mean deviation
median
mode
500
U
. 242
U. 95/350701
O.y/84429985
0. /92 / 92
l
Distribution of
sample size
maximum
minimum
range
mean
variance
standard deviat
mean deviation
median
mode
Red
500
1 .286
1 .026256513
ion
1.013043194
0.823216
Figure
i
at
Time
§s^?l 7
#18
#^^%
:3^
l^^p«a
<7d,7R0002001500i 1^
207031230702317030303301 33703
301 70
1 0203
1 7307303003303
1 37
I 3
01 007777373707303777
1 7377727337731 07707771 30777373773
20707370731 77737007703737000273
I 777707077777073777777 377773
0173033032037033032701370301
3037
I 703320730307377301 3023737203
0373737303373032173233377! 73733707371
23707377313033333703773/73707! 73777377373270
1 31 07303737730
1 0333337073731 3707700
333737077307303733331 30373370707770733
033037737703337337777077777327777301027337333
0303037200003773 733 777077377 33030332
33032
1 33270323233
1 30 1 2
1 330
1070! 101301 101 3130302301 23
300703300723730030371 7771 37777033002
031 3373737030003200030001 003
302 332
1 3
1 00000
1 37
1 30370303 7770
77201 77
1 0077030723703
1 373 10! 3777377
1 77777303
337
I 7
1 01 77
1 37
1 30021 7 333733030733
307173737 17077
1 301
1 7303707301 373370071
0330320302007
1 027
1 07 377121 270703
0323! 32732037302377033
1.1 0077700
1 7370737
1 07
1 3
1 733
1 33
1 730
t 7207073
2713131 07327033277731177130323303
30003733000330037
1 030307
1 330
30127001 333301 307773707737 3303377770770
03037030370737323
1 370710732001773
3773307007200077030037313000300?
1 3200200030030377030073! 723370
30707207020773307033030303777377737377073
07077730703700377777707731707330307307077770737373
00707737377003073730777777707377777737773770300077773333
1 30
1 037
1 320
1 07
1 730
1 002720073723
3101310317001300001730073020
03777720070773100770707373007200730700700
30300007
1 00000232
1 3002002
3031 301 3013201 3023
I 033003
230120313012031031 1303120
30)30231031737130730323001 31
301301301 3201 302101302303
1 3023
1 0323037
1 3273031 030
1 30
30 103
1 03 107732303
I 3073021 331
310313031737701373001 330033777713
31301 03031 03303073770700377
1 7003
023130332013700137230201 330
021 7373 103101 30370007302 77773
1 0373
1 370731 07
1 03702373 13271 033 1073703
331 300301 70730107070037
1 0737007
Figure
2.1
(Continued)
S2 Color
Choices
for Last
50 Trials
Approved For Release 2003/04/18
: CIA-RDP96-00787R0002001 5001 1-4
—In
m
o
tn
c
w
Approved For Release 2003/04/18
: CIA-RDP96-00787R0002001 5001 1-4
Yellow
Green
Blue
Red
Total
Times
Chosen
881
411
237
971
% of Total
35%
16.5%
9.5%
39%
The first inclination
is
to try and determine how his strategy of choosing
so many yellows and
reds
benefitted
him.
Examine the following
table:
Yellow
Green
Blue
Red
Total
Number of Hits
255
127
GO
S0r
292
% of Total
Hits
35%
17%
8%
40%
% of Success
in Color
29%
31%
25%
30%
(Hits
- Correct Choices)
As can be seen
his
results with blue are significantly lower than the others.
However,
assuming
the probability of success
to
be
.24
and using the
binomial
distribution the expected value =69 and the standard deviation
=
7.
The
inference from this
is
that the 60 Blue
hits are not
a statistical
abnormality.
However,
it
is
curious that
he did
so much worse on
his
lowest preference.
State Transition Color Choice
This investigation consists of examining
the states of the machine verses
the choice on
the next sample of the subject
(i.e.,
if the machine shows
"red"
does the subject consistently choose one color on the next turn).
