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ORD Z240-75
12 June 1975
MEMORANDUM FOR: OTS/CB SG1 I
ATTENTION:
SUBJECT: Evidence for Non-Randomness of "Pour-State
Electronic Random Stimulus Generator"
REPERENCE: OTS/CB Memorandum 075-60
As requested in the last PaTagraph of the referenced
memoranduTq, we have investigated the data provided to establish
evidence for randomness. The basis for suggesting non-Tindorness
is as follows:
Table I of the Reference provides data concerning fre-
quencies of:
A. Initial States
R. State Transitions
Since the experiment consisted of requiring the subjects
to indicate the next-to-be presented state, it would seem 'most
important to establish that all possible transitions occur
with equal probability. To test for possible non-equality
of transitions, we extracted the observed frequencies of non-
identity transitions to form the following table:
Yellow Green Blue Red
Y - 764 765 790
G 777 - 773 863
B 776 796 773
R 787 SS2 803 -
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This table can be restructured as a two-by-six table
as follows:
yLG VB X/R 2/R E,./ B/R
R
Porward, 764 765 790 773 863 773
Backward 777 776 797 '796 8S2 903
The table thus restructured brings together all possible
ton-identity transitions viewed as state-paIrs. for instance,
Col. 1 shows that there were 764 trans t ons Yom the yellow
state to the green state and there were 777 transitions from
the green state to the yellow state.. Under the hypothesis that
all state transitions are equally probable and equally affected
by chance the Observed frequency with which forward transitions
occur should be unrelated to that with which backward transitions
occur in the Same Pair. This condition is not met. There is
a very Strong relationship between the observed forward and back-
ward transition frequencies. The coefficient of correlation
between frequencies for these two directions, computed across
&11 six possible non-identity transitions is .93, (p< .01)
(see attacbed graph). This finding shows that there were, in
fact, systematic pair-wise blasts associated with the electronic
processes by which the transitions were selected.
The finding that the forward and backward transitions are
closely associated with respect to joint probability of occurrence
susgests that they can be considered as having been drawn from
the same population. To test this, we computed the forward and
backward mean and the Standard Deviation (SD) of the observed
frequencies. They are#
Mean SD
forward 788 37.9
Backward 798 28.25
The standard error of the difference between these two means is
IS.S9 while the difference between ther, is only ten; clearly
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those data may be merged. Merging them, provides the following
table:
Observed
Frequency
Expected
Frequenc
Under Null
Hypothesis
Chi Square
YIG )2R G/B R/R R Total
MR !L
1541 1541 1S77 1S69 171S 1576 9519
1586.S 1SMS
1S86.5 IS86.5 1586.5
1SMS 9519
1.305 1.30S
.0$7 .193 10.408
Total Chi Square - 13.337 df-5 p-.02
.069
In the above table it can be seen that the large excess of
observed transitions involving the red-gTeen pair Is significant
at the .02 level. Inspection of the observed frequencies reveals
that there are almost ten percent more transitions involving the
red-green pair than the average of the other five possible no-n-
idontity transitions.
Those results su gest that adopting (fOT whatever conscious-
or unconscious reasons a strategy of "When green,, press red,
when red, press gTeen and, OtherWige USO the 'pass' button as
much as possible" will increase one's hit.score. Usin an
instrument with the above-described characteristics ana
strategies such as this is certain to-produce "statistically
significant" results, given enough trials and the asstuaption
of random transition robabilities. Other biases also exist
which could form the Uses of other enhancing strategies but
the above discussion would seem adequate to establish the
existence of non-randonness which we have suggested.
The report available to us contains data only upon one test
of one instrument. It must, therefoye, be Assume4 that the other
instruments demonstrated non-randor characteristics of a similar
nature. Further, the report does not reveal which subject used
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which instrument so we are unable to ascertain whether or not
subject number 2's results could be due to the effects discussed
above, but the magnitude of the effect is adequate to explain
the results If one assumes the adoptlonof a selection strategy
which "capitalizes" upon the non-random characteristics which
are demonstrably present.
SG1 I
LSR ORDMD 1k
Attachment
Distribution-
Original & 1 - Addressee, w/att
-1 - LSR File, w/att
I - LSR Chrono, w/att
I - ORD Chrono, w/att
LSR/ORD/DD/S&T~~:mav-3191
SG1 1
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