Consider
the following
table:
SUBS
Machine
MACH'N^
Yellow
Green
Blue
Red
Pass
% Pass
Yel 1 ow
106
119
314
210
26%
Green
177
2.5
316
252
30%
Blue
241
198
302
35%
Red
322
157
218
25%
/ 3 °
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Approved For Release 2003/04/18
: CIA-RDP96-00787R0002001 5001 1-4
The subject obviously avoids repeats
(i.e,,
he assumes
the machine
vfon’t repeat
a color) which,
based on the machine data analysis,
isn't
a
Strategy which would
give him
a
statistical
advantage.
Previous analysis
showed that
Identify" transitions are approximately equally probable as
nonidentity.
Notice also that
he passes
35% of the time after seeing
a
The same state transitions
Yellow
are shown below separated
by machine.
Green
Blue
Red
Pass
M
A
Yellow
150
C
H
Green
153
I
N
E
Blue
105
115
Red
133
v 7 .am
tV
M
A
Yellow
164
127
C
H
Green
115
163
169
I
N
E
Blue
136
120
187
Red
189
154
The negative state transition
(i.e.,
relationship of the subject color
choice to the machine state on the next sample)
is considered too bizarre of
a concept
to
be presented
in
this
section.
Results of that investigation
is
found
in the section entitled
"miscellaneous"
Approved For Release 2003/04/18
: CIA-RDP96-00787R0002001 5001 1-4
Number
of
Hits
Approved For Release 2003/04/18
: CIA-RDP96-00787R0002001 5001 1-4
12.5M
M
M
M
M
IO.OM
M
M
M
M
0.
7.5M
MO
-00 0
M
M
O
t)
M
5. OM
M
M
M
.
M
2.5M
M
M
M
M
,
•-
O.OM
M
M
M
M
M
M
M
M
M
M
M
oo
o
o
n
o o o
o
0000
M
Trial
Figure 2.7
Plot of Number of Hits
on Machine
Approved For Release 2003/04/18
: CIA-RDP96-00787R0002001 5001 1-4
Approved For Release 2003/04/18
: CIA-RDP96-00787R0002001 5001 1-4
normal
approximation
the probability P(X
71)=. 02 of such an occurrence
is
quite
low.
Although there are only
56 data points
in this population
and
the
apparent abnormalities
are statistically possible
(with
low probability)
this
investigation concludes
that the subject's
learning for this case must be
flagged
as
a
real
possibility.
Figure 2,7
(Number of hits
on Machine
1)
has
been added
to provide clarity.
It appears
that the subject just didn't have
"low hit"
days
toward
the
end.
Learning within
a Trial
The question of learning within
a
trial
or run
has
bqen investigated^ _
by summing the number of hits of the
Ith sample for the
^un.
The results
are somewhat distorted
because of the inequitable distribution of passes.
The lower numbered samples
have significantly more hits
because of this.
A plot of the number of hits
per sample
vs.
sample number
is shown
in
Figure
2r7."
Notice that the first sample
has
a value of 34 hits.
This means that
everytime
he
ists down
for
a new 25 sample
trial
he hits 34% of the time on
his first
try.
With this
in mind along with the rest of the data
points,
it
is obvious that the subject doesn't learn throughout the
trial.
Approved For Release 2003/04/18
: &8a-RDP96-00787R0002001 5001 1-4
Approved For Release 2003/04/18
: CIA-RDP96-00787R0002001 5001 1-4
0 00
000
40M
M
M
MO
M
30M
M
M
MOO
M
000
Number
20M
of
M
Hits
MO
M
M
1 OM
M
M
M
M
OM
M
M
00 00000
Of)
Of)
M
M
MO 0000000000000
Sample Number
Figure 2.3
Total
Number of Hits Within
a Trial
Approved For Release 2003/04/18
: CIA-RDP96-00787R0002001 5001 1-4